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Preface

Chapter 1 OFDM & Why OFDM: Chapter 1 highlights the importanceof OFDM and its applications are also mentioned.Multipath propagation isdiscussed and also the fading caused due to multipath propagation.Chapter 2 OFDM Basics: It explains the basic principles of OrthogonalDivision Multiplexing (OFDM).OFDM symbol generation and orthogonality isexplained in detail.Chapter 3 Modulation Schemes: PSK, FSK, BPSK,BFSK,QPSK,QAMmodulation schemes are described which are used in OFDM systems.Chapter 4 OFDM Transceiver: Basic OFDM transceiver is shown inthis chapter which includes Encoding,Srambling,Convolutional code,viterbidecoder as well as modulation techniques to be used.Chapter 5 Detection & Synchronization: This chapter covers TimingEstimation, Frequency synchronization, Energy Detection, Packet detection.Chapter 6 MIMO Fundamentals: MIMO(Multiple Input Multiple Output)basics are discussed.MIMO applications are explained which shows how itreduces the Mutipath propagation effects like fading,rayleigh fading etc. Andthis chapter focuses on space division multiplexing systems (SDM) and spacetime block codes (STBC).Chapter 7 MIMO OFDM MIMO OFDM transceiver design is explained inthis portion of our thesis.It also explains how MIMO OFDM minimizes Intersymbol interference ISI. The PAC V-BLAST Detection and Decoding Block isdiscussed briefly. Different parameters are used to explain the SNR values forthe MIMO OFDM systems.

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Chapter No.1OFDM & Why OFDM

1.1 Introduction

The telecommunications industry faces the problem of providing telephoneservices to rural areas, where the customer base is small, but the cost ofinstalling a wired phone network is very high. One method of reducing the highinfrastructure cost of a wired system is to use a fixed wireless radio network. Theproblem with this is that for rural and urban areas, large cell sizes are required toobtain sufficient coverage. This result in problems cased by large signal path lossand long delay times in multipath signal propagation.

Currently Global System for Mobile telecommunications (GSM) technology isbeing applied to fixed wireless phone systems in rural areas.However, GSM uses Time Division Multiple Access (TDMA), which has a high symbolrate leading to problems with multipath causing inter-symbol interference.

Several techniques are under consideration for the next generation of digitalphone systems, with the aim of improving cell capacity, multipath immunity, andflexibility. These include Code Division Multiple Access (CDMA) and CodedOrthogonal Frequency Division Multiplexing (COFDM). Both these techniques could beapplied to providing a fixed wireless system for rural areas. However, eachtechnique has different properties, making it more suited for specific applications.

COFDM is currently being used in several new radio broadcast systemsincluding the proposal for high definition digital television, Digital Video Broadcasting(DVB) and Digital Audio Broadcasting (DAB). However, little research has beendone into the use of COFDM as a transmission method for mobile telecommunicationssystems.

With CDMA systems, all users transmit in the same frequency band usingspecialized codes as a basis of channelization. The transmitted information isspread in bandwidth by multiplying it by a wide bandwidth pseudo random sequence. Boththe base station and the mobile station know these random codes that are used tomodulate the data sent, allowing it to de-scramble the received signal.OFDM/COFDM allows many users to transmit in an allocated band, bysubdividing the available bandwidth into many narrow bandwidth carriers. Each user isallocated several carriers in which to transmit their data. The transmission isgenerated in such a way that the carriers used are orthogonal to one another, thusallowing them to be packed together much closer than standard frequencydivision multiplexing (FDM). This leads to OFDM/COFDM providing a high spectralefficiency.

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1.2 Attenuation

Attenuation is the drop in the signal power when transmitting from one point toanother. It can be caused by the transmission path length, obstructions in the signal path,and multipath effects. Figure 1.1 shows some of the radio propagation effectsthat cause attenuation. Any objects that obstruct the line of sight signal from thetransmitter to the receiver can cause attenuation.Shadowing of the signal can occurwhenever there is an obstruction between the transmitter and receiver. It is generallycaused by buildings and hills, and is the most important environmental attenuationfactor.

Figure1.1 Multi-path Propagation

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1.3 Multipath Effects

1.3.1 Rayleigh FadingIn a radio link, the RF signal from the transmitter may be reflected from objects such ashills, buildings, or vehicles. This gives rise to multiple transmission paths at the

Figure1.2 Multi-path Propagation

receiver. Figure 1.2 show some of the possible ways in which multipath signalscan occur.The relative phase of multiple reflected signals can cause constructive or destructiveinterference at the receiver. This is experienced over very short distances (typically at halfwavelength distances), thus is given the term fast fading. These variations can varyfrom 10-30dB over a short distance. Figure 4 shows the level of attenuation that canoccur due to the fading.

1.3.2 Frequency Selective Fading

In any radio transmission, the channel spectral response is not flat. It has dipsor fades in the response due to reflections causing cancellation of certainfrequencies at the receiver. Reflections off near-by objects (e.g. ground, buildings,trees, etc) can lead to multipath signals of similar signal power as the direct signal. Thiscan result in deep nulls in the received signal power due to destructive interference.For narrow bandwidth transmissions if the null in the frequency response occursat the transmission frequency then the entire signal can be lost. This can bepartly overcome in two ways.By transmitting a wide bandwidth signal or spread spectrum as CDMA, any dipsin the spectrum only result in a small loss of signal power, rather than a complete loss.Another method is to split the transmission up into many small bandwidthcarriers, as is done in a COFDM/OFDM transmission. The original signal isspread over a wide bandwidth and so nulls in the spectrum are likely to only affect asmall number of carriers rather than the entire signal. The information in the lostcarriers can be recovered by using forward error correction techniques.

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1.3.3 Delay Spread

The received radio signal from a transmitter consists of typically a direct signal, plusreflections off objects such as buildings, mountings, and other structures. Thereflected signals arrive at a later time then the direct signal because of the extra pathlength, giving rise to a slightly different arrival times, spreading the received energy intime. Delay spread is the time spread between the arrival of the first and lastsignificant multipath signal seen by the receiver.

In a digital system, the delay spread can lead to inter-symbol interference. Thisis due to the delayed multipath signal overlapping with the following symbols. This cancause significant errors in high bit rate systems, especially when using time divisionmultiplexing (TDMA). Figure 5 shows the effect of inter-symbol interference dueto delay spread on the received signal. As the transmitted bit rate is increasedthe amount of inter-symbol interference also increases. The effect starts to becomevery significant when the delay spread is greater then ~50% of the bit time.

Figure 1.3 Multipath Effects

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Table 8 shows the typical delay spread for various environments. The maximumdelay spread in an outdoor environment is approximately 20ms, thus significantinter symbol interference can occur at bit rates as low as 25 kbps.

Environment orcause

Delay Spread Maximum Path LengthDifference

Indoor (room) 40ns – 200 ns 12 m – 60 m

Outdoor 1 ms – 20 ms 300 m – 6 km

Table Typical Delay Spread

Inter-symbol interference can be minimized in several ways. One method is toreduce the symbol rate by reducing the data rate for each channel (i.e. split thebandwidth into more channels using frequency division multiplexing, or OFDM).Another is to use a coding scheme that is tolerant to inter-symbol interferencesuch as CDMA.

1.3.4 Doppler Shift

When a wave source and a receiver are moving relative to one another thefrequency of the received signal will not be the same as the source. When theyare moving toward each other the frequency of the received signal is higherthen the source, and when they are approaching each other the frequency decreases.This is called the Doppler effect. An example of this is the change of pitch in a car’s hornas it approaches then passes by. This effect becomes important whendeveloping mobile radio systems.The amount the frequency changes due to the Doppler effect depends on the relativemotion between the source and receiver and on the speed of propagation of thewave.

1.4 Frequency Division Multiple Access

For systems using Frequency Division Multiple Access (FDMA), the availablebandwidth is subdivided into a number of narrower band channels. Each user isallocated a unique frequency band in which to transmit and receive on. During a call, noother user can use the same frequency band. Each user is allocated a forwardlink channel (from the base station to the mobile phone) and a reverse channel (back to thebase station), each being a single way link. The transmitted signal on each of thechannels is continuous allowing analog transmissions.

The channel bandwidth used in most FDMA systems is typically low (30kHz) as eachchannel only needs to support a single user. FDMA is used as the primarysubdivision of large allocated frequency bands and is used as part of most multi-channel systems.

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Figure 1.4 and Figure 1.5 shows the allocation of the available bandwidth intoseveral channels.

Figure 1. 4 FDMA showing that the each narrow band channel is allocated to asingle user

Figure 1.5 FDMA spectrum, where the available bandwidth is subdivided intonarrower band channels

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1.5 Time Division Multiple Access

Time Division Multiple Access (TDMA) divides the available spectrum intomultiple time slots, by giving each user a time slot in which they can transmit orreceive. Figure 1.6 shows how the time slots are provided to users in a roundrobin fashion, with each user being allotted one time slot per frame.

Figure 1.6 TDMA scheme where each user is allocated a small time slot

TDMA systems transmit data in a buffer and burst method, thus the transmission of eachchannel is non-continuous. The input data to be transmitted is buffered over the previousframe and burst transmitted at a higher rate during the time slot for the channel.TDMA can not send analog signals directly due to the buffering required, thusare only used for transmitting digital data. TDMA can suffer from multipath effects asthe transmission rate is generally very high, resulting in significant inter-symbolinterference.TDMA is normally used in conjunction with FDMA to subdivide the totalavailable bandwidth into several channels. This is done to reduce the numberof users per channel allowing a lower data rate to be used. This helps reducethe effect of delay spread on the transmission. Figure 1.7 shows the use ofTDMA with FDMA. Each channel based on FDMA, is further subdivided usingTDMA, so that several users can transmit of the one channel. This type oftransmission technique is used by most digital second generation mobile phonesystems. For GSM, the total allocated bandwidth of 25MHz is divided into 125,200 kHz channels using FDMA. These channels are then subdivided further byusing TDMA so that each 200 kHz channel allows 8-16 users .

Figure 1.7 TDMA / FDMA hybrid, showing that the bandwidth is split into 1.3.1Frequency Division Multiple Access

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For systems using Frequency Division Multiple Access (FDMA), the availablebandwidth is subdivided into a number of narrower band channels. Each user isallocated a unique frequency band in which to transmit and receive on. During a call, noother user can use the same frequency band. Each user is allocated a forwardlink channel (from the base station to the mobile phone) and a reverse channel (back to thebase station), each being a single way link. The transmitted signal on each of thechannels is continuous allowing analog transmissions. The channel bandwidthused in most FDMA systems is typically low (30kHz) as each channel only needs tosupport a single user. FDMA is used as the primary subdivision of largeallocated frequency bands and is used as part of most multi-channel systems.

Figure 1.8 and Figure 1.9 shows the allocation of the available bandwidth intoseveral channels.

Figure 1.8 FDMA showing that the each narrow band channel is allocated to asingle user

Figure 1.9 FDMA spectrums, where the available bandwidth is subdivided intonarrower band channels

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Figure 1.10 Code division multiple access (CDMA)

1.6 Code Division Multiple Access

Code Division Multiple Access (CDMA) is a spread spectrum technique thatuses neither frequency channels nor time slots. With CDMA, the narrow bandmessage (typically digitized voice data) is multiplied by a large bandwidth signalthat is a pseudo random noise code (PN code). All users in a CDMA systemuse the same frequency band and transmit simultaneously. The transmitted signal isrecovered by correlating the received signal with the PN code used by thetransmitter. Figure 1.10 shows the general use of the spectrum using CDMA.

CDMA technology was originally developed by the military during World War II.Researchers were spurred into looking at ways of communicating that would besecure and work in the presence of jamming. Some of the properties that have madeCDMA useful are:

• Signal hiding and non-interference with existing systems.• Anti-jam and interference rejection• Information security• Accurate Ranging• Multiple User Access• Multipath tolerance

For many years, spread spectrum technology was considered solely for militaryapplications. However, with rapid developments in LSI and VLSI designs,commercial systems are starting to be used.

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1.7 ADVANTAGES of OFDM

u Efficient way to deal ISI.u It can better cope with selective fading.u It uses the spectrum more efficiently.

1.8 APPLICATIONS OF OFDM

1) Digital Audio Broadcasting (DAB)2) Digital Video Broadcasting (DVB)3) Wireless Communication

1.8.1DIGITAL AUDIO BROADCASTING

DAB was the first commercial use of OFDM technology [19], [20].Development of DAB started in 1987 and services began in U.K and Swedenin 1995. DAB is a replacement for FM audio broadcasting, by providing highquality digital audio and information services. OFDM was used for DAB due toits multipath tolerance.

Broadcast systems operate with potentially very long transmission distances(20 - 100 km). As a result, multipath is a major problem as it causes extensiveghosting of the transmission. This ghosting causes Inter-Symbol Interference(ISI), blurring the time domain signal.For single carrier transmissions the effects of ISI are normally mitigated usingadaptive equalization. This process uses adaptive filtering to approximate theimpulse response of the radio channel. An inverse channel response filter isthen used to recombine the blurred copies of the symbol bits. This process ishowever complex and slow due to the locking time of the adaptive equalizer.Additionally it becomes increasing difficult to equalize signals that suffer ISI ofmore than a couple of symbol periods.OFDM overcomes the effects of multipath by breaking the signal into manynarrow bandwidth carriers. This results in a low symbol rate reducing theamount of ISI. In addition to this, a guard period is added to the start of eachsymbol, removing the effects of ISI for multipath signals delayed less than theguard period. The high tolerance to multipath makes OFDM more suited tohigh data transmissions in terrestrial environments than single carrier transmissions.

ParameterI

Transmission ModeII III IV

Bandwidth 1.536 1.536 MHz 1.536 1.536 MHzModulation DQPSK DQPSK DQPS

KDQPSK

Frequency Range £ 375 £ 1.5 GHz £ 3 £ 1.5 GHz(Mobile reception)Number of subcarriers 1536 384 192 768Symbol Duration 1000

ms250 ms 125 ms 500 ms

Guard Duration 246 ms 62 ms 31 ms 123 msTotal Symbol Duration 1246

ms312 ms 156 ms 623 ms

Maximum Transmitter 96 km 24 km 12 km 48 kmSeparation for SFN

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Table 1-1, DAB Transmission parameters for each transmission modeTable 1-1 shows the system parameters for DAB. DAB has four transmissionmodes. The transmission frequency, receiver velocity and required multipathtolerance all determine the most suitable transmission mode to use.Doppler spread is caused by rapid changes in the channel response due tomovement of the receiver through a multipath environment. It results inrandom frequencymodulation of the OFDM sub carriers, leading to signal degradation. The amount ofDoppler spread is proportional to the transmission frequency and the velocity ofmovement. The closer the sub carriers are spaced together, the more susceptiblethe OFDM signal is to Doppler spread, and so the different transmission modes inDAB allow trade off between the amount of multipath protection (length of the guardperiod) and the Doppler spread tolerance.The high multipath tolerance of OFDM allows the use of a Single FrequencyNetwork (SFN), which uses transmission repeaters to provide improved coverage,and spectral efficiency. For traditional FM broadcasting, neighboring cities must usedifferent RF frequencies even for the same radio station, to prevent multipath causesby re-broadcasting at the same frequency. However, with DAB it is possible for thesame signal to be broadcast from every area requiring coverage, eliminating theneed for different frequencies to be used in neighboring areas.

The data throughput of DAB varies from 0.6 - 1.8 Mbps depending on the amount ofForward Error Correction (FEC) applied. This data payload allows multiple channelsto be broadcast as part of the one transmission ensemble. The number of audiochannels is variable depending on the quality of the audio and the amount of FECused to protect the signal. For telephone quality audio (24 kbps) up to 64 audiochannels can be provided, while for CD quality audio (256 kb/s), with maximumprotection, three channels are available.More information on DAB can be found in [20] and [21].

1.8.2 DIGITAL VIDEO BROADCASTING

The development of the Digital Video Broadcasting (DVB) standards was started in1993 . DVB is a transmission scheme based on the MPEG-2 standard, as a methodfor point to multipoint delivery of high quality compressed digital audio and video. It isan enhanced replacement of the analogue television broadcast standard, as DVBprovides a flexible transmission medium for delivery of video, audio and dataservices. The DVB standards specify the delivery mechanism for a wide range ofapplications, including satellite TV (DVB-S), cable systems (DVB-C) and terrestrialtransmissions (DVB-T). The physical layer of each of these standards. is optimizedfor the transmission channel being used. Satellite broadcasts use a singlecarrier transmission, with QPSK modulation, which is optimized for thisapplication as a single carrier allows for large Doppler shifts, and QPSK allowsfor maximum energy efficiency [16]. This transmission method is howeverunsuitable for terrestrial transmissions as multipath severely degrades theperformance of high-speed single carrier transmissions.

For this reason, OFDM was used for the terrestrial transmission standard forDVB. The physical layer of the DVB-T transmission is similar to DAB, in thatthe OFDM transmission uses a large number of sub carriers to mitigate theeffects of multipath. DVB-T allows for two transmission modes depending onthe number of sub carriers used. Table 1-2 shows the basic transmissionparameters for these two modes. The major difference between DAB and

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DVB-T is the larger bandwidth used and the use of higher modulationschemes to achieve a higher data throughput. The DVB-T allows for three subcarrier modulation schemes: QPSK, 16-QAM (Quadrature AmplitudeModulation) and 64QAM; and a range of guard period lengths and codingrates. This allows the robustness of the transmission link to be traded at theexpense of link capacity. Table 1-3 shows the data throughput and requiredSNR for some of the transmission combinations.

DVB-T is a uni-directional link due to its broadcast nature. Thus any choice indata rate verses robustness affects all receivers. If the system goal is toachieve high reliability, the data rate must be lowered to meet the conditionsof the worst receiver. This effect limits the usefulness of the flexible nature ofthe standard. However if these same principles of a flexible transmission rateare used in bi-directional communications, the data rate can be maximizedbased on the current radio conditions. Additionally for multi-user applications,it can be optimized for individual remote transceivers

Parameter 2kMode

8kMode

Number sub carriers 1705 6817Useful Symbol Duration (Tu) 896 ms 224 msCarrier Spacing (1/ Tu) 1116 Hz 4464 HzBandwidth 7.61

MHz7.61MHz

DVB transmission parameters.

Subcarr Code Rate SNR for BER = 2´ 10-4 Bit rate (Mbps)Modulat Viterbi (dB) Guard Period (Fraction of

Useful symbol duration)GaussianChannel

RayleighChannel 1/4 1/32

QPSK ½ 3.1 5.4 4.98 6.03QPSK 7/8 7.7 16.3 8.71 10.5616-QAM ½ 8.8 11.2 9.95 12.0616-QAM 7/8 13. 22.8 17.42 21.1164-QAM ½ 14. 16.0 14.93 18.1064-QAM 7/8 20. 27.9 26.13 31.67

Table 1-3, SNR required and net bit rate for a selection of the coding and

Modulation combinations for DVB

Note: Code rate can be any of the following values: 1/2, 2/3, 3/4, 5/6,7/8. The Guard Period duration can be any following values: 1/4, 1/8,1/16, 1/32.

1.8.3 Wireless Communication of OFDM application

The proposed final application for OFDM is to use it for wirelesscommunications systems such as cellular mobile phone systems, fixedwireless phone systems, wireless data links and wireless computer local areanetworks. If OFDM is to be used in any of these applications then thebandwidth used must be sufficiently high to compete with other radio

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technologies. This section discusses the processing power required to implementa practical OFDM system.

An OFDM system mainly involves digital signal processing, thus the main focusof the performance of the system depends on the availability of high performance signalprocessing. There are two main ways in which the OFDM signal can be processed,which are using a general purpose DSP, or by implementing the processing inhardware using customized IC’s.

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Chapter No. 2 OFDM Basics

2.1 Orthogonal Frequency Division Multiplexing (OFDM)

Orthogonal Frequency Division Multiplexing (OFDM) is a multicarriertransmission technique, which divides the available spectrum into many carriers,each one being modulated by a low rate data stream. OFDM is similar to FDMAin that the multiple user access is achieved by subdividing the availablebandwidth into multiple channels, which are then allocated to users. However,OFDM uses the spectrum much more efficiently by spacing the channels muchcloser together. This is achieved by making all the carriers orthogonal to oneanother, preventing interference between the closely spaced carriers.

Coded Orthogonal Frequency Division Multiplexing (COFDM) is the same as OFDMexcept that forward error correction is applied to the signal before transmission. This isto overcome errors in the transmission due to lost carriers from frequencyselective fading, channel noise and other propagation effects. For this discussion theterms OFDM and COFDM are used interchangeably, as the main focus of this thesis ison OFDM, but it is assumed that any practical system will use forward errorcorrection, thus would be COFDM.

In FDMA each user is typically allocated a single channel, which is used to transmit all theuser information. The bandwidth of each channel is typically 10 kHz-30 kHz for voicecommunications. However, the minimum required bandwidth for speech is only3 kHz. The allocated bandwidth is made wider then the minimum amountrequired to prevent channels from interfering with one another. This extrabandwidth is to allow for signals from neighboring channels to be filtered out,and to allow for any drift in the centre frequency of the transmitter or receiver. In a typicalsystem up to 50% of the total spectrum is wasted due to the extra spacingbetween channels. This problem becomes worse as the channel bandwidth becomesnarrower, and the frequency band increases. Most digital phone systems usevocoders to compress the digitized speech. This allows for an increased systemcapacity due to a reduction in the bandwidth required for each user. Current vocodersrequire a data rate somewhere between 4-13kbps [13], with depending on the qualityof the sound and the type used. Thus each user only requires a minimumbandwidth of somewhere between 2-7kHz, using QPSK modulation. However,simple FDMA does not handle such narrow bandwidths very efficiently.

TDMA partly overcomes this problem by using wider bandwidth channels, which areused by several users. Multiple users access the same channel by transmittingin their data in time slots. Thus, many low data rate users can be combined together totransmit in a single channel that has a bandwidth sufficient so that the spectrum can beused efficiently.

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There are however, two main problems with TDMA. There is an overhead associatedwith the change over between users due to time slotting on the channel. Achange over time must be allocated to allow for any tolerance in the start time of eachuser, due to propagation delay variations and synchronization errors. This limitsthe number of users that can be sent efficiently in each channel. In addition, the symbolrate of each channel is high (as the channel handles the information frommultiple users) resulting in problems with multipath delay spread.

OFDM overcomes most of the problems with both FDMA and TDMA. OFDMsplits the available bandwidth into many narrow band channels (typically 100-8000). The carriers for each channel are made orthogonal to one another,allowing them to be spaced very close together, with no overhead as in the FDMAexample. Because of this there is no great need for users to be time multiplex as in TDMA,thus there is no overhead associated with switching between users.The orthogonalityof the carriers means that each carrier has an integer number of cycles over asymbol period. Due to this, the spectrum of each carrier has a null at the centrefrequency of each of the other carriers in the system. This results in nointerference between the carriers, allowing then to be spaced as close astheoretically possible. This overcomes the problem of overhead carrier spacingrequired in FDMA.

Each carrier in an OFDM signal has a very narrow bandwidth (i.e. 1 kHz), thusthe resulting symbol rate is low. This results in the signal having a high toleranceto multipath delay spread, as the delay spread must be very long to causesignificant inter-symbol interference (e.g. > 100 ms).

2.2 Basic Principle of OFDM

The basic principle of OFDM (Orthogonal Frequency Division Multiplexing) isto split a high-rate data stream into a number of lower rate streams that aretransmitted simultaneously over a number of sub carriers. Because the symbolduration increases for the lower rate parallel sub carriers, the relative amountof dispersion in time caused by multipath delay spread is decreased. Intersymbol interference (ISI) is eliminated almost completely by introducing aguard time in every OFDM symbol. In the guard time, the OFDM symbol iscyclically extended to avoid inter carrier interference. This whole process ofgenerating an OFDM signal and the reasoning behind it are explained in thefollowing sections.

In OFDM system design, a number of parameters are up for consideration,such as the number of sub carriers, guard time, symbol duration, sub carrierspacing, modulation type per sub carrier, and the type of forward errorcorrection coding. The choice of parameters is influenced by systemrequirements such as available bandwidth, required bit rate, tolerable delayspread, and Doppler values. Some requirements are conflicting. For instance,to get a good delay spread tolerance, a large number of subcarriers with smallsubcarrier spacing is desirable, but the opposite is true for a good toleranceagainst Doppler spread and phase noise.

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Orthogonal Frequency Division Multiplexing (OFDM) is very similar to the wellknown and used technique of Frequency Division Multiplexing (FDM). OFDMuses the principles of FDM to allow multiple messages to be sent over a singleradio channel. It is however in a much more controlled manner, allowing animproved spectral efficiency.

A simple example of FDM is the use of different frequencies for each FM(Frequency Modulation) radio stations. All stations transmit at the same timebut do not interfere with each other because they transmit using differentcarrier frequencies. Additionally they are bandwidth limited and are spacedsufficiently far apart in frequency so that their transmitted signals do notoverlap in the frequency domain. At the receiver, each signal is individuallyreceived by using a frequency tuneable band pass filter to selectively removeall the signals except for the station of interest. This filtered signal can then bedemodulated to recover the original transmitted information.OFDM is different from FDM in several ways. In conventional broadcastingeach radio station transmits on a different frequency, effectively using FDM tomaintain a separation between the stations. There is however no coordinationor synchronization between each of these stations. With an OFDMtransmission such as DAB, the information signal from multiple stations iscombined into a single multiplexed stream of data. This data is thentransmitted using an OFDM ensemble that is made up from a dense packingof many subcarriers. All the subcarriers within the OFDM signal are time andfrequency synchronized to each other, allowing the interference betweensubcarriers to be carefully controlled. These multiple subcarriers overlap in thefrequency domain, but do not cause Inter-Carrier Interference (ICI) due to theorthogonal nature of the modulation. Typically with FDM the transmissionsignals need to have a large frequency guard-band between channels toprevent interference. This lowers the overall spectral efficiency. However withOFDM the orthogonal packing of the subcarriers greatly reduces this guardband, improving the spectral efficiency.All wireless communication systems use a modulation scheme to map theinformation signal to a form that can be effectively transmitted over thecommunications channel

2.3 Generation of subcarriers using IFFT

An OFDM signal consists of a sum of subcarriers that are modulated by usingphase shift keying (PSK) or quadrature amplitude modulation (QAM). If di arethe complex QAM symbols, Ns is the number of subcarriers, T the symbolduration, and fc the carrier frequency, the one OFDM symbol starting at t = tscan be written as:

Ns/2 -1 s(t) = Re d I + Ns/ 2 exp ( j2 ( fc – i+0.5/T )(t – ts)) ts < t < ts+T t = Ns/2 s(t) = 0, t < ts and t > ts + T …………… (1.1)

In the literature, often the equivalent complex baseband notation is used,which is given by equation (1.2). In this representation, the real and imaginaryparts correspond to the in-phase and quardrature parts of the OFDM signals,which have to be multiplied by a cosine and sine of the desired carrier

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frequency to produce the final OFDM signal. Figure 2.1 shows the operation ofthe OFDM modulator in a block diagram.

Ns/2 -1 s(t) = Re d i+Ns+/ 2 exp ( j2 i/T ( fc – i+0.5/T )(t – ts)) ts < t < ts+T t = Ns/2 s(t) = 0, t < ts and t > ts + T ………………(1.2)

serialto

parallel

QAM data

Figure 2.1 OFDM Modulator

As an example, Figure 2.2 shows two subcarriers from one OFDM signal. Inthis example, all subcarriers have the same phase and amplitude, but inpractice the amplitudes and phases may be modulated differently for eachsubcarrier. Note that each subcarrier has exactly an integer number of cyclesin the interval T, and the number of cycles between adjacent subcarriersdiffers by exactly one. This property accounts for the orthogonality betweenthe subcarriers. For instance, if the jth subcarrier from 1.1 is demodulated bydown converting the signal with a frequency of j/T and then integrating thesignal over T seconds, the result is that a complex carrier is integrated over Tiseconds. For the demodulated subcarrier j, this integration gives the desiredoutput dj+N/2 (multiplied by a constant factor T), which is the QAM value for thatparticular subcarrier. For all other subcarrier, the integration is zero, becausethe frequency difference (i-j)/T produce an integer number of cycles within theintegration interval T, such that the integration result is always zero.

exp(-jπNs(t-ts)/T)

exp(jπ(Ns-2)(t-ts)/T)

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Figure 2.2 Example of Four Subcarriers with OFDM

The orthogonality of the different OFDM subcarriers can also be demonstratedin another way. Each OFDM symbol contains subcarriers that are nonzeroover a T-second period and zero otherwise. The amplitude spectrum of thesquare pulse is equal to sinc(pfT), which has zeros for all frequencies f thatare an integer multiple of 1/T. This effect is shown in figure 1.3, which showsthe overlapping sinc spectra of individual subcarriers. At the maximum of eachsubcarrier spectrum, all other subcarrier spectra are zero. Because an OFDMreceiver essentially calculates the spectrum values at those points thatcorrespond to the maxima of individual subcarriers, it can demodulate eachsubcarrier free from any interference from the other subcarriers. Basically,figure 2.3 shows that the OFDM spectrum fulfills Nyquist’s criterion for anintersymbol interference free pulse shape. Notice that the pulse shape ispresent in the frequency domain and not in the time domain, for which theNyquist criterion usually is applied. Therefore, instead of intersymbolinterference (ISI), it is intercarrier interference (ICI) that is avoided by havingthe maximum of one subcarrier of one subcarrier spectrum corresponding tozero crossings of all the others.

Figure 2.3 Spectra of individual subcarriers

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The complex baseband OFDM signal as defined by equation 1.2 is in factnothing more than the inverse Fourier transform of Ns QAM input symbols.The tie discrete equivalent is the inverse discrete Fourier transform (IDFT),which is given by equation:

Ns -1s(n) = di exp(j2 n/N)

i = 0

where the time t is replaced by a sample n. In practice, this transform can beimplemented very efficiently by the inverse fast Fourier transform (IFFT). An Npoint IDFT requires a total of N2 complex multiplications ----- which areactually only phase rotations. Of course, there are also additions necessary todo an IDFT, but since the hardware complexity of an adder is significantlylower that that of a multiplier or phase rotator, only the multiplications are usedher for comparison. The IFFT drastically reduces the amount of calculation byexploiting the regularity of the operations in the IDFT. Using the radix-2algorithm, an N-point IFFT requires only (N/2)-log2(N) complex multiplications.For a 16-point transform, for instance, the difference is 256 multiplications forthe IDFT versus 32 for the IFFT --- a reduction by a factor of 8!. Thisdifference grows for larger numbers of subcarriers, as the IDFT complexitygrows quadratically with N, while the IFFT complexity only grows slightlyfaster than linearly.

The number of multiplications in IFFT can be further reduced by using radix-4algorithm. This technique makes use of the fact that in a four-point IFFT, thereare only multiplications by {1,-1,j,-j}, which actually do not need to beimplemented by a full multiplier, but rather by a simple add or subtract and aswitch of real and imaginary parts in the case of multiplications by j or j.

2.3.1 ORTHOGONALITY

Signals are orthogonal if they are mutually independent of each other.Orthogonality is a property that allows multiple information signals to betransmitted perfectly over a common channel and detected, withoutinterference. Loss of orthogonality results in blurring between theseinformation signals and degradation in communications. Many commonmultiplexing schemes are inherently orthogonal. Time Division Multiplexing(TDM) allows transmission of multiple information signals over a singlechannel by assigning unique time slots to each separate information signal.During each time slot only the signal from a single source is transmittedpreventing any interference between the multiple information sources.Because of this TDM is orthogonal in nature. In the frequency domain mostFDM systems are orthogonal as each of the separate transmission signals arewell spaced out in frequency preventing interference. Although these methodsare orthogonal the term OFDM has been reserved for a special form of FDM.The subcarriers in an OFDM signal are spaced as close as is theoreticallypossible while maintain orthogonality between them.OFDM achieves orthogonality in the frequency domain by allocating each ofthe separate information signals onto different subcarriers. OFDM signals aremade up from a sum of sinusoids, with each corresponding to a subcarrier.The baseband frequency of each subcarrier is chosen to be an integer

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multiple of the inverse of the symbol time, resulting in all subcarriers having aninteger number of cycles per symbol.

2.3.2 FREQUENCY DOMAIN ORTHOGONALITY

Another way to view the orthogonality property of OFDM signals is to look atits spectrum. In the frequency domain each OFDM subcarrier has a sinc,sin(x)/x, frequency response, as shown in Figure 2-2. This is a result of thesymbol time corresponding to the inverse of the carrier spacing. Each carrierhas a peak at the centre frequency and nulls evenly spaced with a frequencygap equal to the carrier spacing.The orthogonal nature of the transmission is a result of the peak of each subcarriercorresponding to the nulls of all other subcarriers. When this signal is detected usinga Discrete Fourier Transform (DFT) the spectrum is not continuous as shown inFigure 2.4 (a), but has discrete samples. The sampled spectrum is shown as ‘o’s inthe figure. If the DFT is time synchronized, the frequency samples of the DFTcorrespond to just the peaks of the subcarriers, thus the overlapping frequencyregion between subcarriers does not affect the receiver. The measured peakscorrespond to the nulls for all other subcarriers, resulting in orthogonality betweenthe subcarriers.

(a) (b)Figure 2.4, Frequency response of the subcarriers in a 5 tone OFDMsignal. (script 0006)(a) shows the spectrum of each carrier, and the discrete frequencysamples seen by an OFDM receiver. Note, each carrier is sinc,sin(x)/x, in shape. (b) Shows the overall combined response of the 5subcarriers (thick black line).

2.3.3 OFDM GENERATION AND RECEPTION

OFDM signals are typically generated digitally due to the difficulty in creating largebanks of phase lock oscillators and receivers in the analog domain. Figure 2-3shows the block diagram of a typical OFDM transceiver. The transmitter sectionconverts digital data to be transmitted, into a mapping of subcarrier amplitude andphase. It then transforms this spectral representation of the data into the timedomain using an Inverse Discrete Fourier Transform (IDFT). The Inverse FastFourier Transform (IFFT) performs the same operations as an IDFT.

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Chapter No. 3 Modulation Schemes

3.1 Signal Encoding Criteria

Digital signal is a sequence of discrete, discontinuous voltage pulses. Eachpulse is a single element. Binary data is transmitted by encoding each data bitinto single elements. Duration or length of a bit is the amount of time neededto transmit that bit, and data rate is bits per second.

Now if data rate is increased then Bit Error Rate (BER) will also increase.However BER will decrease if Signal-to- Noise Ratio (SNR) decreases. Thereis another way to improve performance and that is encoding scheme. Theencoding scheme is simply the mapping from data bits to signal elements. Avariety of approaches are in use. However there are various ways to evaluatethese schemes

3.1.1 Signal Spectrum

Several aspects of the signal spectrum are important. A lack of high-frequencycomponents means that less bandwidth is required for transmission.Interference depends upon the spectral properties. Usually transfer function ofthe channel is worst near the band edges. So good design should concentratethe transmitted power in the middle of the bandwidth so that distortion be less.

3.1.2 Clocking

Receiver must determine in the beginning and end of each bit position.Clocking is expensive and hard to achieve as transmitter and receiver must besynchronized.

3.1.3 Signal interference and noise immunity

Some signal performs much better in the presence of noise.

3.1.4 Cost and complexity

Although digital logic continues to drop in price, this factor should not beignored. In particular, the higher the signaling rate to achieve a given data,greater the cost.

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3.2 Digital Modulation Schemes

There are three basic encoding or modulation techniques for transformingdigital data into analog signals.

• Amplitude Shift Keying (ASK)• Frequency Shift Keying (FSK)• Phase Shift Keying (PSK)

3.2.1 Amplitude Shift Keying

Amplitude shift keying (ASK) in the context of digital communications is amodulation process, which imparts digital data as variations in the amplitudeof a carrier wave. These are related to the number of levels adopted by thedigital message.

For a binary message sequence there are two levels, one of which is typicallyzero. Thus the modulated waveform consists of bursts of a sinusoid.

Figure 3.1 illustrates a binary ASK signal (lower), together with the binarysequence which initiated it (upper). Neither signal has been band-limited.

Figure 3.1: an ASK signal (below) and the message (above)

There are sharp discontinuities shown at the transition points. These result inthe signal having an unnecessarily wide bandwidth. Band-limiting is generallyintroduced before transmission, in which case these discontinuities would be‘rounded off’. The band-limiting may be applied to the digital message, or themodulated signal itself. The data rate is often made a sub-multiple of thecarrier frequency. This has been done in the waveform of Figure 3.1.

One of the disadvantages of ASK, compared with FSK and PSK, for example,is that it has not got a constant envelope. This makes its processing (e.g.,power amplification) more difficult, since linearity becomes an importantfactor. However, it does make for ease of demodulation with an envelopedetector.

The simplest and most common form of ASK operates as a switch, using thepresence of a carrier wave to indicate a binary one and its absence to indicatea binary zero. This type of modulation is called on-off keying.

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Figure 3.2 ASK Generation Method

Figure 3.3 shows the signals present in a model of Figure 3.2, where themessage has been band-limited. The shape, after band-limiting, dependsnaturally enough upon the amplitude and phase characteristics of the band-limiting filter.

Figure 3.3: original TTL message (lower), band-limited message (center),and ASK (above)

It is apparent from Figures 3.1 and 3.4 that the ASK signal has a well definedenvelope. Thus it is amenable to demodulation by an envelope detector. Withband-limiting of the transmitted ASK neither of these demodulation methods(envelope detection or synchronous demodulation) would recover the originalbinary sequence; instead, their outputs would be a band-limited version. Thusfurther processing - by some sort of decision-making circuitry for example -would be necessary. Thus demodulation is a two-stage process:

• recovery of the band-limited bit stream• regeneration of the binary bit stream

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Figure 3.4 ASK Demodulation

The above explanation was for binary modulation. More sophisticatedencoding schemes have been developed which represent data in groupsusing additional amplitude levels. For instance, a four-level encoding schemecan represent two bits with each shift in amplitude; an eight-level scheme canrepresent three bits; and so on. These forms of amplitude-shift keying requirea high signal-to-noise ratio for their recovery, as by their nature much of thesignal is transmitted at reduced power.

If L different symbols are to be sent, L different levels of amplitude will benecessary to achieve the communication. If the maximum amplitude of thecarrier wave is A (with peak-to-peak amplitude of 2A), putting the symbols atthe same distance one from the other, this distance will be:

It is possible to show that the probability to make an error (i.e. a symbol isread that is different from the one that was sent) is:

where is the complementary error function, GT is the total gain of thesystem and N is the standard deviation of the noise. This relationship is validwhen there is no inter-symbolic interference.

3.2.2 Frequency Shift Keying

As its name suggests, a frequency shift keyed transmitter has its frequencyshifted by the message.

There can be more than two frequencies involved in an FSK signal. The word‘keyed’ suggests that the message is of the ‘on-off’ (mark-space) variety, suchas one (historically) generated by a Morse key, or more likely in the presentcontext, a binary sequence. The output from such a generator is illustrated inFigure 3.5.

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Figure 3.5: FSK Waveform

Conceptually, and in fact, the transmitter could consist of two oscillators (onfrequencies f1 and f2), with only one being connected to the output at any onetime. This is shown in block diagram form in Figure 3.6

Figure 3.6: FSK Transmitter

Now in FSK Modulators for Binary FSK

s1 = Acos(2 f1t + ø1 ) kT < t < (k+1)T for 1s2 = Acos(2 f2t + ø2 ) kT < t < (k+1)T for 0

Where ø1 and ø2 are the initial phases at t = 0 and T is the bit period of thebinary data. These two signals are not coherent since the phases are not thesame in general. The waveform is not continuous at the bit transitions. Thisform of FSK is called non-coherent or discontinuous FSK.

Unless there are special relationships between the two oscillator frequenciesand the bit clock there will be abrupt phase discontinuities of the outputwaveform during transitions of the message.

Practice is for the tones s1 and s2 to bear special inter-relationships, and tobe integer multiples of the bit rate. This leads to the possibility of continuousphase, which offers advantages, especially with respect to bandwidth control.

Alternatively the frequency of a single oscillator (VCO) can be switchedbetween two values, thus guaranteeing continuous phase - CPFSK. Thecontinuous phase advantage of the VCO is not accompanied by an ability toensure that s1 and s2 are integer multiples of the bit rate. Such type of FSK iscalled Coherent FSK. In coherent FSK s1 and s2 are of initially of same phaseat t = 0.

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Figure 3.7 Coherent FSK modulator

s1 = Acos(2 f1t + ø ) kT < t < (k+1)T for 1s2 = Acos(2 f2t + ø ) kT < t < (k+1)T for 0

This would be difficult to implement with a VCO. FSK signals can begenerated at baseband, and transmitted over telephone lines (for example). Inthis case, both s1 and s2 (of Figure 3.6) would be audio frequencies.

For coherent demodulation of the coherent FSK signal, the two frequenciesare so chosen that the two signals are orthogonal:

This leads to

Thus we conclude that for orthogonality fl and f2 must be integer multiples of1/4T and their difference must be integer multiple of 1/2T. In terms iffrequency difference we have

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When the separation is chosen as 1/T, then the phase continuity will bemaintained at bit transitions, the FSK called Sunde's FSK, is an importantform of FSK. A particular form of FSK called the minimum shift keying (MSK)not only has the minimum separation but also has continuous phase. Thefigure 3.8 (a) below is of the Sunde's FSK however a coherent FSK mighthave discontinuities are bit boundaries, as shown in figure 3.8 (b) below.

Figure 3.8: FSK Waveform

For two non-coherent FSK signals to be orthogonal, the two frequencies mustbe integer multiple of 1/2T and their separation must be multiple of 1/T. Thisleads to

When n=1, the separation is 1/T, which is minimum. Comparing with coherentFSK, the separation of non-coherent FSK doubles that of FSK. Thus moresystem bandwidth is required for non-coherent FSK for the same symbol rate.

In M-ary FSK, the binary bit stream is divided into n-tuples of n = log2M bits.We denote all M possible n-tuples as M messages mi, where i = 1,2….M.There are M signals with different frequencies to represent these Mmessages. The expression of the ith signal is

Where T is the symbol rate which is n times the bit rate

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If the initial phases are the same for all i, the signal set is coherent. As in thebinary case we can always assume the phase to be 0 for coherent MFSK. Thedemodulation could be coherent or non-coherent. Otherwise the signal set isnon-coherent and the demodulation must be non-coherent. Usually a uniformfrequency separation between two adjacent frequencies is chosen for MFSK.

3.2.3 Phase Shift Keying

In PSK, the phase of the carrier signal is shifted to represent data.

Any digital modulation scheme uses a finite number of distinct signals torepresent digital data. In the case of PSK, a finite number of phases are used.Each of these phases is assigned a unique pattern of binary bits. Usually,each phase encodes an equal number of bits. Each pattern of bits forms thesymbol that is represented by the particular phase.

A convenient way to represent PSK schemes is on a constellation diagram. InConstellation diagram the real and imaginary axes are often called the inphase, or I-axis and the quadrature, or Q-axis. By choosing a set of complexnumbers to represent the modulation symbols in this way, they may bephysically transmitted by varying the amplitude of a cosine wave and a sinewave since these are naturally 90° out-of-phase with one another and are aconvenient representation of the two axes. The amplitude of the cosine-waveis set to the absolute value of the imaginary part of the symbol to betransmitted and the amplitude of the sine wave to the absolute value of thereal part.

3.2.4 Binary PSK

BPSK is the simplest form of PSK. It uses two phases which are separated by180° and so can also be termed 2-PSK. It does not particularly matter exactlywhere the constellation points are positioned, and in this figure they areshown on the real axis, at 0° and 180°. This modulation is the most robust ofall the PSKs since it takes serious distortion to make the demodulator reachan incorrect decision. It is, however, only able to modulate at 1bit/symbol (asseen in the figure) and so is unsuitable for high data-rate applications.

Figure 3.9: Constellation diagram for BPSK.

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The bit error rate (BER) of BPSK in AWGN can be calculated as:

WhereEb = Energy-per-bitN0 = Noise power spectral density (W/Hz)

Q(x) will give the probability that x is under the tail of the Gaussian probabilitydensity function towards positive infinity

Since there is only one bit per symbol, this is also the symbol error rate. In thepresence of an arbitrary phase-shift introduced by the communicationschannel, the demodulator is unable to tell which constellation point is which.As a result, the data is often differentially encoded prior to modulation.

3.3 Quadrature Phase-shift Keying (QPSK)

More efficient use of bandwidth can be achieved if each signaling elementrepresents more than one bit. For example, instead of phase shift of 180º, asallowed in PSK, a common encoding technique, know as Quadrature PhaseShift Keying (QPSK), uses phase shift of multiples of /2(90º).

Among all the MPSK schemes, QPSK is the most often used scheme since itdoes not suffer from BER degradation while the bandwidth efficiency isincreased. Other MPSK schemes increase bandwidth efficiency at theexpenses of BER performance.

Since QPSK is a special case of MPSK, its signals are defined as

Where

The initial signal phases are . The carrier frequency is chosenas integer multiple of the symbol rate, therefore in any symbol interval[kT,(k+l)T], the signal initial phase is also one of the four phases. The aboveexpression can be written as

Where ø1 (t) and ø2 (t) are defined previously.

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3.3.1 QPSK signal in the time domain

The modulated signal is shown below for a short segment of a random binarydata-stream. The two carrier waves are a cosine wave and a sine wave, asindicated by the signal-space analysis above. Here, the odd-numbered bitshave been assigned to the in-phase component and the even-numbered bitsto the quadrature component (taking the first bit as number 1).

The total signal — the sum of the two components — is shown at the bottom.Jumps in phase can be seen as the PSK changes the phase on eachcomponent at the start of each bit-period. The topmost waveform alonematches the description given for BPSK above.

Figure 3.10: Timing diagram for QPSK.

The binary data stream is shown beneath the time axis. The two signalcomponents with their bit assignments are shown the top and the total,combined signal at the bottom. Note the abrupt changes in phase at some ofthe bit-period boundaries.The binary data that is conveyed by this waveform is: 1 1 0 0 0 1 1 0.

• The odd bits, highlighted here, contribute to the in-phase component: 11 0 0 0 1 1 0

• The even bits, highlighted here, contribute to the quadrature-phasecomponent: 1 1 0 0 0 1 1 0

3.3.2 Applications of PSK

The most popular wireless LAN standard, IEEE 802.11b, uses a variety ofdifferent PSK’s depending on the data-rate required. At the basic-rate of 1Mbit/s, it uses DBPSK. To provide the extended-rate of 2 Mbit/s, DQPSK isused. In reaching 5.5 Mbit/s and the full-rate of 11 Mbit/s, QPSK is employed,but has to be coupled with complementary code keying. The higher-speedwireless LAN standard, IEEE 802.11g has eight data rates: 6, 9, 12, 18, 24,36, 48 and 54 Mbit/s. The 6 and 9 Mbit/s modes use BPSK. The 12 and 18Mbit/s modes use QPSK.

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The recently-standardized Bluetooth uses /4 DQPSK at its lower rate (2Mbit/s) and 8-DPSK at its higher rate (3 Mbit/s) when the link between the twodevices is sufficiently robust. Bluetooth 1 modulates with Gaussian minimum-shift keying, a binary scheme, so either modulation choice in version 2 willyield a higher data-rate.

3.4 Quadrature Amplitude Modulation

FSK, PSK, CPM and MHPM are constant envelope schemes. The constantenvelope property of these schemes is especially important to systems withpower amplifiers which must operate in the nonlinear region of the input-output characteristic for the maximum power efficiency like the satellitetransponders. For some other communication systems constant envelopemay not be a crucial requirement whereas bandwidth efficiency is moreimportant.

Quadrature amplitude modulation (QAM) is such a class of non-constantenvelope schemes that can achieve higher bandwidth efficiency that MPSKwith the same average signal power. QAM is widely used in modemsdesigned for telephone channels. The CCITT telephone circuit modemstandards V.29 to V.33 are all based on QAM schemes ranging from the un-coded QAM to the trellis coded 128-QAM. The research of QAM applicationsin satellite systems, point-to-point wireless systems and mobile cellulartelephone systems also has been very active.

Ask can also be made M-ary amplitude modulation (MAM). MAM is usuallynot used because of its poor power efficiency. However, since QAM signalsconsist of two MAM components and they can be demodulated in twoseparate channels. It is necessary to understand QAM.

3.4.1 QAM Signal Description

The description of the MAM signal given above was necessary to understandQAM. In MAM schemes the signals have the same phase but differentamplitudes. In MPSK schemes, signals have the same amplitudes butdifferent phases. Naturally, the next step of development is to consider bothamplitude and phase modulations in a scheme (QAM). That is

Where Ai is the amplitude and 8j is the phase of the ith signal in the M-arysignal set. Pulse shaping is usually used to improve the spectrum and for ISIcontrol purpose in QAM. With pulse shaping, the QAM signal is

Where p(t)is a smooth pulse in the interval [O,T].We can write the aboveequation as

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Where

And

Similar to MPSK, QAM signal can be expressed as a linear combination oftwo ortho-normal functions. Expression is

Where

And

Where Ep is the energy of p(t)in [O,T].Basically the basis functions are ortho-normal and when there is no pulse shaping they are perfectly ortho-normal.The energy of the ith signal is

And the average signal energy is

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The average power is

The average amplitude is

3.4.2 QAM Constellation

The first QAM scheme was presented by c.R.Cahn in 1960. He simplyextended phase modulation to a multi-amplitude phase modulation. That isthere is more than one amplitude associated with an allowed phase. In theconstellation a fixed number of signal points (or phasors) are equally spacedon each of the N circles, where N is the number of amplitude levels. This iscalled type I constellation. In this type, the points on the inner ring are closesttogether in distance and are most vulnerable to errors. To overcome thisproblem, type II constellation was proposed by Hancock and Lucky a fewmonths later. In this type, the signal points are still on circles but the numberof points on the inner circle is less than the number of points on the outercircle, making the distance between two adjacent points on the inner circleapprox. equal to that on the outer circle. Type III constellation is the squareQAM constellation which was proposed by Campopiano and Glazer in 1962.Their analysis showed that this system offered a very small improvement inperformance over the type II system but the implementation would beconsiderably simpler than that of both the types. Due to this type IIIconstellation has been the most widely used system. Some of the other twodimensional constellation is shown in the figure below:

Figure 3.11 QAM III Constellation

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3.4.3 Rectangular QAM

Rectangular QAM constellations are, in general, sub-optimal in the sense thatthey do not maximally space the constellation points for a given energy.However, they have the considerable advantage that they may be easilytransmitted as two pulse amplitude modulation (PAM) signals on quadraturecarriers, and can be easily demodulated. The non-square constellations, dealtwith below, achieve marginally better bit-error rate (BER) but are harder tomodulate and demodulate.

The first rectangular QAM constellation usually encountered is 16-QAM, theconstellation diagram for which is shown here. A Gray coded bit-assignment isalso given. The reason that 16-QAM is usually the first is that a briefconsideration reveals that 2-QAM and 4-QAM are in fact binary phase-shiftkeying (BPSK) and quadrature phase-shift keying (QPSK), respectively. 8-QAM presents problems in dividing an odd number of bits between the twocarriers, and is rarely used since 8-PSK is considerably simpler.

Figure3.12 Constellation diagram for rectangular 16-QAM.

3.13 Constellation diagram 3.14 Alternative constellationfor rectangular diagram for rectangular 8-QAM8-QAM.

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Chapter No. 4 OFDM Transceiver

4.1 BLOCK DIAGRAM OF OFDM TRANSCEIVER

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4.2 SCRAMBLER

It is electronic instrument which make the speech unintelligible duringtransmission and restores it at reception. It is also used to remove strings ofzeros & ones. Military makes it's first used.

Figure 4.3 Scrambler

4.3 ENCODER

It is Forward Error Correction (FEC) technique. Encoding Is Used In Order ToEncrypt. The Data So That Only Intended User Can Read It .ConvolutionalEncoder with constraint length ‘7’ is generally used. .

Figure 4.4 Encoder

4.4 Convolutional Codes

A convolutional code maps each k bits of a continuous input stream on noutput bits where the mapping is performed by convolving the input bits with abinary impulse response. The convolutional encoding can be implemented bysimple shift registers and modulo-2 adders. As an example, figure 2.1 showsthe encoder for a rate ½ cod which is actually one of the most frequently

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applied convolutional codes. This encoder has a single data input and twoouputs Ai and Bi, which are interleaved to form the coded output sequence{ A1,B1,A2,B2 … }. Each pair of output bits { Ai,Bi} depends on seven input bits,being the current input bit plus six previous input bits that are stored in thelength 6 shift register. This valued of 7— or in general the shift register lengthplus 1— is called the constraint length. The shift register taps are oftenspecified by the corresponding generator polynomials or generator vectors.

Figure 4.5 Convolutional encoder (k = 7)

Decoding of convoltional codes is most often performed by soft decisionViterbi decoding, which is an efficient way to obtain the optimal maximumlikelihood estimate of the encoded sequence. Simpler versions of decoding ofconvolutional codes are hard decision Viterbi decoding & sequential decoding.The description of Viterbi decoding will be done in the next section.

The complexity of Viterbi decoding grows exponentially with the constraintlength. Hence, practical implementations do not go further than a constraintlength of about 10. Decoding of convolutional codes with larger constraintlength is possible by using suboptimal decoding techniques like sequentialdecoding.

Because convolutional codes do not have a fixed length, it is more difficult tospecify their performance in terms of Hamming distance and a number ofcorrectable errors. One measure that is used is the free distance, which is theminimum Hamming distance between arbitrarily long different code sequencesthat begin and end with the registers of the encoder. For example, the code offigure 2.1 has a free distance of 10. When hard decision decoding is used thiscod can correct up to floor ((10-1)/2) = 4 bit errors within each group ofencoded bits with a length of about 3 to 5 times the constraint length. Whensoft decision decoding is used, however, the number of correctable errorsdoes not really give a useful measure anymore. A better performancemeasure is the coding gain, which is defined as the gain in the bit energy-to-noise density ratio Eb/No relative to an uncoded system to achieve a certain biterror ratio. The Eb/No gain is equivalent to the gain in input signal-to-noiseration (SNR) minus the rate loss in dB because of the redundant bits.

A convolutional code can be punctured to increase the coding rate. Forinstance, increasing the rate of the above rate ½ code to ¾ is done by deleting2 of every 6 bits at the output of the encoder. The punctured output sequencefor a rate ¾ code is { A1B1A2B3A4B4A5B6A7B7 }. For a rate 2/3 code, the

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punctured output sequence is { A1B1A2A3B3A4A5B5 }. To decode thepunctured sequence, the original rate ½ decoder can be used. Beforedecoding, erasures have to be inserted in the data at the locations of thepunctured bits.

4.5 Viterbi decoding

The decoder used for decoding convolutional codes is Viterbi decoder. Viterbidecoder can be of two types: soft decision viterbi decoding or hard decisionviterbi decoding. Here hard decision viterbi decoding is explained.To understand decoding process, it simplifies matters to expand the statediagram to show the time sequence of the encoder. Let's take an example ofthe following convolutional encoder and its state diagram.

Figure 4.6 Convolutional Encoder with ( n , k , K ) = ( 2 , 1 , 3 )

if the state diagram is laid out vertically then the expanded diagram, called atrellis, is constructed by reproducing the states horizontally and showing thestate transitions going from left to right corresponding to time, or data input. Ifthe constraint length K is large, then the trellis diagram becomes unwieldy. Inthat case, 2K-2 simplified trellis fragments can be used to depict the transitions.Any valid output is defined by a path through the trellis. In our example a-b-c-b-d-c-a-a produces the out put 11 10 00 01 01 11 00 and was generated bythe input 1011000. If an invalid path occurs, such as a-c, then the decoderattempts error correction. In essence, the decoder must determine what datainput was most likely to have produced the invalid output.

Figure 4.7 Trellis Diagram for Encoder of fig.4.4

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A number of error correction algorithms have been developed forconvolutional codes. Perhaps the most important is the Viterbi code. Inessence, the Viterbi technique compares the received sequence with allpossible transmitted sequences. The algorithm chooses a path through thetrellis whose coded sequence differs from the received sequence in the fewestnumber of places. Once a valid path is selected as the correct path, thedecoder can recover the input data bits from the output code bits.

There are several variations on the Viterbi algorithm, depending on whichmetric is used to measure differences between received sequences and validsequences. To give an idea of the operation of the algorithm, we use thcommon metric of Hamming distance. We represent a received codedsequence as the word w = w0w1w2 … , and attempt to find the most likely validpath through the trellis. At each time i and for each state we list the active path(or paths) through the trellis to the state. An active path is a valid path throughthe trellis whose Hamming distance from the received word up to time i isminimal. We label each state at time i by the distance of its active path fromthe received word. The following relationship is used:

distance of a path = distance of the last edge + distance of the last-but-onestate

The algorithm proceeds in b+1 steps, where b is pre chosen window size. Foran ( n,k,K ) code, the first output block of n bits, wow1w2 wn, is decoded in thefollowing steps:

Step 0:The initial state of the trellis at time 0 is labeled 0, because there is sofar no discrepancy.

Step i + 1:For each state S at time i + 1, find all active paths leading to S usingthe above equation. Label S by the distance of that path or paths.

Step b:The algorithm terminates at time b. If all the active paths at that timehave the same first edge and the label of that edge is x0x1x2 xn-1, thenthe first code block w0w1w2 wn-1 is corrected to x0x1x2 xn-1. If thereare two active edges, the error is not correctable.

After accepting and, if necessary, correcting, the first code block, the decodingwindow is moved n bits to the right and the decoding of the next block isperformed.

Convolutional codes provide good performance in noisy channels where ahigh proportion of the bits are in error. Thus, they have found increasing use inwireless applications.

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4.6 INTERLEAVING

All encoded data bits shall be interleaved by a block interleaver with a blocksize corresponding to the number of bits in a single OFDM symbol, NCBPS.The interleaver is defined by a two-step permutation.The first permutation is defined by the rule i = (NCBPS/16) (k mod 16) + floor(k/16) k = 0,1,…,NCBPS – 1

The second permutation is defined by the rule j = s × floor (i/s) + (i + NCBPS – floor (16 × i/NCBPS)) mod s i = 0, 1,…NCBPS – 1

Because of the frequency selective fading of typical radio channels, the OFDMsubcarriers generally have different amplitudes. Deep fades in the frequencyspectrum may cause groups of subcarriers to be less reliable than others,thereby causing bit errors to occur in bursts rather than being randomlyscattered. Most forward error correcting codes are not designed to deal witherror burst. Therefore, interleaving is applied to randomize the occurrence ofbit errors prior to decoding. At the transmitter, the coded bits are permuted ina certain way, which makes sure that adjacent bits are separated by severalbits after interleaving. At the receiver, the reverse permutation is performedbefore decoding. A commonly used interleaving scheme is the blockinterleaver, where input bits are written in a matrix column by column and readout row by row.

4.7 SUBCARRIER MAPPING

Different types of Mapping technique are used.BPSK,QPSK,16-QAM, 64-QAM Depending upon the data rate required. Max Data rate of 54Mbits/s canbe achieved using 64-QAM.The OFDM subcarriers shall be modulated by using BPSK, QPSK, 16-QAM,or 64-QAMmodulation depending on the RATE requested. We use BPSK MODULATIONin the signal field. For Data field Transmission we used 16-QAM which canachieve max data rate of 36 Mbits/s with coding rate of 3/4. d = (I + jQ) * KMOD is the output.

4.7.1 Quardrature amplitude modulation

Quardrature amplitude modulation (QAM) is the most popular combinationwith OFDM (other modulation techniques used are: BPSK and QPSK).Especially rectangular constellations are easy to implement as they can besplit into independent pulse amplitude modulated (PAM) components for boththe in-phase and quardrature part. Figure 4.8 shows the rectangularconstellations of Quradrature Phase Shift Keying (QPSK), 16-QAM and 64-QAM. The constellations are not normalized; to normalize them to an averagepower of one — assuming that all constellation points are equally likely tooccur — each constellation has to be multiplied by the normalization factorlisted in table 4.1. The table also mentions Binary Phase Shift Keying (BPSK),which uses two of the four QPSK constellation points { 1+j , -1-j }.

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Table 4.1 Modulation-dependent normalization factor KMOD

Figure 4.8 BPSK, QPSK, 16-QAM, and 64-QAM constellation bit encoding

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4.7.2 SUBCARRIER MODULATION

Once each subcarrier has been allocated bits for transmission, they aremapped using a modulation scheme to a subcarrier amplitude and phase,which is represented by a complex In-phase and Quadrature-phase (IQ)vector. Figure 4.9 shows an example of subcarrier modulation mapping. Thisexample shows 16-QAM, which maps 4 bits for each symbol. Eachcombination of the 4 bits of data corresponds to a unique IQ vector, shown asa dot on the figure. A large number of modulation schemes are availableallowing the number of bits transmitted per carrier per symbol to be variedDigital data is transferred in an OFDM link by using a modulation scheme on eachsubcarrier. A modulation scheme is a mapping of data words to a real (In phase) andimaginary (Quadrature) constellation, also known as an IQ constellation.

Figure 4.9, Example IQ modulation constellation. 16-QAM, with graycoding of the data to each location. (script s0045)

4.8 PILOT INSERTION

In each OFDM symbol, four of the subcarriers are dedicated to pilot signals inorder to make the coherent detection robust against frequency offsets andphase noise. These pilot signals shall be put in subcarriers –21, –7, 7 and 21.In each OFDM symbol, four of the subcarriers are dedicated to pilot signals inorder to make the coherent detection robust against frequency offsets andphase noise. These pilot signals shall be put in subcarriers –21, –7, 7 and 21.The pilots shall be BPSK modulated by a pseudo binary sequence to preventthe generation of spectral lines. The contribution of the pilot subcarriers toeach OFDM symbol is described in the following section

4.9 IFFTInverse Fast Fourier Transform (IFFT) is used to Convert Frequency DomainData into Time Domain.

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4.9.1 FREQUENCY TO TIME DOMAIN CONVERSION

After the sub carrier modulation stage each of the data subcarriers is set to an amplitude andphase based on the data being sent and the modulation scheme; all unused subcarriers are set tozero. This sets up the OFDM signal in the frequency domain. An IFFT is then used to convert thissignal to the time domain, allowing it to be transmitted. Figure 6.10 shows the IFFT section of theOFDM transmitter. In the frequency domain, before applying the IFFT, each of the discretesamples of the IFFT corresponds to an individual subcarrier. Most of the subcarriers are modulatedwith data. The outer subcarriers are unmodulated and set to zero amplitude. These zerosubcarriers provide a frequency guard band before the nyquist frequency and effectively act as aninterpolation of the signal and allows for a realistic roll off in the analog anti-aliasing reconstructionfilters.

Figure 4.10 IFFT section of OFDM

4.9.2 Cyclic Extension/Guard Interval

It is used to avoid Iner Symbol Interference (ISI).Guard Time must be larger than expecteddelay spread such that multipath components from one symbol cannot interfere with nextsymbol.

One of the most important properties of OFDM transmissions is its high level of robustnessagainst multipath delay spread. This is a result of the long symbol period used, which minimizes theinter-symbol interference. The level of multipath robustness can be further increased by theaddition of a guard period between transmitted symbols. The guard period allows time formultipath signals from the pervious symbol to die away before the information from thecurrent symbol is gathered. The most effective guard period to use is a cyclic extension of thesymbol. If a mirror in time, of the end of the symbol waveform is put at the start of the symbol as theguard period, this effectively extends the length of the symbol, while maintaining theorthogonality of the waveform. Using this cyclic extended symbol the samples required forperforming the FFT (to decode the symbol), can be taken anywhere over the length of thesymbol.

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For a given system bandwidth the symbol rate for an OFDM signal is much lower than asingle carrier transmission scheme. For example for a single carrier BPSK modulation, thesymbol rate corresponds to the bit rate of the transmission. However for OFDM the systembandwidth is broken up into Nc subcarriers, resulting in a symbol rate that is Nc times lowerthan the single carrier transmission. This low symbol rate makes OFDM naturally resistantto effects of Inter-Symbol Interference (ISI) caused by multipath propagation.

Multipath propagation is caused by the radio transmission signal reflecting off objects in thepropagation environment, such as walls, buildings, mountains, etc. These multiple signals arrive atthe receiver at different times due to the transmission distances being different. This spreads thesymbol boundaries causing energy leakage between them.

The effect of ISI on an OFDM signal can be further improved by the addition of a guard period tothe start of each symbol. This guard period is a cyclic copy that extends the length of the symbolwaveform. Each subcarrier, in the data section of the symbol, (i.e. the OFDM symbol with no guardperiod added, which is equal to the length of the IFFT size used to generate the signal) has aninteger number of cycles. Because of this, placing copies of the symbol end-to-end results in acontinuous signal, with no discontinuities at the joins. Thus by copying the end of a symbol andappending this to the start results in a longer symbol time. Figure 4-11 shows the insertion of aguard period.

Symbol N

Figure 4.11, Addition of a guard period to an OFDM signal

The total length of the symbol is Ts=TG + TFFT, where Ts is the total length of thesymbol in samples, TG is the length of the guard period in samples, and TFFT is the size of the IFFTused to generate the OFDM signal.In addition to protecting the OFDM from ISI, the guard period also provides protection against time-offset errors in the receiver.

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Chapter No. 5 Packet Detection

5.1 Introduction

In this chapter, robust and efficient frame detection and symbol timing synchronizationtechnique suitable for IEEE 802.11a wireless LAN system is proposed. The proposedmethod does frame detection using a threshold comparison mechanism and performsOrthogonal Frequency Division Multiplexing (OFDM) symbol boundary detection usingcorrelation techniques. This algorithm is a novel combination of self and cross correlationinformation to achieve symbol timing synchronization. The proposed algorithm can robustlydetect the symbol boundary even under low SNRs, high frequency offset, and multipath.

The algorithm proposed for frame detection and symbol timing synchronization is designedby exploiting the repetitive nature of the short preambles provided in the 802.11a preamble.Finding the symbol timing for OFDM systems is nothing but finding the beginning of theOFDM symbol. This can be achieved by finding any boundary in the preamble.

5.2 OFDM-WLAN system

Figure 7.1 shows a simplified transceiver structure of OFDM based 802.11a system. TheOFDM signal can be generated by taking IDFT (Inverse Discrete Fourier Transform) ofQAM or PSK symbols. As per IEEE 802.11a specification, each OFDM symbol consists of48 data carriers, 4 pilot carriers and 12 null carriers. Hence, IDFT size is 64 point and canbe implemented using efficient IFFT algorithm. The output of IFFT becomes one OFDMsymbol, with duration of Ts (3.2ms). Each OFDM symbol is cyclically extended with 16samples of duration Tg (0.8 ms) and they will be removed at the receiver. The cyclic prefixlength should be more than the channel impulse response to avoid Inter SymbolInterference (ISI). The expression for the OFDM baseband signal (output of IDFT) is:

………… (1)

Where Ck is the QAM or PSK modulated complex signal and N = 64. This baseband signalis then up-converted, modulated to radio frequency (RF) and transmitted. IEEE 802.11a isa packet-based communication system. Each packet is preceded by a preamble as definedin IEEE 802.11a specification. The preamble structure is as shown in figure 6.2. This figurealso shows the information regarding signal field and data payload.

As shown in the figure, the preamble consists of 10 short symbols each having 0.8 sduration, and two long preambles of 3.2 s duration each.

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Figure 5.1 Frame format and Preamble structure of IEEE 802.11a

5.3 Detection of frame

At receiver, the received signal is correlated with itself with a delay of one short symbol,given by

…………….. (2)

Where r(n) is the received sequence, A(n) is the correlation output and L is the length of theshort symbol. The incoming frame at receiver can be detected by comparing the magnitudeof auto-correlation result with some threshold. It is advisable to have a dynamic thresholdbased on incoming signal power. The initial 2-3 short symbols are assumed to be non-reliable, as Automatic Gain Control (AGC) logic requires some time to finalize the gainsetting.

5.4 Symbol boundary detection

In this chapter, a robust algorithm to detect OFDM symbol boundary using auto-correlationand cross correlation of short preamble is described. In (2) the value of N should be inbetween 16 and 144 and a multiple of 16. For any particular value of N, if we plot the auto-correlation magnitude values, we get a curve as shown in figure 3. The curve rises to somevalue, remains flat for about N-CP samples duration and then falls down as shown. In ouralgorithm, we detect the index of the (N-CP+1)th sample when counted from the start of thepreamble. The auto-correlation magnitude values are passed through a moving averagefilter to smoothen the curve. The moving average filter is defined by:

Where A(n) is the auto-correlation magnitude and l is the size of the moving average filterand it is chosen as 3. The falling edge of the curve corresponds to the (N-CP)th sample.We can detect this falling edge by observing the slope of the curve. However, at low SNRsand high delay spread situations, exact detection of this edge is difficult. This edge can belocalized with the help of cross correlation of the received sequence. If we do crosscorrelation of the received sequence with the local copy of the short symbol, we get peaksat the end of each short symbol. However, the frequency offset of the local oscillatordisturbs the magnitude of these cross correlation peaks significantly. Instead of averaging

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this cross correlation for one short symbol, if we average over more short symbols, asindicated by (4), we can still detect the peak.

Where s(n) is the local copy of the short symbol. M is the number of short symbols overwhich we are averaging the cross correlation. The simulation result shows that this type ofaveraging can with stand ±20ppm frequency offset, which is the worst-case possiblefrequency offset specified 802.11a standard.

Figure 5.2 Auto-Correlation curve and Cross-Correlation peaks for ideal case (No noise, nomultipath and no frequency offset)

Figure 5.2 shows the auto-correlation curve and the cross correlation peaks in the case ofan ideal channel. Our objective is to detect the cross correlation peak at which the fallingedge of the auto-correlation curve starts. This can be achieved by tracking the slope of thecurve with the help of another dynamically set threshold. To detect the corresponding crosscorrelation peak, we need to do peak search by taking a window of 16 cross correlationmagnitude values around that falling edge. The window size can be decided throughsimulations. The detected peak corresponds to the index of the (N-CP+1)th sample whencounted from the start of the preamble. Thus, in the proposed algorithm, cross correlation isused to localize the exact boundary of the short symbol. The difference between thedetected boundary and the actual boundary is the boundary detection error. This boundarydetection error results in corresponding rotation of the signal constellation in frequencydomain. This rotation can be taken care by channel estimation and equalization up to someextent.

Robust frame detection and symbol timing detection algorithms were proposed for IEEE802.11a WLAN system. In particular, a novel combination of auto-correlation and cross-correlation information was used to increase the reliability of the frame boundary detectionalgorithm.

Synchronization

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5.5 INTRODUCTION

Synchronization is an essential task for any digital communication system. Without anysynchronization algorithms, it is not possible to reliably receive the transmitted data. Fromthe digital baseband algorithm design engineer’s perspective, synchronization algorithmsare the major design problems that have to be solved to build a successful product.

OFDM is used for both broadcast type systems and a packet switched networks, likeWLANs. These two systems require somewhat different approach to the synchronizationproblem. Broadcast system transmit data continuously, so a typical receiver, like EuropeanDigital Audio Broadcasting (DAB) or Digital Video Broadcasting (DVB) system receivers,can initially spend a relatively long time to acquire the signal and then switch to trackingmode. On the other hand, WLAN systems typically have to use so called “single-shot”synchronization; that is, the synchronization has to be acquired during a very short timeafter the start of the packet. This requirement comes from the packet switched nature of theWLAN systems and also from the data rates used. To achieve the good system throughput,it is mandatory to keep the receiver training information overhead to minimum. To facilitatethe single-shot synchronization, current WLAN standards include problems, like IEEE802.11a preamble shown in figure 3.5 or the various HiperLAN/2 preambles, in the start ifpacket. The length and the contents of the preamble have been carefully designed toprovide enough information for good synchronization performance without any unnecessaryoverhead.

The current waveform makes most of the synchronization algorithms designed for a singlecarrier system unusable, thus algorithm design problem has to be approached from theOFDM perspectives. This distinction is especially visible on the sensitivity difference tovarious synchronization errors between single carrier and OFDM systems. The frequencydomain nature of OFDM also allows the effect of several synchronization errors to beexplained with the aid of the properties of the Discrete Fourier Transform (DFT). Anothermain distinction can be performed either in time- or frequency-domain. This flexibility is notavailable in single carrier systems. The tradeoffs in how to perform the synchronizationalgorithms are usually either higher performance versus reduced computational complexity.

The order of algorithms described in this chapter follows to some extent the order of howan actual receiver would perform the synchronization.

The main assumption usually made when WLAN systems are designed is that the channelimpulse response does not change significantly during one data burst. This assumption isjustified by the quite short time duration of transmitted packets, usually a couplemilliseconds at maximum and that the transmitter and receiver in most applications movevery slowly relatively to each other. Under this assumption most of the synchronization forWLAN receivers is done during the preamble and need not be changed during the packet.

5.6 TIMING ESTIMATION

Timing estimation consists of two main tasks: packet synchronization and symbolsynchronization.The IEEE 802.11 MAC protocol is the essentially a random access network, so the receiverdoes not know exactly when a packet starts. The first task of the receiver is to start of anincoming packet. HiperLAN/2 medium access architecture is a hybrid of both randomaccess and time scheduled networks. Thus HiperLAN/2 receiver also has to be able toreliably detect the start of an incoming packet, without prior knowledge.

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Broadcasting systems naturally do not require packet detection algorithms, becausetransmission is always on. However, for packet oriented network architecture, finding thepackets is obviously of central importance for high network performance.

5.7 PACKET DETECTION

Packet detection is the task of finding an approximate estimate of the start of the preambleof an incoming data packet. As such it is the first synchronization algorithm that isperformed, so the rest of the synchronization process is dependent on good packetdetection performance. Generally packet detection can be described as a binary hypothesistest. The test consists of two complementary statements about a parameter of interest.These statements are called the null hypothesis, H0, and the alternative hypothesis, H1. Inthe packet detection test, the hypotheses assert whether a packet is present or not. Thisset up as shown below.

H0 : Packet not presentH1 : Packet present

The actual test is usually of the form that test is whether decision variable mn exceeds apredefined threshold Th. The packet detection case is shown below.

H0 : mn < Th => Packet not present H1 : mn > Th => Packet present

The performance of the packet detection algorithm can be summarized with twoprobabilities: probability of detection PD and probability of false alarm PFA. PD is theprobability of detecting a packet when it is truly present, thus high PD is desirable quality forthe test. PFA is the probability that the test incorrectly decides that the packet is present,thus PFA should be as small as possible. In general, increasing PD increases PFA and viceversa, hence the algorithm designer must settle for some balanced compromise betweenthe two conflicting goals.

Generally it can be said that a false alarm is a less severe error than not detecting a datapacket at all. The reason is that after a false alarm, the receiver will synchronize tononexistent packet and will detect its error at the first received data integrity check. On theother hand, not detecting a packet always results in lost data. A false alarm can also resultlost data, in case an actual receiver will not be able to catch the packet. The probability ofthis occurring depends on several issues like the network load and the time it takes for thereceiver to detect its mistake. In conclusion, a little higher PFA can be tolerated to guaranteethe good PD.

5.8 RECEIVED SIGNAL ENERGY DETECTION

The simplest algorithm for finding the start edge of the incoming packet is to measure thereceived signal energy. When there is no packet being received, the signal rn consists onlyof noise rn = wn. When the packet starts, the received energy is increased by the signalcomponent rn = sn + wn, thus the packet can be detected as a change in the receivedenergy level. The decision variable mn is then the received signal energy accumulated oversome window of length L to reduce the sensitivity to large individual nose samples.

L – 1 Lmn = rn k r*

n k = | rn k|2

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k =0 Equation 5.1

Calculation of mn can be simplified by nothing that it is moving sum of its received signalenergy. This type of sum is also called a sliding window. The rational for the name is thatthe energy time instant n, one new value enters the sum and one old value is discarded.This structure can be used to simplify the computation of equation 5.1. Equation 5.2 showshow to calculate the moving sum recursively.

mn+1 = mn + | rn+1 |2 - | rn-L+1 |2Equation 5.2

Thus the number of complex multiplications is reduced to one per received sample;however, more energy is required to store all the value of |rn|2 inside the window. Theresponse of this algorithm is show in Figure 3.1. The figure shows the value of mn for IEEE802.11 a packet with 10dB Signal to Noise Ratio (SNR) and sliding window length L = 32.The true start of the packet is at n = 500, thus in this case the threshold could be setbetween 10 and 25. The value of the threshold defines the PD and PFA of the test. Thissimple method suffers from a significant drawback; the value of the threshold depends onthe received signal energy. When the receiver is searching for an incoming packet, thereceived signal consists of only noise. The level of the noise power is generally unknownand can change when the receiver adjusts its Radio Frequency (RF) amplifier setting s or ifunwanted interferers go on and off in the same band as the desired system. When awanted packet is incoming, its received signal strength depends on the power setting of thetransmitter and on the total path loss from the transmitter to the receiver. All these factorsmake it quite difficult to set a fixed threshold, which could be used to decide when anincoming packet starts. The next section describes an improvement to the algorithm thatalleviates the threshold value selection problem.

Figure 5.1 Received Energy based packet detection algorithm

5.9 DOUBLE SLIDING WINDOW PACKET DETECTION

The double sliding window packet detection algorithm calculates two consecutive slidingwindows of the received energy. The basic principle is to form the decision variable mn as aratio of the total energy contained inside the two windows. Figure 2.2, the A and B windowsand response of mn to a received packet. In figure 2.2, the A and B windows areconsidered stationary relative to the packet that slides over them to the right. It can be seen

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that when only noise is received the response is flat, since both windows contain ideally thesame amount of noise energy. When the packet edge starts to cover the A window, theenergy in the window A gets higher until the point A is totally contained inside the start ofthe packet. This point is the peak of the triangle shaped mn and the position of the packet inFigure 5.2 corresponds to this sample index n. After this point B window starts to alsocollect signal energy, and when it is also completely inside the received packet, theresponse of mn is flat again. Thus the response of mn be thought of as a differentiator, inthat its value is large when the input level changes rapidly. The packet detection is declaredwhen mn crosses over the threshold value Th.

Figure 5.2 Double sliding window packet detection

Equation 5.3 shows the calculation of A window value and the equation 5.4 the calculationfor B window.

M – 1 M – 1an = rn m r*

n m = | rn m|2m = 0 m = 0

Equation 5.3 L L

bn = rn+l r*n+l = | rn+l |2

l = 1 l = 0

Equation 5.4

Both an and bn are again sliding windows, thus computation can be simplified in the samerecursive manner as for the energy detection window. Then the decision variable is formedby dividing the value of an by bn.

mn = an / bnEquation 5.5

A simulated response of the variable mn is shown in the figure 5.3. The figure is again forthe IEEE 802.11 a preamble with 10dB SNR. The figure clearly shows how the value of mndoes not depends on the total received power. After the peak, the response levels off to thesame as before the peak, although the received energy level is much higher. An additionalbenefit of this approach is that, at the peak point of mn the value of an contains the sum ofthe signal energy N and the bn value is equal to to the noise energy N, thus the value of mnat the peak point and Equation 5.6 is the ratio an and bn at the peak point and Equation 5.7is the SNR. Equation 5.6 is the ratio an and bn at the peak point and Equation 5.7 is theSNR estimate calculated from the ratio.

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mpeak = apeak / bpeak

= S+N

= S + 1N

Equation 5.6^

SNR = mpeak - 1Equation 5.7

Using the double sliding window algorithm is a good approach if the receiver does not haveadditional information about the received data.

Figure 5.3 Double sliding window packet detection

5.10 FREQUENCY SYNCHRONIZATION

One of the main drawbacks of OFDM is its sensitivity to carrier frequency offset. Thedegradation is caused by two main phenomena; reduction of amplitude of the desiredsubcarrier and ICI caused by neighboring carrier carriers. The amplitude loss occursbecause the desired subcarrier is no longer sampled at the peak of the sinc-function ofDFT. The sinc-function is defined as sinc (x) = sin (x)/x. Adjacent carriers causeinterference, because they are not sampled at the zero-crossing of they sinc-function. Theoverall effect on SNR is analyzed and for relatively small frequency errors, the degradationin dB was approximated by

SNR = 10 ( T f )2 EsN0 N0

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where f is the frequency error as a fraction of subcarrier spacing and T is the samplingperiod. The performance effect varies strongly with the modulation used; naturally,constellations with fewer points can tolerate larger frequency errors than largeconstellations. Figure 5.4 illustrates the effect for QPSK and 64-QAM constellations.

The figure shows that 64-QAM, the largest constellation in IEEE802.11a, cannot toleratemore than 1% error in the carrier frequency for negligible SNR loss of 0.5dB, whereasQPSK modulation can tolerate up to 5% error for the same SNR loss.

The analysis above would seem to indicate that large constellations are exceedinglydifficult to use with an OFDM system. However, keep in mind that a large constellationautomatically implies higher operating SNR than with a small constellation. This directlyimproves the performance of the frequency error estimation.

In Hseih and Wei, the various algorithms that have been developed to estimate carrierfrequency offset in OFDM systems are divided in three types.

Figure 5.4 Symbol error rate (SER) degradation due to frequency offset at SER = 10-4

Type 1 Data-aided algorithms; these methods are based on special training information embedded into the transmitted signal.Type 2 Non-data-aided algorithms that analyze the received signal in the frequency domain.

Type 3

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Cyclic prefix based algorithms that use the inherit structure of the OFDM signalprovided by the cyclic prefix.

For WLAN applications, type 1 is the most important. The preamble allows the receiver touse efficient maximum likelihood algorithm to estimate and correct for the frequency offset,before the actual information portion of the packet starts. The algorithm belonging to type 2and 3 are better suited for broadcast or continuous transmission type OFDM.

Figure 5.5 The IEEE 802.11a standard preamble

Chapter No. 6MIMO Fundamentals

6.1 Introduction

The objective of this chapter is to describe and compare the multiple-inputmultiple-output (MIMO) techniques which have been proposed in literature in the pastyears. Unfortunately most of the available papers focus on narrowband (single carrier)wireless communication. Few papers consider broadband applications and usually they useassumptions tailored for mobile communication. The following describes for a number ofnarrowband MIMO algorithms and, when available, the broadband adaptation orapplication.Now the focus is on the use of smart antennas as a candidate for next generationbroadband cellular or wireless systems. The use of smart antennas is a potentialbreakthrough in the improvement of quality, transmission capacity and data rates inwireless and cellular systems. Basically, the idea is to make use of a strong multi-pathpropagation environment instead of being limited by it. In the receiver, the multi-pathstreams are transformed into independent channels by using a combination of adaptiveantennas, appropriate transmission coding and receiver detection algorithms. The ‘hidden’capacity of a wireless medium could be exploited by the introducing spatial (de-)multiplexing of several communications channels within the same bandwidth and the sametime-slot. This is shown in Figure

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Figure6.1 Multiple Communication Channels

The use of multiple antennas at both transmit and receive side is also referred to asmultiple-input multiple-output (MIMO) systems. MIMO systems could serve multipleobjectives. This is shown in Table 6-1.

Table 6.1 Several ways to exploit the unbounded air-interface to improve either coverage,link

quality, capacity or data rates.

Multiple receive antennas will lead to array gain (3 dB signal-to-noise improvement whendoubling the number of receive antennas) even in a non multipath environment. This couldbe used to increase the coverage of a base-station or access point. Another possibility isuse interference reduction schemes at the receive array to suppress interference fromunwanted sources and/or users.Basically, this will improve the link quality but also moreusers can be used in a cell, which will lead to more capacity. In a multi-path fadingenvironment, a large improvement (more than 10 dB) can be obtained by using multiplereceive antennas by mitigating the weak signal fades. The focus of this work package willbe on high data rates; therefore the spatial multiplexing is chosen as the suitable candidate.Spatial multiplexing has the potential to increase the transmission rate with a factor n,where n is the minimum of the number of transmit and receive antennas.

6.2 MIMO Theoretical CapacityBefore analyzing different MIMO techniques, it is important to show the capacity that canbe achieved by using multiple transmitters and multiple receivers. These theoretical bounds

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will be used later to compare how close the algorithm capacity is to the theoretical one.Here, a summary is given of the capacity for different channels as reported in [Fos98].

The following assumptions have been considered to formulate the results given below:

• Number of transmit and receive antennas is, respectively, Nt and Nr• The total transmit signal vector is composed of Nt statistically independentequal power components. The total irradiated power is independent of thenumber of transmit antennas.• The communication channel H is assumed to be flat over frequency• Average SNR at each receiver branch: = P/N0 where P is the received powerindependent of Nt• Noise at the receiver is modeled as AWGN vector of dimension Nr, withindependent components of identical power N0 for each of the Nr branches.

The capacity for a MIMO system, for the assumptions given above is:

where (.)H denotes the conjugate transpose of a vector or matrix. Since usually in indoorenvironments, we come across channels that can be modeled by a Rayleigh distribution, itis useful to report the capacity achievable in such channels for different antennasconfigurations.

We now assume:

• Quasi-static channel H (Nt columns, Nr rows): i.e. the randomly selectedchannel is not changing during a single packet transmission.• Channel follows the Rayleigh distribution. The element of the channel H (Nr x Nt matrix)are i.i.d., complex, zero-mean, unit variance entries:

consequently, |hij|^2 is a ^2 variate but normalized so E(|hij|^2) = 1.• H is known at the receiver.

The capacity for different antennas configurations becomes [Uys01]:

A) No diversity: Nr = Nt = 1

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B) Receive Diversity: Nt = 1, Nr = N

C) Transmit Diversity: Nt = N, Nr = 1

D) Combined Transmit-Receive Diversity: Nt = Nr

The best theoretical capacity is achieved in case D. This theoretical result confirms that thecombination of transmit and receive diversity improves the data rate and the performanceof wireless links.

6.3 MIMO and SIMO Feasibility Study under RayleighConditions

6.3.1Introduction

The feasibility study is confined to the prediction of capacities in indoor non lineof-sightwireless channels. The propagation environment typically consists of many scatterers, sothat the signal travels multiple paths before arriving at the receiver. Such a propagationenvironment is shown in Figure 6.2.

Figure 6.2 Indoor Wireless Fading Environment

In the limit of many scatterers, it can be shown that the Rayleigh distribution isappropriate to describe the spatial fluctuations of the amplitude of a narrowband signal.Shannon’s equation explains the dependency of the capacity C on the bandwidth B andsignal-to-noise ratio SNR.

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Let’s take the bandwidth fixed (because of spectral regulations or systemrequirements). A Rayleigh number generator is taken for the signal-to-noise ratio and westudy the probability density function (PDF) of the normalized capacity (given by log2(1+SNR)).

Figure 6.4 Probability density function of the capacity [bit/s-Hz] under Rayleigh fadingconditions

The capacity is treated as a stochastic variable. It is characterized by its mean value (around5 bits/s-Hz in the figure above) and the variation around the mean. The variation around themean has a relation to the reliability of the wirelesscommunications link. MIMO aims to propose systems with high data rates and a goodreliability. The reliability can be evaluated by having a look at the tail of the PDF. Therefore,the concept ‘outage’ is now introduced. Outage is the chance that the user will experience acapacity below x bits/s-Hz.

In the remainder of this report, outage levels of 10 % and 1 % will be taken.Drawing a cross-section of the CDF with those outage levels will give us thecapacity. This capacity is guaranteed within 90 % or 99 % of the indoor space,respectively.

6.3.2 Average capacity of SIMO and MIMO systems

Consider a system with nT transmit antennas and nR receive antennas. Thegeneralized Shannon capacity for this MIMO system can be written as shown in Eq. (1). ARayleigh number generator is used to describe the spatial variations of the signal-to-noiseratio . The Rayleigh fading model is the most popular model which describes fading as acomplex Gaussian process. The elements of the channel matrix are taken as unit variancecircular symmetric Gaussian stochastic variables.

The average capacity for various MIMO systems as a function of the averagesignal-to-noise ratio is shown in Figure 6-5. In addition, the capacity for a single inputmultiple-output system (SIMO) is also shown. The SIMO case denotes the classicaldiversity system with only multiple antennas on one side of the communication link.

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Figure 6.5Average capacity of a n = 1...4 SIMO system (‘oc’) compared to (n,n) MIMO system

(‘orth’) for uncorrelated Rayleigh fading channels.

As a reference, the conventional single antenna system (SISO) is included as a reference.Consider that conventional systems (GSM, UMTS etc..) have rather low spectralefficiencies around 1 – 2 bits/s-Hz. Take an arbitrary target of 8 bits/s-Hz for our broadbandMIMO research, the following table shows the signal-to-noise ratio to reach this capacitytarget.

Table Signal-to-noise ratio [dB] to get a average spectral efficiency of 8 bits/s-Hz.

6.3.4 Outage capacity of SIMO and MIMO systems

A mean capacity of 8 bit/s-Hz is an interesting figure, but it does not tell us what thecapacity will be 90 % or 99 % of the time or space. Therefore, another interestingperformance measure for the reliability of the service is the outage capacity. Outagecapacity means that the capacity equal or higher than a certain fixed value is guaranteed

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for 90 % or 99 % of all spatial locations. The SNR threshold for an outage capacity of 8bit/s-Hz is shown in Table.

Table: Signal to noise ratio to get an outage spectral efficiency of 8 bit/s-Hz for outage of10 %

and 1 %, respectively.

Note that a conventional single antenna system requires an unrealistic 44 dBsignal-to-noise ratio to achieve a reliable capacity of 8 bits/s-Hz, while a (4,4)MIMO system only needs a signal-to-noise ratio of 10 dB.

6.4 Multi-path Propagation and MIMO

Multipath propagation is a feature of all wireless communication environments. There isusually a primary (most direct) path from a transmitter at point “A” to a receiver at point “B.”Inevitably, some of the transmitted signal takes other paths to the receiver, bouncing offobjects, the ground, or layers of the atmosphere.

Signals traversing less direct paths arrive at the receiver later and are oftenattenuated. A common strategy for dealing with weaker multipath signals is tosimply ignore them—in which case the energy they contain is wasted. The strongestmultipath signals may be too strong to ignore, however, and can degrade the performanceof wireless LAN equipment based on existing standards.

Radio signals can be depicted on a graph with the vertical axis indicating amplitude and thehorizontal axis indicating time as sine waves. See Figure 1, a. When a multipath signalarrives slightly later than the primary signal, its peaks and troughs are not quite aligned withthose of the primary signal, and the (combined) signal seen by the receiver is somewhatblurred. See Figure 1, b. If the delay is sufficient to cause the multipath signal’s peaks toline up with the primary signal’s troughs, the multipath signal will partially or totally cancelout the main signal. See Figure 1, c.

Traditional radio systems either do nothing to combat multipath interference, relying on theprimary signal to out-muscle interfering copies, or they employ multipath mitigationtechniques. One mitigation technique uses multiple antennas to capture the strongest

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signal at each moment in time. Another technique adds different delays to received signalsto force the peaks and troughs back into alignment. Whatever the mitigation technique, allassume multipath signals are wasteful and/or harmful and strive to limit the damage.

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MIMO, in contrast, takes advantage of multipath propagation to increase throughput,range/coverage, and reliability. Rather than combating multipath signals, MIMO putsmultipath signals to work carrying more information. This is accomplished by sending andreceiving more than one data signal in the same radio channel at the same time. The useof multiple waveforms constitutes a new type of radio communication—communicationusing multi-dimensional signals—which is the only way known to improve all three basiclink performance parameters (range, speed and reliability). Because MIMO transmitsmultiple signals across the communications channel (rather than the conventional system’ssingle signal), MIMO has the ability to multiply capacity (which is another word for “speed”).A common measure of wireless capacity is spectral efficiency—the number of units ofinformation per unit of time per unit of bandwidth—usually denoted in bits per second perHertz, or b/s/Hz.

Using conventional radio technology, engineers struggle to increase spectral efficiencyincrementally (i.e. one b/s/Hz at a time). By transmitting multiple signals containing differentinformation streams over the same frequency channel, MIMO provides a means of doublingor tripling spectral efficiency.MIMO can also be thought of as a multi-dimensional wireless communications system.Conventional radio systems try to squeeze as much information as possible through a one-dimensional pipe. In order to do that, engineers must adapt their designs to the noise andother limitations of a one-dimensional channel. MIMO empowers engineers to work inmultiple dimensions, creating opportunities to work around the limitations of a one-dimensional channel.Greater spectral efficiency translates into higher data rates, greater range, an increasednumber of users, enhanced reliability, or any combination of the preceding factors. Bymultiplying spectral efficiency, MIMO opens the door to a variety of new applications andenables more cost-effective implementation for existing applications.

An interesting sidelight: Guglielmo Marconi demonstrated the first non line-of-sight (NLOS)wireless communications system in 1896 by communicating over a hill. From that dayforward, engineers viewed multipath signals as an annoyance at best and serious problemat worst. The first paper describing wireless MIMO’s capacity multiplying capability waspublished 100 years later in the 1996 Global Communications Conference proceedings.

How Does MIMO Differ from the Smart Antenna?MIMO and “smart antenna” systems may look the same on first examination: Both employmultiple antennas spaced as far apart as practical. But look under the hood, and you will

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see that MIMO and smart antenna systems are fundamentally different. Smart antennasenhance conventional, one-dimensional radio systems. The most common smart antennasystems use beamforming (a.k.a. beam switching) to concentrate the signal energy on themain path and receive combining (a.k.a. diversity) to capture the strongest signal at anygiven moment. Note that beamforming and receive combining are only multipath mitigationtechniques, and do not multiply data throughput over the wireless channel. See Figure 2.That’s not to say beamforming and receive combining aren’t useful. Both havedemonstrated an ability to improve performance incrementally in point-to-pointapplications (e.g., outdoor wireless backhaul applications). However, whilebeamforming and receive combining are valuable enhancements to conventionalradio

systems,MIMO isaparadigm shift,dramaticallychangingperceptions of andresponses tomultipathpropagation.Whilereceivecombining andbeamformingincreasespectralefficiency one ortwob/s/Hz ata time;MIMOmultiplies theb/s/Hz.

6.5MIMOIEEEStandard802.11n

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MIMO-OFDM technology is more than the latest technical improvement for wireless LANs.MIMO-OFDM is a major technology upgrade enabling demanding new applications withhuge market potential and facilitating significant growth in existing applications. Though theIEEE 802.11n task group is developing a standard for MIMO-OFDM wireless LAN devicesaround which the entire industry should rally, the delivery of pre-standard MIMO enhancedWi-Fi devices today can only boost development of a robust market for MIMO-OFDMwireless LAN devices.

MIMO Algorithms6.6 MIMO Algorithms and Architectures

Different MIMO architectures have been proposed in literature of the last fewyears. This chapter reviews the different MIMO techniques. It focuses on space divisionmultiplexing systems (SDM) and space time block codes (STBC).

6.7 Space Division Multiplexing and Layered Architectures

SDM techniques exploit the spatial dimension using multiple antennas at bothtransmitter and receiver. These techniques transmit different signals on different transmitantennas simultaneously. The goal is to increase the capacity and the SNR performance.At the receiver, the different signals are recovered using the Space Division Multiplexingtechnique. Multiple antennas are required at the receiver to recover the transmit signalsmore accurately.

Figure 6.6 The physical model of a system with SDM.

6.8 Signal Model

A communication system comprising Nt transmit (TX) and Nr receive (RX)antennas are considered. This system, assumed to operate in a Rayleigh flat-fadingenvironment, exploits the spatial dimension by using Space Division Multiplexing (SDM)(see Figure 6.6, where MAPU stands for Multi Antenna Processing Unit). Suppose wemodel the channel impulse response H as a zero-mean complex Gaussian variable, like:

H = A + jB (1)

where A and B are zero-mean statistically independent real Gaussian variables, eachhaving a variance 2/2. The variance of the complex Gaussian variable H can be shown tobe:

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Suppose that at discrete times, the transmitter sends an Nt-dimensional (complex) signalvector s (i.e., it transmits Nt parallel streams of data), and the receiver records an Nr-dimensional complex vector x. Then the following signal model describes the relationbetween s and x:

where H is an Nr × Nt complex propagation matrix that is constant with respect to thesymbol time and assumed known at the receiver (e.g. via transmitting training sequences)and the vector n (Nr -dimensional) represents additive receiver noise.The vector s is assumed to have zero-mean, uncorrelated random variables with varianceequal to s2. The total power of s (i.e., E[sHs]) is assumed to be Ps. Thus, the covariancematrix of s equals:

where H denotes the conjugate transpose of a vector or matrix and the matrix I withsubscript Nt represents the identity matrix with dimension Nt. Note that the total transmittedpower does not depend on the number of transmit antennas but is assumed fixed at Ps.The vector n is Nr -dimensional and represents additive receiver noise. The vector n isassumed to have zero-mean, uncorrelated random variables with variance ^2 and acovariance matrix equal to:

Furthermore, it is assumed that the vectors s and n are independent and thus the followingholds: E[snH ] = 0. To explain the different Space DivisionMultiplexing techniques, the following notations will be used:

where xi and si represent the i-th element of x and s respectively. The Hi and hi vectorsdenote the i-th row and i-th column of H, respectively.

Transmission schemesDepending on the coding architecture used in the multiple antenna transmitter, two maintypes of SDM scheme are possible: per antenna coding and joint coding scheme.

Joint coding:In this transmission scheme a single code is used to encode all the signals going todifferent antennas. After coding, interleaving and mapping, the Serial input bit stream isconverted to Nt Parallel sub-streams (S/P). See figure 6.7.

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Figure 6.7

6.9 Antenna coding:In this transmission scheme the serial input bit stream is first converted in Nt parallel sub-

streams, then each sub-stream is separately coded. See figure 6.8.

Figure 6.8 MIMO transmission scheme deploying a per antenna coding architecture.

6.10 Linear receiver scheme The Zero Forcing Algorithms

The ZF algorithm is based on a conventional adaptive antenna array (AAA)technique, namely, linear combinatorial nulling [Wol98]. In this technique, each sub-streamin turn is considered to be the desired signal, and the remaining data streams areconsidered as “interferers”. Nulling of the interferers is performed by linearly weighting thereceived signals so that all interfering terms are cancelled.For Zero Forcing, nulling of the “interferers” can be performed by choosing weight vectorsdi (with i = 1, 2, …, Nt) such that

where T stands for the transpose of a vector or matrix and hj denotes the j-thcolumn of the channel matrix H. However, when we take a closer look to thiscriterion, solving the weight vectors is equal to finding a matrix D such that:

where D is a matrix that represents the linear processing in the receiver. The i-th row of Dis equal to the transpose of the i-th weight vector di and I is the identity matrix. So, by

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forcing the “interferers” to zero, each desired element of s can be estimated. If H is notsquare, D equals the pseudo-inverse of H:

where + represents the pseudo-inverse. In order for the pseudo-inverse to exist, Nt must beless than or equal to Nr, because for Nt larger than Nr, HHH is singular and its inverse doesnot exist [Str88]. Furthermore, note that in order for the inverse to exist, the columns of Hmust be independent. Regarding the independent and identically distributed (i.i.d.)assumption of the elements of H, independence is usually an approximation, which isjustifiable if 1) the antenna spacing is chosen equal to or larger than /2 [Fos98] (where represents the wavelength of the transmission frequency) and 2) the system operates in arich-scattered environment, which can be modeled by Rayleigh flat-fading. Thus, for Nr Ntand if the inverse of HHH exists, the estimates of s (given by sest) can be found by:

or, equivalently:

Using Formula (11), (sest)i, i.e. the i-th component of sest, can be written as:

where +Hi represents the i-th row of H+ , which, according to Formula (7), isequal to the transpose of the i-th weight vector di. Note that di is a so-called nulling vector[Wol98]. As a final step, (sest)i can be sliced to the nearest Quadrature AmplitudeModulation (QAM) constellation point, these sliced signals are denoted by s . In this way,all Nt elements of s can be decoded at the receiver. The diversity order of an (Nt,Nr)system based on ZF is equal to Nr–Nt+1, as shown in [Win94].Note that a diversity order of one means that the BER improves by a factor of 101 if theSNR is increased by 10 dB. In case of a diversity order of two, if the SNR is increased by10 dB, the BER improves 102 times, etc.

6.11 The Minimum Mean Square Error solution

Another approach in estimation theory to the problem of estimating a randomvector s on the basis of observations x is to choose a function g(x) that minimizes theMean Square Error (MSE).

An exact function g(x) is usually hard to obtain, however, is we restrict thisfunction to be a linear function of the observations, an exact solution can beachieved. Using linear processing, the estimates of s can be found by:

Now, to obtain the linear Minimum Mean Square Error (MMSE), D must bechosen such that the Mean Square Error 2 is minimized:

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To minimize the Mean Square Error (over D), the processing at the receiver must be equalto:

where is equal to n^2/ s^2 = Nt / .

From Formula (10) it becomes clear that the ZF solution correspond to an MMSE solutionwith = 0.

6.12 Non Linear receiver scheme ZF with Decision Feedback Decoding

The linear nulling approach as described in the previous section is viable, but as willbecome clear from the results in Section 4, superior performance is obtained if non-lineartechniques are used. One can imagine that if somehow first the most reliable element ofthe transmitted vector s could be decoded and used to improve the decoding of the otherelements of s, superior performance can be achieved. This is called symbol cancellation[Wol98] and it exploits the timing synchronism inherent in the system model (theassumption of co-located transmitters makes this completely reasonable). Furthermore,linear nulling (i.e., ZF) is used to perform detection. In other words, symbol cancellation isbased on the subtraction ofinterference from already detected components of s from the receiver signal vector x. Thisresults in a modified receiver vector in which, effectively, fewer interferers are present.Because this principle is somewhat analogous to decision feedback equalization, it is alsocalled Decision Feedback Decoding (DFB).When symbol cancellation is used, the order in which the components of s aredetected becomes important to the overall performance of the system. To determine agood ordering of detection, the covariance matrix of the estimation error s – sest will beused. For ZF, this covariance matrix can be shown to be:

or, using the pseudo-inverse:

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Let (sest)i be the i-th entry of sest, then, the "best" estimate, (sest)i, is the one for which Pii(i.e., the i-th diagonal element of PH) is the smallest, because this is the estimate with thesmallest error covariance. From Formula (18) it becomes clear that Pii is equal to thesquared length of the i-th row of the pseudo-inverse. So find the minimum squared lengthrow of H+ is equivalent. Suppose that the order in the pseudo-inverse of H is arranged sothat the row with the least squared length becomes the last row (the i-th row of H+ ispermuted with the Nt-th row), then the Nt-th element of sest can be independentlydecoded. Let N s denote the decoded value, then this value can be used to improve theestimate of the remaining Nt–1 signals (i.e., symbol cancellation). If this procedure to findthe “best” estimate isperformed in a recursive way, the so-called Optimal Detection (OD) method as described in[Wol98] is obtained. Here it is called the Decision Feedback Decoding algorithm withoptimal detection. The recursive algorithm can be described as follows:

1. Compute H+ ;2. Find the minimum squared length row of H+ and permute it to be the last row,permutethe columns of H accordingly;3. Form the estimate of the last component of s. In case of ZF:

where the transpose of +Nt H is said to be the Nt-th nulling vector [Wol98] ;

4. Obtain s Nt (via slicing) from

5. (While 1 > 0 t N ) go back to step 1, but now with:

Note that in case step 2 is skipped, the DFB algorithm is performed withoutoptimal detection and the overall performance will be less, however, processing time issaved.

6.13 Minimum Mean Square Error with Decision Feedback Decoding (V-BLAST)

In order to perform Decision Feedback Decoding with Minimum Mean SquareError decoding, the DFB algorithm of Section 2.6.1 has to be adapted somewhat.Again, the covariance matrix of the estimation error s – sest will be used todetermine a good ordering of detection. For MMSE, this covariance matrix can be shown tobe:

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Note that P is somewhat different from the case where ZF is used as detection. In order thedo DFB based on the MMSE algorithm, the DFB algorithm is adapted and becomes:

1. Compute D (P is obtained while computing D);2. Find the smallest diagonal entry of P and suppose this is the i-th entry. Permute the i-thcolumn of H to be the last column and permute the rows of D accordingly;3. Form the estimate of the “best” component of s:

where Nt D represents the last row of D and its transpose is the Nt-th nulling vector[Wol98];

4. Obtain s Nt (via slicing) from

5. (While 1 > 0 t N ) go back to step 1, but now with:

In the following chapters, we will refer to this algorithm as V-BLAST (VerticalBell Laboratory Space Time Architecture) which is the widely spread name used inliterature to identify this technique.

6.14 Maximum likelihood Decoding

MLD is a method that compares the received signal with all possible transmitted signalsand estimates s according to the Maximum Likelihood principle. Suppose a matrix C givesall possibilities in s that could occur (the dimensions of C are N K t × , where K = QNt andQ represents the number of constellation points).

Then, the receiver should store a matrix Y such that:

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At the receiver, the most likely transmitted signal is determined, as the one forwhich

is minimal (with 1 j K), i.e., the signal sj that corresponds with the vector yjwhich lays closest to the received vector is said to be the most likely signal to betransmitted. Thus, s is chosen to be the j-th column of C. This can be rewritten to thefollowing formula where sml represents the maximum likelihood detection of the transmittedsignal s:

MLD is optimal in terms of BER performance. However, a major disadvantage is that thecomplexity of MLD is proportional to QNt , due to the fact that the size of Y growsexponentially with Nt .Another way to show the superiority in BER performance of MLD over the other SDMtechniques is by checking its diversity order. It is shown in [Nee00-1] that the diversity orderof a MLD system with Nr receive antennas is equal to Nr.Note that in the case of MLD, it isnot required that Nt Nr.

Soft Output MLDThe MLD technique can be modified to deliver not only the most likely transmitted symbol,but also reliable values, which are known as soft-decision outputs. Hagenauer presents in[Hag89] a method to derive soft-decision values. There, the log likelihood ratio is used asan indication for the reliability of a bit. If x denotes the received vector, bl is the l-th bit toestimate, H is the estimated channel matrix and sj is one of the possible transmittedvectors (with 1 j K, where K = QNt and Q represents the number of constellationpoints), then the L-value of the estimated bit is:

Because the vectors sj are equally likely to be transmitted, P(sj) is equal for all vectors sj.Using the probability density function of a multivariate normal distribution give a certainchannel, we find the soft-output decisions:

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Soft Output technique will be used together with MLD for simulation. We willrefer to it as SOMLD.

6.15 Space time block codes

In STBC the input to the encoder is a stream of modulated symbols from a real or complexconstellation. The encoder operates on a block of K symbols which are distributed ondifferent antennas (space) and on T symbol times. The results are matrix code wordswhose rows correspond to antennas and columns correspond to symbol times. The ratioK/T gives the coding rate.

6.15.1 Alamouti schemeAt the transmitter side Alamouti scheme exploits two transmitting antennas that in twotransmission time slots (T1, T2), emit two symbols according to the following scheme[Ala98]:

Alamouti scheme.

Where the sign ‘*’ means conjugation.

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The first stage receiver combines the signals coming from two different transmit branchesin the two consecutive times while the second stage performs Maximum LikelihoodDetection (MLD).

The received signal will be:

The above equations can be written using the equivalent orthogonal channel matrix as:

If the channel is known, the estimated transmit signal can be easily found through thechannel match-filter. This algorithm reaches the optimum capacity [Ala98].

6.15.2Generalization of Alamouti Scheme

The generalization of orthogonal matrix code words for more than 2 transmitantennas does not reach unitary transmission rate. Different Space Time Blocks schemesfor 3 and 4 antennas were proposed. see Table

Proposed STBC schemes.

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Conclusions

Different MIMO algorithms are presented in this chapter.Space Division Multiplexing techniques:• ZF: is linear and does not use any other knowledge that the channelestimation. Its diversity is equal to Nr-Nt+1• MMSE: is also linear but requires the noise variance estimation andchannel estimation.• ZF and MMSE with DFB: Direct feedback is used together withrespectively ZF and MMSE to improve their performance. VBLAST isanother name for theses techniques.• MLD: non linear, but provides the maximum likelihood solution. Itsdiversity is equal to Nr.Space Time Block Codes algorithms:• Alamouti: it is a simple algorithm at both transmitter and receiver. Itreaches the optimum capacity but only for a 2x1 system.

Chapter No. 7 MIMO OFDM

7.1 MIMO with OFDM

The previously described SDM algorithms are narrowband single carrieralgorithms. WLAN system are generally broadband and based on orthogonalfrequency division multiplexing (OFDM). OFDM is a multi carrier technique and, within thestandards, the signal time per subcarrier is defined to be TS = 3.2 s. Based on theobservations that indoor rms delay spreads are most likely smaller then 250 ns [Nee00], wecan assume that every subcarrier undergoes flat-fading, since TS is (much) larger than therms delay spread [Rap89]. So, in order to combine SDM with OFDM, a SDM algorithm canbe performed per subcarrier.Thus, suppose the transmitter consists of Nt transmitantennas, then every Sub-carrier carries Nt data streams. At the Nr-th receive antennas thesubcarrier information is separated by using FFTs. After that the Nr information symbols

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belonging to sub-carrier i are routed to the i-th MIMO decoder where one of the algorithmsof is implemented to recover the transmitted data signals (d1,i,…, dN,i), where the firstsubscript indicates the transmit antenna and the second one indicates the subcarriernumber. This is shown in Figure 7-1 and Figure 7-2.

Figure 7.1 Multi-antenna joint coding architecture transmitter using OFDM.

7.2 Transmitter and receiver design

The transmitting part consists of a multi-antenna transmitter, which is representedschematically in Figure 7-1. The binary input data is fed to the encoder. A convolutionalcode with the IEEE 802.11a standard rate 1/2, constraint length 7 and generatorpolynomials (133,171) is chosen as a forward error correction code. Higher coding rates of2/3 and 3/4 are obtained by puncturing the rate 1/2 code. In order for the forward errorcorrection to correct for subcarriers and/or antennas that are in deep fades, the coded datais interleaved over frequency and space to reduce the number of bit errors in one burst.The interleaver size is chosen based on the assumption that the channel is quasi-static.The bits are then mapped on QAM symbols according to the IEEE 802.11a standard. Theoutput of the decoder is then demultiplexed into Nt blocks of Nc streams, where Nc is thenumber of sub-carriers. After pilot insertion, the Inverse Fast Fourier Transform (IFFT) isperformed on each block, resulting in Nt signals in the time domain. Cyclic extension andwindowing are based on the IEEE 802.11a standard.At the receiver, as depicted in Figure 12-2, perfect synchronization (time andfrequency wise) and channel knowledge is assumed. After the payload is received, thecyclic extension is removed, the FFT is executed and the pilots are removed. Once thesubcarrier information is retrieved, the desired MIMO processing (i.e. ZF, VBLAST orMLD…) can be performed. The output of the MIMO processing is sliced (i.e.,

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demodulated), deinterleaved and depunctured. Finally, the de-punctured bits are decodedusing a Viterbi decoder.

Figure 7.2 Multi-antenna receiver using SDM with OFDM.

Per-Antenna-Coding (PAC) architecture, as illustrated in Figure 7-3, is alsoassessed through link level simulations. V-BLAST (Section 4.5.2) is used at the receiver.Per Antenna Coding V-BLAST is a variant of V-BLAST based on per antenna codingarchitecture . The difference with joint coding architecture is that the coding and theinterleaving at the transmitter are now done per antenna branch. At the receiver, the idea isfirst to go through the decoding stage before the Successive Interference Cancellation(SIC) is executed. In this way Forward Error Correcting coding is performed on the SICinformation. In Figure 7-3 and Figure 7-4 a schematic representation of the transmitter andthe receiver of a system deploying PAC V-BLAST is represented. The MIMO OFDMtransmitter consists of Nt OFDM transmitters among which the incoming bits are spread,then each branch in parallel performs encoding, interleaving ( ), QAM mapping, Nc-pointInverse Fast Fourier Transformation (IFFT), and adds the cyclic extension before the finalTX signal is upconverted to RF and sent.

Figure 7.3 PAC MIMO OFDM transmitter scheme.

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At the Nr receivers, the subcarrier information is separated by performing the Ncpoint FastFourier Transformation (FFT). Then, in general, the symbols mapped onto subcarrier i arerouted to the i-th MIMO detector to recover the M transmitted data signals per subcarrier(see Figure 7-4). Finally, demapping, deinterleaving ( -1) and decoding are performed perreceiver branch and the resulting data are combined to obtain the binary output data.

Figure 7.4 The PAC V-BLAST Detection and Decoding Block.

7.3 Performance evaluation: noise-limited scenarios

The goal of this section is to present the PER (64 bytes) versus SNR performance of theMIMO algorithms presented. Although more results are presented in Chapter 6, results forsome test case are presented here to provide a more practical understanding of theperformance of the different MIMO algorithms. The channel used for the simulations isdescribed in [B4-D2.2] and exhibits a RMS delay of 50ns. The algorithms deployed at thereceiver were ZF, MMSE and MLD.

Figure 12-5 shows the PER (64 byte packet) versus SNR for a 2x2 system using codingrate 1/2 and QPSK modulation. MLD clearly achieves the best performance followed byMMSE and ZF. The spectral efficiency achieved by a 2x2 system with 1/2 rateconvolutional code and QPSK modulation is 1.2 bps/Hz. This translates into a data rate of24Mbps.In Figure 7.5 coding rate 0.75 and 16QAM modulation are used at the transmitter. Thespectral efficiency achieved by a 2x2 system with 3/4 rate convolutional code and 16QAMmodulation is 3.6 bps/Hz. This translates into a data rate of 72 Mbps.

All curves shift to the right due to the higher data rate that is now transmitted.MLD still shows the best performance. MMSE loses the advantage over ZFobserved for lower constellations.The performance degradation going from QPSK to16QAM for MLD and ZF is around 11-12 dB at PER=10-2, while for MMSE is almost 15dB.

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Figure 7.5PER versus SNR performance of a 2x2 system for different receive algorithms. At the

transmitter QPSK modulation and a convolutional coding rate of 1/2 are used. The RMSdelay spread of the channel is 50ns.

Figure 7.6PER versus SNR performance of a 2x2 system for different receive algorithms. At the

transmitter 16QAM modulation and a convolutional coding rate of 3/4 are used.The RMSdelay spread of the channel is 50ns.

Figure 7-7 and Figure 7-8 use the same coding rate and modulations as Figure 7-5 andFigure 7-6, respectively, only then for a 4x4 system. The MLD curve is steeper than in theprevious figures, which is due to the fact that the diversity order, which is proportional to thenumber of receive antennas, is now higher. As expected, the slope of the ZF curve does

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not change since the diversity order, which is given by Nt-Nr+1 is still equal to 1 for the 4x4case. Again for higher constellation MMSE degrades more than MLD and ZF.

The spectral efficiency achieved by a 4x4 system with coding rate equal 1/2 using QPSK is2.4 bps/Hz, which translates in a data rate equal to 48Mbps. The spectral efficiencyachieved by a 4x4 system with 3/4 rate convolutional code using 16 QAM is 7.2 bps/Hz.This translates into a data rate of 144 Mbps.

Figure 7.7PER versus SNR performance of a 4x4 system for different receive algorithms.At thetransmitter QPSK modulation and convolutional coding rate of 1/2 are used. The RMS

delay spread of the channel is 50ns.

Figure 7.8PER versus SNR performance of a 2x2 system for different receive algorithms.

At the transmitter 16QAM modulation and convolutional coding rate of 3/4 are used. TheRMS delay spread of the channel is 50ns. algorithm, especially for high number ofantennas, followed by MMSE and ZF.

7.4 Performance evaluation: interference-limited scenarios

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The goal of this section is to asses the performance of MIMO based WLAN system in co-channel interference limited environment. We regard the case where no attempt is made tocancel interference. First the co-channel interference model is described. Subsequently,the results from simulation with this model are presented.

Co-channel Interference model

Figure 7.9 Co-Channel Interference Model

MIMO system model in presence of two sources of co-channel interference.A source of interference has been implemented in MATLAB in order to test the robustnessof a MIMO system in an interference-limited scenario. The interferers are OFDM systemstransmitting in the same bandwidth of the desired user. The number of antennas used bythe interferer can be selected to be single or multiple.

Unless it is specified, the term interference will always be used for co-channelinterference. The interference signal is implemented as a random sequence of modulatedsymbols constantly overlapping the desired user signal and with power equal to one. Thetime version of the interference signal is convolved with a channel created in a similar wayas the one of the desired user. To come to the right average signal-to–interference ratio(SIR), the signals from each interference source are multiplied by the square root of afactor beta defined as:

Where, Nt is the number of transmit antennas of the desired user, Nint is the number oftransmit antennas of the interferer, numint is the number of interferers and SIR is the signalto interference ratio. With int N num interference sources, the interference power isint int N num . Whereas the power of the desired user is Nt. Thus we get the following ratio:

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dependent on the number of transit antennas.

Finally, interference, desired signal and White Gaussian noise are added together. In thesimulation presented in next section, the interference source is constantly present duringthe transmission of the desired user (i.e. it has the same length D of the desired userpacket and no temporal shift). Moreover the channel of the desired user is supposed ideallyknown and for all simulations and its RMS delay spread used is 50ns. When co-channelinterference is considered, the signal model is described by:

7.5 Synchronous versus asynchronous model when the channel isideally known

In the simulations that will follow, it is assumed that the interference source isconstantly present during the transmission of the desired user. We will refer to this sort ofinterference as synchronous interference. When a uniformly distributed shift in the interval[-D, D] is created to produce a random temporal overlapping between the desired user andthe interference, the average interference energy is half of the one experienced in thesynchronous interference scenario. This result comes from the fact that the averageoverlapping time is D/2. Now let’s assume that the channel is ideally known. It can beshown by means of simulations that the synchronous model and the asynchronous modelproduce the same BER versus SIR curves if the power of the asynchronous interference isdoubled. It can be concluded that when the channel is considered perfectly known, theasynchronous case is a special case of the synchronous one. It is possible by a properscaling together the BER performance for the asynchronous case from the synchronousone.For this reason in next sections, where channel is assumed perfectly known, thesynchronous interference model has been used for the link level simulations.

Noise to model co-channel interference

When the number of co-channel interferers is high (>>1), the total interferencesignal can be more easily modeled as White Gaussian noise. The result of this is a betterBER versus SIR performance, when coding is used. This is shown in Figure.

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Figure 7.10BER versus SNR performance for SIR=15dB, with 1 OFDM co-channel interference

source, 10 OFDM sources, 1 noise modeled co-channel interference. In general it is not expected that a high number of co-channel interference sources will beobserved. However, it appears that an interference source exploiting multiple transmitters isless harmful that one exploiting a single antenna.

7.6 Impact of Co-Channel Interference on MIMO and SISO systems

In this section we analyze the performance of MIMO transceivers in aninterference-limited scenario. Our first goal is to compare the performance of a MIMO andSISO system in the same interference scenario. Figure 7-11 shows the performance, interms of BER versus SNR, of a 1x1 system versus a 2x2 system with different level of co-channel interference (SIR).

QPSK modulation with no coding is used. There are two sources of interference, bothhaving a single antenna. It is clear from Figure 12-11 that for high level of interference (SIR

10dB) the performance of both SISO and MIMO system is the same. When the SIR =20dB, the spatial diversity exploited by the MIMO receiver produce a better BERperformance. It is worthy to notice that the spectral efficiency achieved by MIMO is doubleof the one achieved by the SISO system. Thus we can conclude that a SISO and a MIMOsystem using the same data rate per antenna offer the same performance at low SIRvalues.

Figure 7.11 BER vs SNR for a 1x1 and a 2x2 system using QPSK no coding.

For the results shown in Figure 7-12 and Figure 7-13, coding and modulation are chosen insuch a way that the spectral efficiency is the same in both systems. Figure 7-12 shows thecomparison in BER versus SIR and SNR, of a 2x2 system using BPSK modulation andcoding rate ½ and a 1x1 system using QPSK modulation and coding rate ½. In both casesthe spectral efficiency is equal to 1,2 bps/Hz. We can conclude that for a given spectralefficiency, a MIMO system is more robust to interference than a SISO system. This is due

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to the fact that MIMO uses lower modulation schemes (per antenna) than SISO to achievethe same data rate. At system level more packets will be correctly delivered by a MIMOsystem increasing the total throughput. Figure 5-13 shows the same as 2x2 BPSK vs 1x1QPSK, R=1/2. Both systems achieve the same spectral efficiency, equal to 2.4bps/Hz.

Figure7.122x2 BPSK vs 1x1 QPSK, R=0.5. Both systems achieve the same spectral efficiency,

equal to 2.4bps/Hz.

Figure 7.134x4 BPSK vs 1x1 16QAM, R=1/2. Both systems achieve the same spectral efficiency,

equal to 2.4bps/Hz.

7.7 Robustness of MIMO to co-channel interference

Figure 7.15 and 7.16 show the BER performance versus SIR of a 2x2 system using PAC V-BLAST. BPSK modulation and a half rate code have been used. The difference between

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the two figures is the RMS delay spread: which is respectively 50ns and 250ns. For bothsimulations two interference sources has been considered: a single antenna transmitter(indicated in the legend of the figures below as SIMO) and a multiple antenna transmitterone (indicated in the legend of figures below as MIMO). The figures depicted below showthe BER performance versus the SIR for the given SNR. The SNR value is chosen to get aBER around 10-4 or lower. As expected, all the curves tend to reach, for high SIR values(no interference), the BER value at the chosen SNR, which is identified in each figure bythe asymptote. Note that in PAC V-BLAST the ideal knowledge of beta is assumed. So inorder to minimize the Mean Square Error (over D), the processing at the receiver is equalto:

where equals Nt/SNR and is as defined as in (4), where H is the NrxNt channel matrix.For low delay spread, there is no difference in performance when the reception of a 2x2system is corrupted by a single transmit antenna interference or by a multiple transmitantenna interference.

At a delay spread of 250 ns the performance in presence of a multiple antenna interferer isslightly better than in the case of a single antenna interferer. This is due to the fact that ahigher number of interferers make the spectrum of the overall interferer signal flatter overfrequency. For high delay spreads and when coding is used, this kind of spectrum has alighter impact, on average, on each subcarrier of the received signal. This is more visible inFigure 7-17 for a 4x4 system.

Figure7.15BER versus SIR for a 2x2 system. The RMS delay spread is 50 ns and the Eb/No is fixed

at 5 dB. The source of interference is one terminal with either one or two transmit antennas.

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Figure 7.16BER versus SIR for a 2x2 system. The RMS delay spread is 250 ns and the Eb/No is fixedat 5 dB. The source of interference is one terminal with either one or two transmit antennas.

Figure 7.17 and Figure 7.18 depict the same results as Figure 7-15 and Figure 7-16, onlynow for the 4x4 case. Here the source of interference is either a single transmit antennasystem or a four transmit antenna system. For low delay spread there is no differencebetween the performances in presence of different sources of interference.

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Figure 7.17BER versus SIR for a 4x4 system. The RMS delay spread is 50 ns and the Eb/No is fixed

at 0 dB. The source of interference is one terminal with either one or four transmitantennas.

Figure7.18BER versus SIR for a 4x4 system. The RMS delay spread is 250 ns and the Eb/No is fixedat 1 dB. The source of interference is one terminal with either one or two transmit antennas.

For high delay spread, as previously seen, the system is more robust when amultiple transmit antenna interferer is present. This is due to the flatter spectrum of the interference signal. From thefigures above, we can conclude that at a SIR of 20 dB, the degradation on performance due to the interference isnegligible; at a SIR of about 10 dB, the BER performance looses 1 decade and for values of SIR lower than 10 dB theBER performance of PAC V- BLAST rapidly decrease (circa 1 decade per 2 dB for 250 ns delay spreads and 1decadefor 4 dB for 50 ns delay spread). It is important to notice that these results were obtained for the worse case scenario inwhich the interference is constantly present.