analysis of an alternative interleaving scheme in idma (wip)
DESCRIPTION
Work in progress! Bachelor's thesis.TRANSCRIPT
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CHAPTER 1
INTRODUCTION
1.1. Literature Review and Motivation
A 4G system is expected to provide a comprehensive and secure all possible solution where
facilities such as IP telephony, ultra-broadband internet access, gaming services and streamed
multimedia may be provide to users. There are various numbers of multiple access techniques
which are proposed for 4G system named as DS-CDMA (Direct Spread- Code Division Multiple
Access), MCCDMA (Multicarrier-CDMA), OFDMA (Orthogonal FDMA), IDMA (Interleave
Division Multiple Access) etc. IDMA (Interleave Division Multiple Access) is a new technology
that can remove the disadvantages of existing CDMA technique i.e. Multiple Access Interference
(MAI) and Inter-Symbol Interference (ISI). [6] [17]
In CDMA interleaver are used for coding gain while in IDMA, they are employed for user
separation. IDMA is a recently proposed scheme that employs chip- level interleavers for user
separation and the receiver employ a simple chip- level iterative multiuser detector (MUD). Such
a system is a logical development of the earlier research on introducing chip- level interleaving
as a means of mitigating burst impulsive noise disturbances, multiple access interference, as well
as Inter-Symbol Interference. The basic principle of IDMA is that two users are separated by an
interleaver (and the interleavers should be different for different users) while, OCDMA/IDMA,
which uses the orthogonal spreading code and interleaver to distinguish different users, increase
the receiver complexity of the user ends (UEs). [6]
1.2. Objectives
In IDMA the users are separated via independent and random interleavers. In the transmitter of
IDMA scheme, a chip-interleaver is followed by spreading process which is different from
conventional CDMA scheme. This method makes the sequences of low-correlation. Applying
the Central Limit Theorem, Multiple Access Interference is approximated as a Gaussian Random
Variable with mean and variance at the receiver. Consequently there is a limitation that the sum
of the users may have high correlation. After the interleavers are assigned to the users, they
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become fixed or permanent, hence it becomes necessary to design an interleaver which is free
from this problem.
1.3. Major contribution of Thesis
The major contribution of thesis are summarized as follows:
Brief history of Access technologies and their introductions.
Understanding the major concept behind IDMA (Interleave Domain Multiple Access)
Technique.
Understanding the mechanism of Interleavers and codes used in IDMA.
Understanding the problems faced in current random interleavers and a solution is
provided that does solve the problem to a great extent.
1.4. Organization of Thesis
This thesis consists of six chapters. Chapter 2 consists of some old access technologies and
history of wireless communication is also discussed. Chapter 3 describes the IDMA concepts and
the transmitter and receiver principles, features, future implementation and application of IDMA.
Chapter 4 gives an insight about different codes and interleavers used in a typical IDMA system.
Chapter 5 discusses the problems encountered in IDMA systems and remedy for the problems is
also discusses, while an algorithm is also given. Chapter 6 discusses the simulation results and
the future work is also briefed.
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CHAPTER 2
INTRODUCTION TO ACCESS TECHNIQUES
2.1. Background
With the advent of Internet and the advancement of technology, there has been an increased
interest in wireless connectivity. This trend began in the 1880s. The first successful wireless
transmission was achieved by the Italian Physicist whose name is Guglielmo Marconi. Marconi
created an equipment that achieved the wireless transmission of electrical signal through the air
which was the beginning of telegraphy or radio transmission, in September 1895. [1]
In the last 20 years, science has grown rapidly in the area of Digital Signal Processing in forward
error control coding and circuit designing which had a huge impact on wireless communication.
As time passed, wireless communication became more dominant, which gave rise to the need for
new applications such as video conferencing, online gaming, social network applications, and it
plays a huge role in military applications in encoding and encrypting important information to
provide security. [1]
2.2. Ages of Wireless Communication
In 1957, Clark Maxwell derived a theory based on electromagnetics which laid the basis for the
concept given by Guglielmo Marconi. This was a great achievement and a milestone for wireless
communication. However, it was unable to achieve reasonable data transmission rates for years
to come. [2]
The first prototypes for wireless telephony were introduced in the late 1940s in the US, and
1950s in the Europe. These early mobile phone were heavily constrained by limited mobility
and poor service. These devices were both heavy and expensive. The evolution of wireless
cellular communication is divided into several generations. The first and second generation
utilized analog communication, the third generation was revolutionary and the fourth generation
utilized broadband technology. [2]
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In the 1970s, the first generation of mobile telephony was introduced to the commercial
markets. These systems were referred to as cellular systems, and the name was later shortened to
cell phones. Due to this, the signals were handed off to the towers. The signals for these cell
phones were based on analog signals. 1G devices were a little less expensive than earlier
prototype devices and were less heavy. The most important protocol in the 1st generation was
known as AMPS, TACS and NMT. The mobile phone market worldwide increased 30-50%
annually due to 1G networks and the number of subscribers globally reached to 20 million in
1990s. In the early 1990s, 2G technology was introduced which was known as GSM
technology and it was based on digital modulation techniques to improve quality of service, but
the networks offered limited data service in 2nd generation. [2]
As demand drove uptake of cellphones, 2G networks were further improved to improve the
coverage and transmission quality and offer additional services such paging, voice mail, faxes,
and text messages. The limited data services under 2G included WAP, HSCST and MLS. [2]
An intermediary stage, referred to as 2.5G, was introduced in late 1990s which introduced
GPRS standard. GPRS introduced packet-switched data capabilities to existing GSM networks,
which allowed users to send multimedia data as packets, and convolved the cellular networks
with the Internet. As time went on, the importance of packet-switching became paramount with
the rise of the Internet or IP. EDGE networks, which was a further advancement of the existing
GSM network, also comes under 2.5G technologies. What 3G revolution allowed the users to do,
was to use audio, graphics and video data with acceptable Quality of Service. It is possible in 3G
networks to stream videos and engage in video telephony, although such activities are severely
constraint by network bottlenecks and over-usage. [2]
The main objective behind 3G technology was to unify the various different standards with a
single Global Network Protocol, in Europe, the US and other regions. In 3G phones the speed of
2 Mbps was achieved under ideal conditions. Moving at higher speeds can drop 3G bandwidth to
a mere 145 kbps due to Doppler-shift fading. [2]
3G cellular services is also known as UMTS. To sustain higher data-rates and to open the way
for internet style applications, 3G technology supports both packet-switching and circuit-
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switching data transmission and a single set of standards can be used worldwide with
compatibility over a variety of mobile devices. [2]
UMTS introduces 1st possibility of global roaming with potential access of internet from any
location. In the current generation of mobile telephony, 4G technology was deployed. The
purpose of 4G networks was to provide transmission rates up to 20 Mbps while simultaneously
accommodating QoS features. QoS allows users and telephone carries to prioritize traffic
according to the type of application and adjust between your different telephony needs at a
moments notice. [2]
Only now can we truly see the potential of 4G applications, which is expected to include high-
performance streaming of multimedia content. With the deployment of 4G technology, video
conferencing functionality is improved. 4G is also expected to provide wider bandwidth for high
speed mobile application within the network area. [2]
In 2008, the ITU-R organization specified the IMT-Advanced (International Mobile
Telecommunications Advanced) requirements for 4G standards, setting peak speed requirements
for 4G service at 100 Mbit/s for high mobility communication (such as from trains and cars) and
1Gbit /s for low mobility communication (such as pedestrians and stationary users). A 4G system
is expected to provide a comprehensive and secure all-IP based mobile broadband solution to
laptop computer wireless modems, smart phones, and other mobile devices. Facilities such as
ultra-broadband Internet access, IP telephony, gaming services, and streamed multimedia may be
provided to users. [22]
Pre-4G technologies such as mobile WiMAX and first-release 3G Long term evolution (LTE)
have been on the market since 2006 and 2009 respectively, and are often branded as 4G. The
approaching 4G (fourth generation) mobile communication systems are projected to solve still-
remaining problems of 3G (third generation) systems and to provide a wide variety of new
services, from high-quality voice to high-definition video to high-data-rate wireless channels.
The term 4G is used broadly to include several types of broadband wireless access
communication systems, not only cellular telephone systems. One of the terms used to describe
4G is MAGICMobile multimedia, anytime anywhere, Global mobility support, integrated
wireless solution, and customized personal service. As a promise for the future, 4G systems, that
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is, cellular broadband wireless access systems have been attracting much interest in the mobile
communication arena. The 4G systems not only will support the next generation of mobile
service, but also will support the fixed wireless networks. This article presents an overall vision
of the 4G features, framework, and integration of mobile communication. [22]
2.3. Multiple Access Techniques
Multiple Access Techniques are used so that we can allow many different mobile users to share
the allocated radio spectrum in the most efficient way. We know that the spectrum is limited,
thus sharing is important to increase the capacity of the cell over a geographical area by allowing
the available bandwidth to be used in different areas. It is paramount to achieve this in such a
way that the quality of service doesnt degrade for the existing users. [19]
2.3.1. Frequency Division Multiple Access (FDMA)
FDMA is one of the earliest multiple access technologies for cellular systems in which a separate
pair of frequency bands is allocated to each different user for making and receiving calls. One of
the frequencies is allocated to uplink and one to downlink. The frequencies allocated to certain
users can only be allocated once per cell, or adjacent cell, during a call which reduces co-channel
and intra-channel interference. The spectrum cannot be reassigned as long as the call is in place.
Different users can use different frequencies within a cell, whether they transmit at the same time
or at different times. [19]
The features of FDMA are as follows: [19]
1. FDMA channel carries one phone circuit at one time. When the FDMA channel is not
being used, then it sits idle and no other uses it to increase shared capacity.
2. After voice channel assignment, BS and MS transmit the data simultaneously and
continuously.
3. FDMA bandwidth is generally narrow, i.e. FDMA is generally implemented in
narrowband systems.
4. The symbol time is large compared to the average delay spread.
5. Complexity of FDMA mobile system is lower than that of TDMA mobile system.
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6. FDMA requires highly efficient filters at the receiver end to minimize the adjacent
channel interference.
Figure 2.1. FDMA R. Victor Jones, Harvard University
Source: http://people.seas.harvard.edu/~jones/cscie129/nu_lectures/lecture3%20/FDMA%2001.html
2.3.2. Time Division Multiple Access (TDMA)
There is no requirement for continuous transmission in digital systems because the users do not
use the allocated bandwidth at all time. In such cases, TDMA is a complementary access
technique to FDMA. Oftentimes they are used in conjunction such as in GSM which uses
TDMA/FDD. [19]
In TDMA, the entire bandwidth is available to the users but only for a finite period of time. In
most cases of TDMA, the available bandwidth is divided into fewer channels with compared to
FDMA and the users are allocated distinct timeslots because of which they have the entire
channel bandwidth at their disposal. TDMA requires careful time synchronization unlike FDMA
as long as the user shares the bandwidth and frequency domain. There are fewer number of
channels, and inter-channel interference is negligible.
When TDMA uses different timeslots for transmission and reception, this type of duplexing is
known as Time Division Duplexing (TDD). [19]
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Figure 2.2. TDMA R. Victor Jones, Harvard University
Source: http://people.seas.harvard.edu/~jones/cscie129/nu_lectures/lecture3%20/TDMA01.html
2.3.3. Code Division Multiple Access (CDMA)
The basic principle in CDMA allows us to use the same frequency bandwidth for every user, as
each individual user is assigned a unique spreading code so that we may differentiate different
users. CDMA utilizes spread spectrum techniques, in which you one can use a spreading signal
(code that is uncorrelated to the signal and allows us to spread the message signal to a much
larger bandwidth) to spread the narrowband message signal. This technique is most commonly
used in CDMA systems. [19]
There are two main types of CDMA spreading techniques known as Direct Sequence Spread
Spectrum (DSSS) and Frequency Hopping Spread Spectrum (FHSS). In DSSS, the message
signal is directly multiplied with a pseudorandom noise code (PN Code). Every user is allocated
a unique PN code, which is orthogonal to all other codes in the sequence, so that the receiver can
determine which device or receiver the data is intended for. For orthogonality, we generally use
64 x 64 Walsh-Hadamard codes and an m-sequence. [19]
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The near-far problem is a serious problem faced in CDMA systems. This problem arises when
the signal of interest is attenuated as the distance from receiver increases, because of which
regardless of how strong the transmitted signal is, it would be read as a weak signal. This
problem does not arise in TDMA and FDMA because the mutual interference is filtered out. In
CDMA, however, near-far effect combined with imperfect orthogonality between codes (e.g. due
to different time-shifts), leads to substantial interference. Accurate and fast power-control is
essential to reliable operation of multiuser DS-CDMA systems. [19]
Figure 2.3. Comparison between FDMA, TDMA and CDMA
2.3.4. Orthogonal Frequency Division Multiple Access (OFDMA)
OFDMA is also known as digital modulation technique and not a multi-user channel access
technique. It is used for transferring one bit stream over one communication channel using
OFDMA symbols. However, it can be mix with other multiple accesses using coding separation,
time or frequency of other users. [21]
OFDMA employs multiple closely spaced sub-carriers. The sub-carriers are divided among
group of sub-carriers. The sub-carrier that carriers should not be adjacent. OFDMA provides
multiplexing operation of data streams from multiple users onto the downlink sub-channels and
uplink multiple access by means of uplink sub-channels. [22]
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This is achieved by assigning different OFDM sun-channels to different user. In this downlink, a
sub-channel may be intended for other receivers. In the uplink, a transmitter may be assigned one
or more channels [21]
Orthogonal Frequency Division Multiplexing (OFDM) not only provides clear advantages for
physical layer performance, but also a framework for improving layer 2 performance by
proposing an additional degree of free- dom. Using OFDM, it is possible to exploit the time
domain, the space domain, the frequency domain and even the code domain to optimize radio
channel usage. It ensures very robust transmission in multi-path environments with reduced
receiver complexity. [21] [22]
OFDM also provides a frequency diversity gain, improving the physical layer performance. It is
also compatible with other enhancement Technologies, such as smart Antennas and MIMO
(multiple-input and multiple-output) radar antenna .OFDM modulation can also be employed as
a multiple access technology (Orthogonal Frequency Division Multiple Access). In this case,
each OFDM symbol can transmit information o/from several users using a different set of sub
carriers (sub channels). This not only provides additional flexibility for resource allocation
(increasing the capacity), but also enables cross-layer optimization of radio link usage. [21] [22]
Figure 2.4. Comparison between OFDMA and SC-FDMA. Agilent Technologies
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2.3.5. Single-Carrier Frequency Division Multiple Access (SC-FDMA)
SC-FDMA is a relatively new multiple access technique that utilizes single carrier modulation,
DFT-spread orthogonal frequency multiplexing, and frequency domain equalization. It has a
similar structure and performance as OFDM. SC-FDMA is currently adopted as the uplink
multiple access scheme for 3GPP LTE. [23]
SC-FDMA is the multiple access equivalent of Single-Carrier Frequency-Domain Equalization
(SC-FDE), which is similar to OFDM, in that they both perform channel estimation and
equalization in the frequency domain. Multiple access is achieved in frequency domain in SC-
FDMA. Thus to transition from SC-FDE to SC-FDMA requires division frequency amongst
frequencies.
2.4. Future of Development of Multiple Access Techniques
With the tremendous increment in the users count and introduction of new features including
web browsing. In the past few years, the request for bandwidth has started to surpass the
availability in wireless networks. Different techniques have been studied to improve the
bandwidth, efficiency and increase the number of users that can be accommodated within each
cell. [18]
The International Telecommunication Union (ITU) also defined recommendations for mobile
communication system for fourth generation (4G).In these recommendations, data rates up to
100 Mbps for high mobility and up to 1 Gbps for low mobility or local wireless are predicted.
Systems fulfilling these requirements are usually considered as fourth generation (4G) systems.
But 3G systems provide data rate of around 3.6-7.2 Mbps. [18]
Existing multiple access techniques used in 1G/2G/3G systems (such as FDMA/TDMA/CDMA
respectively) are basically suitable for voice communication only and unsuitable for high data
rate transmission and burst data traffic which would be the dominant portion of traffic load in 4G
system. There are various numbers of multiple access techniques which are proposed for 4G
system named as DS-CDMA (Direct Spread- Code Division Multiple Access), MC-CDMA
(Multicarrier-CDMA), OFDMA (Orthogonal FDMA), IDMA (Interleave Division Multiple
Access) etc. [18]
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CHAPTER 3
IDMA SYSTEMS
3.1. Introduction
As we know that, CDMA (specifically DS-CDMA) is an effective transmission technique which
is used in second generation (IS-95 and CDMA 2000) and third generation (UMTS, TD-
SCDMA) systems. IDMA can be seen as a special case of DS-CDMA with a spreading gain of
one using very low rate code and user specific interleaver for user separation. The main
difference between IDMA and DS-CDMA is that in conventional DS-CDMA the data is
transferred through FEC, then Interleaver (d), then at the end Spreading is done by Spreader
whereas in IDMA the spreading is done before interleaver. [4]
Computer simulations are performed in various scenarios and the performance is analyzed by
BER as well as by the Extensive transfer information chart. The analysis revelers the advantages
of IDMA over DS-CDMA in terms of performance and complexity under practical
considerations, particularly in a highly user loaded scenarios. [4] [15]
In communication systems, interleaving is referred to be technique commonly used to overcome
correlated channel noise such as burst error or fading. In interleaving mechanism, the input data
rearranges itself, such that consecutive data bits are split among different blocks and is swapped
in a known pattern amongst them. At the receiver end, the interleaved data are arranged back into
the original sequence with the help of de-interleaver. As a result of interleaving, correlated noise
introduced in the transmission channel appears to be statistically independent of the receiver and
thus allows better error correction. [5] [16]
3.2. Advantages of IDMA
As the demand for high data rate services grows in wireless networks, various challenging
problems arise when the existing multiple access technologies are used. For orthogonal multiple
access (MA) technologies such as TDMA, FDMA and OFDMA, the major problems include
their sensitivity to inter-cell interference and frame synchronization requirement for maintaining
orthogonality. [6] [16]
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For non-orthogonal MA technologies such as random waveform CDMA, although it mitigates
inter cell interference and supports asynchronous transmission, the challenge is to combat intra-
cell interference. So, there is a new technique known as IDMA (Interleave Division Multiple
Access) which seems to be the solution for these problems. [6]
The advantages of interleaving over scrambling seems very important for cell edge subscriber
stations to receive broadcast services such as common signaling broadcasting because some
advanced transmitting techniques for any casting cannot be used for broadcasting. Interleave-
division multiple accesses (IDMA) can be considered as a special case of direct-sequence code
division multiple accesses (DS-CDMA). [6]
In IDMA, data streams are separated by different interleavers rather than by different spreading
codes as employed in DS-CDMA. Each data stream is encoded by the same low-rate channel
encoder. The data rate can be adapted by superimposing many encoded and interleaved data
streams. In contrast to other system designs, channel coding is an integral part of the system
design. Separation of the data streams at the receiver can be done in an iterative, low complexity
way. These properties are advantageous for multi-user detection at the uplink and therefore make
IDMA an attractive candidate for the 4G uplink, but also for an evolution of existing DS-CDMA
systems. [6]
3.3. Comparison of IDMA and CDMA
Important features of all named multiple access are compared IDMA have been compared with
the existing MA technologies. With the existing CDMA, high data rates can be achieved by
reducing spreading factor or adopting multi-code CDMA, but the former leads to reduced
spreading gain against fading and interference, and the latter needs to overcome the interference
among spreading sequences. [24]
In contrast, high data rate transmission can be achieved in IDMA systems by assigning the FEC
codes with high coding rates. Neglecting intra-cell interference at low computational cost the
multiple access interference (MAI) is a major concern for both CDMA and IDMA cellular
networks. [24]
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Figure 3.1. Difference between CDMA and IDMA. Source: [24]
The existing CDMA mitigates the MAI by multi-user detection (MUD). However, the high
computational Cost involved in MUD which limits the high number of user- application in
practical systems. In contrast to CDMA, IDMA uses the iterative chip-by-chip (CBC) detection
algorithm to combat intra-cell interference. The per-user computational complexity of the CBC
is independent of the number of users involved. It achieves multi-user gain in the case of each
user with a rate constraint. This means that given the same sum-rate, the more users in a system,
the less average transmitted sum-power is required. The features of IDMA distinguished from
the other MA techniques must be considered in MAC design for IDMA based networks. IDMA
involves dynamic power control to improve link capacity and guarantee QoS for users. [18]
3.4. IDMA Transmitter and Receiver
3.4.1. Transmitter
The upper part of Figure 3.1 demonstrates the transmitter structure of the IDMA scheme under
consideration with K simultaneous users. The input data sequence deck of user-k is encoded
based on a low-rate code C, generating a coded sequence: [5]
Where J is the frame length.
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The elements are referred to as coded bits which are then permutated by an interleaver , thus,
producing:
Following the CDMA convention, the element in xk will be denoted as chips. Users are solely
distinguished by their interleavers, hence the name interleave division multiple access (IDMA)
scheme. [5]
The key principle of IDMA is that the interleavers {k}, opted for user separation and should be
orthogonal for all the users. It is assumed that the interleavers are generated independently and
randomly. The randomly generated interleavers disperse the coded sequences so that the adjacent
chips are approximately uncorrelated, facilitating the simple chip-by-chip detection scheme as
discussed below. [5]
Figure 3.2. IDMA Transmitter and Receiver structure
Assuming that the channel with no memory and after chip matched filtering, the received signal
from K users can be written as:
Where hk is the channel coefficient for user-k and {n (j)} are samples of an AWGN process with
zero mean and variance, assuming that the channel coefficient {hk} are known a
priori at the receiver. Due to the use of random interleaver {k}, the PSE operation can be carried
out in a chip-by-chip manner, with only one sample used at a time. [5]
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3.4.1. Receiver
Adopting an iterative sub-optimal receiver structure, consisted of the primary signal estimator
(PSE) and K single user a posteriori probability (APP) decoders (DECs), the data is iterated for
pre-decided number iterations before finally taking hard decision on it. For single path
propagation, there is only one path for the transmission. The multiple access and coding
constraints are considered separately in the PSE and DECs. The outputs of the PSE and DECs
are extrinsic log-likelihood ratios (LLRs) about {xk(j)} defined below as;
Those LLRs are further distinguished by subscripts, i.e., ePSE (xk(j)) and eDEC (xk(j)), depending
on whether they are generated by the PSE or DECs.
For the PSE section, y in the above given equation denotes the received channel output while for
the DECs, y in the same equation is formed by the de-interleaved version of the outputs of the
primary signal estimator (PSE) block. A global turbo type iterative process is then applied to
process the LLRs generated by the PSE and DECs blocks. [5]
3.5. Features of IDMA
3.5.1. Flexible Rate adaptation
The multi-code technique can be used for a rate/power adaptation as proposed in. A large variety
of data rates can be supported. As opposed to conventional adaptive modulation/channel coding
techniques, the modulation scheme is fixed (and even binary) and the same channel code is used
for all layers. Power adaptation/savings are particularly useful for the uplink. [7]
3.5.2. Soft-information
The mentioned receiver inherently delivers reliable soft-output information, which is useful for
rate adaptation and cross-layer optimization. [7]
3.5.3. Resource allocation
Resource allocation is greatly simplified since the same interleaver set is used at all times. [7]
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3.5.4. Low delay
Due to chip-by-chip interleaving, the block size can optionally be reduced compared to
conventional DSCDMA (which employs symbol-by-symbol interleaving), because the
interleaver length is increased by the spreading factor. [7]
3.5.5. Scalable Bandwidth
For reasons of scalability and ease of implementation we propose to divide the available
bandwidth. Since the frequency bins allocated to 4G systems are not known yet, we suppose to
divide the 40 MHz into multiples of 5 MHz. That could be 220 MHz but also an
inhomogeneous allocation. Following this proposal, the available frequency bins need not to be
contiguous. Even dynamic bandwidth allocation may be considered. [7]
3.5.6. Low Complexity Receiver
In conjunction with IDMA, a possible low-complexity receiver is the simplified version of the
Wang & Poor receiver. The task of this receiver is to cancel any type of interference (multilayer
interference, multiuser interference, multi-antenna interference, inter-symbol interference, etc.)
jointly. The receiver is based on the Gaussian assumption and turbo processing in conjunction
with the low-rate encoder. Its complexity is only linear with respect to the number of layers,
number of chips/layer, number of users, number of receive antennas, number of channel taps,
and the number of iterations. [7]
3.5.7. Quality of Service
The quality of service (QoS) is mainly defined by a maximum bit error rate, a minimum data
rate, and a maximum delay (especially for packet based services). These parameters are highly
dependent on the application, e.g. text message, voice transmission or video transmission.
IDMA-based systems can be made highly adaptive in order to guarantee a certain QoS level.
Hence, we do not seek quasi error-free transmission, but apply the mentioned soft link adaption
strategy to guarantee a certain bit error rate for a layer or group of layers allocated to a user or
application. On the other hand, we keep the transmission power as low as possible for longer
battery life and less emitted radiation. [7]
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The bit error rate that can be tolerated is application-dependent, e.g. voice transmission
allows higher bit error rates than data transmission. Instead of using adaptive modulation
and/or channel coding, in IDMA the number of layers and the transmission power are
modified to meet this requirement. The number of layers used for transmission can be
reduced if the data rate is higher than needed or, if the data rate cannot be reduced for
QoS reasons, the transmit power can be increased until the target BER is achieved. [7]
The data rate is an essential QoS parameter, for example text messaging services need
much lower data rates than video transmission. The data rate is adapted in a similar way
as the target BER is. With a higher number of layers assigned to a user, its data rate is
higher. To ensure a certain BER the power can be adapted as well. [7]
In some applications, e.g. real-time speech transmission, a large delay is very
inconvenient, in other applications even critical, e.g. packet loss in TCP based networks.
To achieve small delays, the block length for IDMA transmission can be chosen to be
quite small. This is possible because the chip-by-chip interleaving is done. [7]
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3.6. IDMA Uplink vs. Downlink
IDMA Uplink features numerous benefits such as security, low receiver cost, cross cell
interference mitigation, decentralized control, diversity against fading, high spectral efficiency,
high power efficiency, suitability for wide and narrowband transmission, and higher gain. The
general methods such as TDMA FDMA and CDMA cant provide all these features whereas
IDMA can fulfill all these necessities and it is somehow suitable for the newly developed
wireless systems in favor of uplink. [9]
On the other hand, while a downlink IDMA system is, in many respects, similar to the uplink
system, such as at the transmitter, the signals for different users are interleaved by user-specific
interleavers and transmitted over a common broadcast channel. However, unlike the uplink
where a common MUD is shared by all users, an individual MUD is required for each user in the
downlink. Therefore, the MUD cost can be a serious concern here. [9]
Nevertheless, significant multiuser gain is also achievable in the downlink. This can be proved
using the duality principle and has been confirmed by simulation. The gain is quite significant, it
may justify the use of MUD in the downlink even at the cost of increased complexity, at least for
a small K (for which the cost increase is moderate). [9]
Figure 3.3. Downlink structure of an IDMA/CDMA scheme [27]
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3.7. Drawbacks of TDMA FDMA & CDMA:
3.7.1. FDMA
FDMA, or frequency division multiple access, allows users to access a single channel, through a
shared frequency; this system is advantageous as it is run through a satellite and offers users the
chance to share a channel easily without time delays. FDMA are strictly sub optimal in fading
environments and they can be seriously inferior in MIMO channel. The disadvantage of FDMA
is the expense of running the system, which requires costly, custom filters and other technical
equipment. [8]
3.7.2. TDMA
A disadvantage of TDMA systems is that they create interference at a frequency which is
directly connected to the time slot length. This is the buzz which can sometimes be heard if a
TDMA phone is left next to a radio or speakers. Another disadvantage is that the "dead time"
between time slots limits the potential bandwidth of a TDMA channel. These are implemented in
part because of the difficulty in ensuring that different terminals transmit at exactly the times
required.
3.7.3. CDMA
CDMA is also known as code division multiple access, and it allows users to share a frequency
through a special technique known as spread spectrum. The disadvantage of CDMA is that the
codes assigned to each user can only be utilized by those people. As the number of users
increases, the overall quality of service decreases Self-jamming Near- Far- problem arises [8]
3.8. Applications of IDMA
3.8.1. Ultra Wideband (UWB) and Sensor Systems
Ultra-Wideband (UWB) is a technology for transmitting information spread over a large
bandwidth that should, in theory and under the right circumstances, be able to share spectrum
with other users. Federal Communications Commission (FCC) authorizes the unlicensed use of
UWB in 3.110.6 GHz. Ultra Wideband was traditionally accepted as impulse radio, but the
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21
FCC and ITU-R now define UWB in terms of a transmission from an antenna for which the
emitted signal bandwidth exceeds the lesser of 500 MHz or 20% bandwidth. [9]
Each pulse in a pulse-based UWB system occupies the entire UWB bandwidth, thus reaping the
benefits of relative immunity to multipath fading (but not to inter-symbol interference), unlike
carrier-based systems that are subject to both deep fades and inter-symbol interference. A
significant difference between traditional radio transmissions and UWB radio transmissions is
that traditional transmissions transmit information by varying the power/frequency/and or phase
in distinct and controlled frequencies while UWB transmissions transmit information by
generating radio energy at specific times with a broad frequency range. [9]
Due to the extremely low emission levels, UWB systems tend to be short-range. However, due to
the short duration of the UWB pulses, extremely high data rates are possible, and data rate can be
readily traded for range by simply scaling the number of pulses per data bit. However, simple
and effective techniques for combating frequency-selective fading and MAI still need to be
developed. [9]
3.8.2. Relay and Ad Hoc Networks
An interesting concept related to IDMA is described in to separate different replicas of a
common signal that arrive at a destination through different relays. Suppose that the signal from
a transmitter is randomly delayed before transmission and its replicas experience different delay
factors through different transmission paths. If the delay difference among these paths is
relatively small, then Rayleigh fading may result. [9]
However, if the delay difference is sufficiently large, these replicas may look as if they are
produced using different interleavers. (Note: The delayed version of a random interleaver is
almost random to itself.) Using this principle, it is shown in that random delay can be
deliberately introduced at the relay nodes to avoid Rayleigh fading and to facilitate IDMA-type
detection at the destination. [9]
This provides an efficient way to exploit the diversity provided by different transmission paths.
If IDMA is used in ad hoc networks, not all receivers will probably afford the full complexity of
MUD. Furthermore, not all signals, which are simultaneously transmitted, are necessary to be
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detected. Then, in addition to desired signals, only a few strong interferers may be important to
be detected and canceled. In such scenarios, our strategy may be found useful since, as we will
see, the complexity can be signicantly reduced while achieving graceful performance
degradation. [9]
3.8.2. Optical Networks
Interleave Division Multiple Access (IDMA) is a recently proposed multiple access scheme
which relies on an iterative multiuser detection. With the increasing number of users it is
required to get the higher transmission capacity to support the projected growth in traffic levels,
and the exponential use of the Internet together with an increase in the number and range of new
services. [9]
All optical fiber networking is considered to be the central solution for higher capacity. The huge
inherent bandwidth of single mode optical fiber has already been one of the major transmission
media for long distance Telecommunication with very low losses. To fully utilize the single
mode optical fiber bandwidth, optical multiplexing techniques have been deployed. There are
three multiplexing alternatives: wavelength division multiple access (WDMA), optical time
division multiple access (OTDMA) and optical code division multiple access (OCDMA). [9]
The need of faster and more reliable communication systems has been felt these last years and
the sharing of the huge optical bandwidth between users need appropriate access techniques. In
order to meet these requirements, Optical IDMA (OIDMA) presents an attractive solution. This
scheme inherits many advantages such as flexibility of asynchronous and decentralized
networking, potentially secure and uncongested high-rate data transmission, total bandwidth
utilization by all network users, both high rate and low rate transmission achieved, reduced
multiple access interference (MAI), better bit error rate (BER). [9]
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23
CHAPTER 4
CODES & INTERLEAVERS
4.1. Orthogonal Codes
4.1.1. Walsh Codes
The Walsh matrix was proposed by Joseph L Walsh in 1923. Each row of a Walsh matrix
corresponds to a Walsh function. Walsh codes have the advantage to be orthogonal, in this way
we should get rid of any interference under perfect synchronization. Orthogonal codes are easily
generated by starting with a seed of 0, repeating the 0 horizontally and vertically, and then
complementing the 1 diagonally. This process is to be continued with the newly generated block
until the desired codes with the proper length are generated. Sequences created in this manner are
referred as Walsh code. [26]
The Walsh code is used to differentiate the user in the forward CDMA link. In any given sector,
each forward code channel is assigned a distinct Walsh code. In mathematics, a Walsh matrix is
a specific square matrix, with dimension a power of 2, the entries of which are +1 or -1, and the
property that the dot product of any two distinct rows is zero. [26]
4.1.2. Orthogonal Variable Spreading Factor (OVSF):
With the advancement in the cellular technology and convergence of wireless technologies, now
it is the need to combine two messages having different data rates in an orthogonal manner. Take
an example, the date rate of user 1 is r1 and of user 2 is r2 and we have to spread the user 1
message by spreading factor s1 and that of user 2 by s2, so that we can produce and overall chip
rate of . We can use Walsh-Hadamard sequences if the spreading factors are powers of 2. The
result so obtained is referred to as Orthogonal Variable Spreading factor. For OVSF the
orthogonality requirement can be stated mathematically as:
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24
That is, code 1 of duration T1 is orthogonal to all subsequences of code 2, of the same length, and
offset by a multiple of T1, the length of code 1. [20]
4.1.3. Importance of Orthogonality:
Orthogonal codes and orthogonal signals are used frequently today in the communications
industry. They range from a simple sine/cosine quadrature signals to multiple signals whose
inner product is equal to zero. Orthogonal signals can be used for many other applications.
Quadrature signals can be used to transmit and reception of separate information channels on
each orthogonal signal with minute interference between them. [25]
Orthogonality can also be used and can be applicable to polarization in an antenna system. Two
signals can be sent on separate polarizations or two parallel channels can be used with the same
frequency for better data rates. Orthogonal principles are also used to differentiate desired signals
from jammers using a Gram Schmidt Orthogonalizer (GSO). Another application for orthogonal
signals is to prevent adjacent channel interference. [25]
4.2. Channel Codes:
Channel coding deals with error control techniques. If the data at the output of a communications
system has errors that are too frequent for the desired use, the errors can often be reduced by the
use of a number of techniques. Coding permits an increased pace of information transfer at a fixed
error rate, or a reduced error rate for a fixed transfer rate. The two primary methods of error control
are: Automatic Repeat Request (ARQ) when a receiver circuit detects errors in a block of data, it
requests that the data is retransmitted. Forward Error Correction (FEC) the transmitted data is
encoded so that the data can correct as well as detect errors caused by channel noise. [10]
4.2.1. Convolutional Coding:
Convolutional Codes the coded sequence of n bits depends not only on the present k information
bits, but also on the previous information bits. The primary objective of coding is that the
decoder can determine if the received word is a valid code word, or if it is a code word which has
been corrupted by noise (i.e. detect one or more errors). Ideally the decoder should be able to
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25
decide which code word was sent even if the transmitted code word was corrupted by noise (i.e.
error correction). [11]
If a convolutional code that produces r parity bits per window and slides the window forward by
one bit at a time, its rate (when calculated over long messages) is 1/r. The greater the value of r,
the higher the resilience of bit errors, but the trade-off is that a proportionally higher amount of
communication bandwidth is devoted to coding overhead. In practice, we would like to pick r
and the constraint length to be as low as possible. [11]
Figure 4.1. Rate 1/3 non-recursive, non-systematic convolutional encoder
with constraint length 3. (Public domain image.)
4.3. Introduction to Interleaving
Interleaving has been frequently employed in digital communication and storage systems to
improve the performance of forward error correcting codes. Many communication channels
which are not memory less in nature, errors typically occur in bursts rather than independently. If
the number of errors within a code word exceeds the error-correcting code's capability, it fails to
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26
regain the original code word. Interleaving ameliorates this problem by shuffling source symbols
across several code words, thereby producing a more uniform distribution of errors. [5]
The user-specific interleavers play vital role in the efficiency of IDMA system. It not only
provides de-correlation between adjacent bit sequences as provided in the case of orthodox turbo
coding and decoding, but also facilitates a means for de-correlating various users. The
correlation between interleavers should measure how strongly signals from other users affects
the decoding process of a specific user. The better the interleaver de-correlation, the lesser the
iterations, required for detection in multiuser detection (MUD) mechanism. The de-correlation
between the user- specific interleavers provides a mean to reduce the multiple access interference
(MAI) from other users thus helping in the intersection of the detection process. [5] [15]
A set of interleaved is considered to be practical if it is easy to generate, and no two interleaved
in the set collide. The sender and receiver need not store or communicate many bits in order to
agree upon an interleaving sequence. It may be shown that a properly defined correlation
between interleavers can be used to develop a collision criterion, where zero cross-correlation
(i.e., Orthogonality) implies no collision. [5]
In case of IDMA systems, the transmitter is required to transmit the interleave matrix consisting
of the interleaving pattern along with spread data related to users, to the receiver. So, greater the
size of the interleaver, the more bandwidth and resources are consumed during transmission.
Also, it is worth to be mentioned that greater the size of interleaver, more the orthogonality is
achieved amongst interleave. [5]
For better understanding of interleaving mechanism, in the next section, interleaving process will
be discussed. [5]
4.3.1. Types of Interleavers:
1. Block interleavers
2. Random Interleavers
3. S- Interleavers
4. Pseudorandom Interleavers
5. Takeshita-Costello interleavers
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27
6. Block random interleavers
7. Optimal interleavers
4.3.1.1. Block Interleavers:
In communication system block interleavers are the most commonly used interleavers. It write in
column wise from top to bottom and left to right and reads out row wise from left to right and top
to bottom. [3]
4.3.1.2. Random Interleavers:
The Random Interleaver rearranges the elements of its input vector using a random permutation.
The incoming data is rearranged using a series of generated permuter indices. A permuter is
essentially a device that generates pseudo-random permutation of given memory addresses. The
data is arranged according to the pseudo-random order of memory addresses. [12]
Figure 4.2. Random interleaving [12]
The de-interleaver must know the permuter-indices exactly in the same order as that of the
interleaver. The de-interleaver arranges the interleaved data back to the original state by knowing
the permuter-indices. The length input sequence assumed to be L. [12]
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28
4.3.1.3. S - Interleavers:
The S interleaver is a random type interleaver. However the design of this interleaver is difficult
because of the complex computations. And unlike the pure random interleaver, by construction a
minimum interleaving distance equal with S is forced. [3]
4.3.1.4. Optimal Interleaver:
The interleaver that produces the fewest output coded sequences with low weights is known as
optimal interleavers. The design of optimal interleaver is tedious and exhaustive. [3]
4.3.1.5. Takeshita-Costello Interleavers:
The Takeshita-Costello interleaver takes the block length to be a power of 2.
4.3.1.6. Pseudo-Random Interleavers:
The pseudo random interleaver has a controlled spreading of bits. This is the high performance
interleaver which combines the advantages of random and block interleavers, i-e it presents a good
spreading at large minimum distances. [3]
4.3.1.7. Block Random Interleavers:
This interleaver is an alternative to S-Interleaver and aims to continue the qualities of the block
interleavers and random interleavers. [3]
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CHAPTER 5
ORTHOGONAL INTERLEAVERS
5.1. Problem Statement
In the IDMA scheme, we use a spreading code to encode the data, followed by chip-level
interleavers to differentiate between different users. This data can be decoded relatively easily at
the receiver end with the help of an iterative chip-by-chip decoder. Interleaving allows the data
to be sent over a multiple access channel such that different users can gain access to their
intended receiver, as well as providing forward error correction which allows the channel
capacity to be increased. However, these random interleavers may have high correlation, thus it
is necessary to design an interleaving scheme that prevents this from occurring. [9] [13] [14]
5.2. Proposed Solution
We propose a solution to this problem by introducing an alternative scheme for interleaving that
has lower correlation and high spectral efficiency. This alternative scheme is based on the
concept of orthogonality, by having random interleavers maintain orthogonality between each
other as it is the most commonly used interleaving scheme. Random interleavers also provide a
higher level of security. This orthogonality is achieved by having the interleavers be based on
Walsh Codes matrices, which are also the most commonly used orthogonal codes.
5.3. Algorithm
We term this alternative interleaving scheme Orthogonal Interleaving. We interleave the data
(from the Encoder), such that it resembles the orthogonal Walsh codes and get a random
permutations code for the bit positions. This code allows us to de-interleave the data at the
receiving end. This allows for little to zero correlation between the interleaver codes.
We can change the size of the interleavers by changing the size of the Walsh matrix. For
instance, if we take a 128 by 128 Walsh matrix, we can accommodate 127 users by allocating a
Walsh sequence to each user. (Note: we ignore the first row of the Walsh Matrix as it is an all-
zero sequence.)
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30
We describe the algorithm as follows:
Generate a Walsh Matrix for the interleaving sequences. (In this case, we take a 128 x
128 matrix).
We estimate the number of 1s and number of 0s in the input data sequence we get from
the Encoder.
Each bit in the data sequence is compared with a given Walsh sequence from left-to-
right, such that the first position in the Walsh sequence that equals the input data is
allocated to that position.
The allocated positions are saved in a separate matrix called Scramble Rule.
If the number of 1s in the input sequence exceed that of the Walsh matrix, we allocate the
remaining ones to the extra 0s after all the 0 data bits have been allocated.
If the number of 0s in the input sequence exceed that of the Walsh matrix, we allocate the
remaining zeros to the extra 1s, after all the 1 data bits have been allocated.
This process is repeated for every user.
At the receiving end, the reverse process is applied to estimate the input data sequence
with the help of a chip-by-chip (CBC) iterative detector or elementary signal estimator
(ESE).
This is followed by the Decoder (DEC) which despreads the data, and sends an
estimation back to the ESE to estimate the original data signal.
Figure 5.1. Orthogonal Interleaving
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31
5.4. Advantages
1. The algorithm for establishing such an interleaving scheme is relatively simple to design.
2. Such an algorithm does not require large memory spaces to store the data.
3. This sort of algorithm is fast and simple as it is cost-effective.
5.5. Drawbacks
The one major drawback of this technique is that the number of users supported by the Walsh
matrix is limited. However, as in CDMA schemes, we can reuse the allocated codes in different
cells to increase spectral efficiency.
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CHAPTER 6
Simulation Results
6.1. Simulation
These simulation have been executed on MATLAB R2009a ver. 7.8.0.347 software. We have
simulated two systems, one using random interleavers and one using our proposed orthogonal
interleavers and calculated both their correlation and BER. The results are shown below:
6.2. Results
6.2.1. Random Interleavers
The autocorrelation of the first random interleaver in a randomly interleaved IDMA system can
be seen below:
Figure 6.1. Autocorrelation of the first random interleaver
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33
The next result is shown in Figure 6.2. of the first five random interleavers being cross-correlated
with the first random interleaver.
Figure 6.2. Correlation of 1st random interleaver with the first five interleavers
If we focus on the colored lines, we can see that there is some extent of correlation that exists in
the random interleavers. The graph on the next page shows the BER of the randomly interleaved
system:
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34
Figure 6.3. BER of the system implementing random interleavers
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35
6.2.2. Orthogonal Interleavers
Here we introduce orthogonal interleavers into the system in order to lower the correlation
between the users. The simulation results of the auto-correlation of the orthogonal interleavers
are shown below:
Figure 6.4. Autocorrelation of the 1st orthogonal interleaver
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36
Figure 6.4. Correlation of the 1st orthogonal interleaver with the first five interleavers
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37
Figure 6.6. BER of the system implementing orthogonal interleavers
6.3. Conclusions
IDMA conventionally utilizes fixed random permutations to interleave the data. This creates a
higher correlation among the users. In our thesis, we proposed an interleaver that has reduced
correlation and simulated the results.
The results obtained showed that the correlation is reduced significantly. The values of the
random interleaver correlation are very high. Comparatively, a reduction is observed with the use
of the algorithm for orthogonal interleavers.
6.4. Future Work
Further work is intended to reduce this minimum correlation to zero as is standard for orthogonal
codes and sequences. Further changes can be made in the Walsh matrix size and the number of
interleavers used in the process.
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References
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[3] John M. Cioffi, Code Concatenation and Advanced Codes, Digital Communications.
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[4] KusumeK, IDMA vs. CDMA: Analysis and Comparison of Two Multiple Access Schemes [Online] Available from: http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=6092790&url=http%3A%2F%2Fi
eeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D6092790 [Accessed on: 24 Jan 2014]
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Technology, Dehradun 248001, India
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Uplink Proposal Based on Interleave-Division Multiple Access Faculty of Engineering,
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[8] Lou Frenzel, Fundamentals of Communications Access Technologies: FDMA, TDMA,
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[10] Dr. Aoife Moloney, Channel Coding [Online]. Available from:
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[16] Performance Evaluation of IDMA Scheme in Wireless Communication, Thesis Submitted
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Appendix: Simulation Code
clear all; close all;
%% Initialization
clc; %clear screen N = 8; %length of data User_num = 5; %number of users SF = 16; %spreading factor A = 1; ChipLen = N*SF; %length of chip D_num = 5; % SNR = -20:5:20; Num = length(SNR); h = ones(1,User_num); count = 100; %error accuracy iterations Blocklength = ChipLen; m_length = Blocklength; interleaver_num = 1; spread_seq = ones(1,ChipLen);
b = zeros(User_num,N); l_ESE = zeros(User_num,ChipLen); E_rj = zeros(1,ChipLen); Var_rj = zeros(1,ChipLen); ScrambleRule = zeros(User_num,Blocklength); d = zeros(User_num,N); dd = zeros(User_num,N); a = zeros(SF,N); c = zeros(User_num,Blocklength); x = zeros(User_num,Blocklength); rnd_noise = zeros(User_num,Blocklength); E_Xkj = zeros(User_num,Blocklength); Var_Xkj = zeros(User_num,Blocklength);
%% Generation of spreading sequence for i=1:ChipLen if (mod(i,2))==0 spread_seq(i)=-spread_seq(i); end end
for i=1:SF spread_seq_temp(i)=spread_seq(i); end
%% Simulation for interleaver=1:interleaver_num
for x_num=1:Num var1=SNR(x_num);
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43
snr=(10^(var1/10))/SF N0=A*A/(2*snr); sigma=sqrt(N0); var=sigma*sigma;
%Error error_total=0; for j=1:count d=sign(randn(User_num,N)); dd=(d+A)/2;
%% Spreading for o = 1:User_num c(o,:) = spread(dd(o,:),SF); end
cc = xor(1,c) - c;
%% Interleaving for o = 1:User_num [x(o,:),ScrambleRule(o,:)]=intrlv3(c(o,:),(o*2)); end
x = xor(x,1) - x; c = cc;
%% Noise noise=randn(1,ChipLen); rnd_noise=sigma*noise;
%% Multiple Access Channel r=zeros(1,ChipLen); for i=1:User_num r=r+x(i,:); end r=r+rnd_noise;
%% ESE
for i=1:ChipLen TotalMean(i)=0; TotalVar(i)=var; end
for nuser=1:User_num for i=1:ChipLen Mean(nuser,i)=0; Var(nuser,i)=1; TotalVar(i)= TotalVar(i)+1; end end
for it=1:D_num for nuser=1:User_num
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44
% LLR values for the de-interleaved chip sequence for i=1:ChipLen TotalMean(i)=TotalMean(i)-Mean(nuser,i); TotalVar(i)=TotalVar(i)-Var(nuser,i); e_ESE_Xkj(nuser,ScrambleRule(nuser,i))=2*(r(i)-
TotalMean(i))/ TotalVar(i);
end
%Decoder (DEC) for l=1:N L_bkj(nuser,l)=0; for k=1+(l-1)*SF:SF*l
L_bkj(nuser,l)=L_bkj(nuser,l)+e_ESE_Xkj(nuser,k)*spread_seq(k); end end
L_bkj_=spread_seq_temp'*L_bkj(nuser,:); a1=L_bkj_(:); L_bkj_back(nuser,:)=a1';
e_dec_ckj=L_bkj_back-e_ESE_Xkj;
for i=1:Blocklength
l_ESE(nuser,i)=e_dec_ckj(nuser,ScrambleRule(nuser,i)); end
for i=1:ChipLen Mean(nuser,i)=tanh(l_ESE(nuser,i)/2); Var(nuser,i)=1-Mean(nuser,i)*Mean(nuser,i); TotalMean(i)=TotalMean(i)+Mean(nuser,i); TotalVar(i)= TotalVar(i)+Var(nuser,i); end end end
L_bkj = L_bkj*(-1); b=(1+sign(L_bkj))/2;
error=xor(b,dd); error=error'; error_num=sum(error); error_num=error_num'; error_num=sum(error_num); error_total=error_total+error_num; end error_percentage(interleaver,x_num)=error_total; end
x = (x + 1)/2;
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45
for o = 1:User_num [check(o,:),lags(o,:)] = xcorr(x(1,:),x(o,:)); end
figure(1),plot(lags(1,:),check(1,:),lags(2,:),check(2,:),lags(3,:),check(3,:)
,lags(4,:),check(4,:),lags(5,:),check(5,:)),grid; legend('1st Interleaver', '2nd Interleaver', '3rd Interleaver', '4th
Interleaver', '5th Interleaver');
end
%% BER error_percentage=error_percentage/(N*User_num*count);
figure(2) semilogy(SNR,error_percentage(1,:),'-db') axis([-20 6 0 1]) grid on xlabel('Eb/No /dB'); ylabel('BER'); title('BER OF the SYSTEM using Orthogonal Interleavers');
Additional user-defined functions:
1. intrlv3.m:
function [interleave,key,offset] = intrlv3(hopped_sig,n)
m = length(hopped_sig);
w = walsh(m); interleave = w(n,:); key = zeros(1,length(interleave)); inv_hopped_sig = xor(hopped_sig,1); marker_0 = 0; marker_1 = 0; marker_1_off = 0; marker_0_off = 0; off_m = 0;
offset = sum(hopped_sig)-(length(hopped_sig)/2); n1 = (length(hopped_sig)/2) + offset; n0 = -((length(hopped_sig)/2) - offset);
for k=1:length(interleave) if hopped_sig(1,k) == 0 if offset 0 marker = offmarker(interleave,n0,n1,offset,marker_1,1,off_m); else
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marker = marker_1_off; end
off_m = marker; h = inv_hopped_sig(1,k);
else marker = marker_0; h = hopped_sig(1,k); end else if offset >= n1 if n0 < 0 marker = offmarker(interleave,n1,n0,offset,marker_0,0,off_m); else marker = marker_0_off; end
off_m = marker; h = inv_hopped_sig(1,k); else marker = marker_1; h = hopped_sig(1,k); end end
for j=marker+1:length(interleave) if h == interleave(1,j); key(1,k) = j;
if h == 0 if hopped_sig(1,k) == 0 marker_0 = j; n0 = n0 + 1;
if n1>=offset && n0==0 marker_0_off = j; off_m = j; % end else marker_0_off = j; off_m = j; % n1 = n1 - 1; end else if hopped_sig(1,k) == 1 marker_1 = j; n1 = n1 - 1;
if n0
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off_m = j; % n0 = n0 + 1; end end break
else continue end end end end
2. offmarker.m
function [m] = offmarker(interleave,n0,n1,offset,marker_1,n,off_m)
count = 0;
if offset == n0 off_m = marker_1; end
for l = off_m+1:length(interleave) if offset == n0 if interleave(1,l) == n count = count + 1;
if count == abs(n1) m = l; break end end else m = off_m; end end end
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3. spread.m
function [spread_sig]=spread(hopped_sig,s)
m = length(hopped_sig); spread_sig = zeros(m,s); spread_seq = zeros(1,s);
for k=1:s if mod(k,2) == 1 spread_seq(k) = 0; else spread_seq(k) = 1; end end
for i = 1:m spread_sig(i,:) = xor(hopped_sig(i),spread_seq); end
spread_sig = reshape(spread_sig',1,m*s); end
4. walsh.m
function [w] = walsh(n)
if mod(n,2)~= 0 disp('Incorrect matrix parameters. Enter an even number.'); return else
w=0;
for k = 1:log2(n); i = xor(w,1); w = [w w; w i]; end end