blind channel shortening for mimo-ofdm system using zero padding and eigen decomposition approach

8/12/2019 Blind Channel Shortening for MIMO-OFDM System Using Zero Padding and Eigen Decomposition Approach

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I JSRD - I nternational Jour nal for Scientifi c Research & Development| Vol. 1, I ssue 7, 2013 | ISSN (onli ne): 2321-0613

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Abstract — This paper deals with multiple-input multiple-output (MIMO) broadband wireless communicationsystems, employing orthogonal frequency-divisionmultiplexing (OFDM). In order to exploit the benets ofOFDM in highly frequency-selective channels, without anysignicant increase in receiver complexity, a channelshortening prelter is inserted at the receiver. The main aimof inserting channel shorteners is to shorten the channel sothat the main energy of the composite channel isconcentrated within a duration smaller than the guardinterval inserted while transmission. Thus by includingchannel shortening equalizers at the receiver the intersymbol interference or the inter block interference can besuppressed. The new approach proposed in this thesis is zero

padding approach with Eigen decomposition approach. Theadvantages of the proposed approaches include immunity todelay spread, resistance to frequency selective fading andsimple equalization. This shortening design is a blind one,i.e., a priori knowledge of the MIMO channel impulseresponse to be shortened is not required, and can be carriedout in closed-form.

Keywords: Blind channel shortening, cyclic prefix, multipleinput multiple output systems, orthogonal frequencydivision multiplexing, space time frequency block coding,zero padding.

I. INTRODUCTION

With the recent advances in wireless communication a greatleap in communication system was observed. Instead of asingle carrier in the system multiple sub-carriers areimplemented to make the process easier. In single carriertransmission schemes, one frequency carrier is used totransmit or receive information. Data or information will betransmitted serially on the channel at low data rate. Highdata rate is creating a problem of ISI in single carrierschemes [1]. In order to support the symbol rate Rs, the

minimum required bandwidth is the Nyquist bandwidth (Rs/2 Hz) [2]. It means that wider bandwidth is required tosupport a higher data rate in a single-carrier transmission.When the signal bandwidth becomes larger than thecoherence bandwidth in the wireless channel, the linksuffers from multi-path fading, incurring the inter-symbolinterference (ISI) [4].In general, adaptive equalizers are employed to deal with theISI created by the time-varying multi-path fading channel.Furthermore, the complexity of an equalizer increases withthe data rate, modulation order and the number of multi-

paths. In conclusion, a high data rate single-carriertransmission may not be practically possible due to too

much complexity of the equalizer in the receiver. Simple flatfading channel is used in single carrier transmissionschemes therefore guard interval and guard band are not

required. Due to drawbacks of single carrier system,multicarrier transmission system is used in Next generationcommunication system. In frequency-selective channels, theuse of multiple input multiple output (MIMO) systems incombination with orthogonal frequency-divisionmultiplexing (OFDM) is an efficient approach to supportreliable transmission at high data rates.

Many non-blind channel-shortening algorithms have been proposed for single input single output (SISO) OFDMsystems, [8] – [13] some of which have also been extendedto MIMO channels [13] – [15]. These techniques, which arenon-blind channel shortening require a priori knowledge ofthe impulse responses of the channels to be shortened,which can be obtained via the transmission of trainingsequences. The amount of training to be used increases withorder of MIMO finite- impulse response (FIR) channelwhich, for highly dispersive channels, leads to considerablewaste of resources. Furthermore, in the MIMO case, channelestimation is significantly more complicated than in theSISO one. A viable alternative is to shorten the channel in

blind mode, by deriving the parameters of the channel-shortening prefilter directly from the received data, without

performing any explicit channel-estimation procedure. Blind

FIR channel-shortening techniques for SISO - OFDMsystems have been developed in [4]–[7], some of whichhave been generalized [7], [8] to MIMO-OFDM systems.The challenge of any channel shortening algorithm is tosupress the inter symbol interference to maximum extendsuch that the received information at the receiver will beexactly same as that of the transmitted information.This paper is organized as follows: Section II describes theMIMO-OFDM System model. Section III describes thechannel shortening method. Section IV presents the different

blind channel shortening algorithms such as cyclic prefix,zero-padding and Eigen decomposition. Section V gives theexperimental results and discussions, followed by

concluding remarks in Section VI.

II. MIMO-OFDM SYSTEM MODEL

A. Orthogonal Frequency Division MultiplexingOrthogonal Frequency Division Multiplexing (OFDM)system uses the guard interval (GI) to combat the intersymbol interference (ISI) and the Inter Carrier Interference(ICI). The presence of the GI and Fourier transform inOFDM system ensures a low equalization complexitycompared to single carrier systems. For this reason, manydigital communication standards adopt OFDM system suchthat DVB, DAB, ADSL, etc. In OFDM system, the GI

length must be higher than the channel size; otherwise, theISI and ICI persist. To preserve a high effective flow and toeliminate the ICI and ISI, we must reduce the channel length

Blind Channel Shortening for MIMO-OFDM System Using ZeroPadding and Eigen Decomposition Approach

Aksa Mini Sabu 1

1M. Tech 1Communication Engineering1KMEA Engineering College



Blind Channel Shortening for MIMO-OFDM System Using Zero Padding and Eigen Decomposition Approach(IJSRD/Vol. 1/Issue 7/2013/0001)


by using channel shortening techniques.In this technique, Frequency band is divided into number ofsubcarriers. These subcarriers are orthogonal to each other.The basic principle of OFDM is to split high-rate datastream into number of lower rate streams that aretransmitted simultaneously over a number of subcarriers.Because the symbol duration increases for the lower rate

parallel subcarriers, the relative amount of dispersion in timecaused by multipath delay spread is decreased. Inter-symbolinterference is eliminated by using guard time in OFDMsymbol. In OFDM system design, a number of parametersare used such as subcarrier, guard time, symbol duration,subcarrier spacing, modulation type and error correctingcode. The choice of parameters depends on bit rate,

bandwidth, and delay.The three main component of OFDM system are as follows:

1. Main component of OFDM is FFT/ IFFT witchmodulates a block of input QAM values onto anumber of subcarriers. In the receiver, subcarriersare demodulated by FFT, which perform reverse

operation of IFFT. In practice, IFFT can be made by using FFT. Therefore same hardware will beused for the both which reduces the complexity ofcommunication system.

2. Important feature of OFDM system is coding andinterleaving. Some successive subcarriers in theOFDM system may suffer from deep fading, inwhich the received SNR is below the required SNRlevel. In order to deal with the burst symbol errors,it may be essential to use of FEC (Forward ErrorCorrection) codes.. There are two types ofinterleaving: block interleaving and convolutioninterleaving. Bit-wise, data symbol-wise, or OFDM

symbol-wise interleaving can be used for blockinterleaving. Interleaving type and size must bedetermined by the type of FEC code, degree offrequency, time fading and delay due tointerleaving.

3. Key principle is the introduction of a cyclic prefixand zero padding as a Guard Interval to reduceinterference between the symbols.

B. MIMO SystemIn MIMO transmission, if antennas are well separated, thesignals at different antennas experience independent fadingin a dispersal environment. Consider T transmits antennas

and R receives antennas as shown in the Fig 1.

Fig. 1: Block diagram of MIMO system

Let hTR be the channel coefficient between the Tth transmit

antenna and Rth receive antenna. Let X = [X1 X2 … XT] / be the transmitted data and Y = [Y1 Y2 …. YR]/ be thereceived data, „/‟ stands for transpose operation. In matrix

Form, the relation is given by

R y

y

.

.

1

=

TRT

T

hh

hh

.....

.

.

.....

1

111

T x

x

.

.

1

+

R

.

.

1

(1.1)

C. MIMO - OFDM SystemEquation 2 shows expression for a MIMO-OFDM systemwith T transmit and R receive antennas, the received signalat the k-th sub-carrier of the n-th block from the j -th receiveantenna:

k nwk n xk n H k nY j

T

ii ji j ,,,,

1

(1.2)

for j = 1,…, R and k = 0,…, K - 1, where xi [n; k] is thesymbol transmitted from the i-th transmit antenna at the k-thsubcarrier of the n-th block, Hji [n; k] is the channel‟sfrequency response at the k-th sub-carrier of the n-th block

corresponding to the i-th transmit and the j-th receiveantenna, and, wj [n, k] is additive (complex) Gaussian noise.Block diagram of MIMO OFDM system is shown in Fig 3.The first figure shows the transmitter section and the secondfigure shows the receiver section. In the transmitter section,the modulation section is followed by the fast Fouriertransform which is then followed by insertion of guardinterval which is zero-padding in this experiment.

Fig. 2: System diagram of MIMO OFDM system

III. CHANNEL SHORETENING METHOD

Channel shortening is usually referred to as the technique ofequalization, usually time domain equalization. It can beconsidered as the pre-processing technique that partiallyequalizes the underlying MIMO channel. Non – blindchannel shortening requires priori knowledge of the impulseresponse of the channel which can be obtained by thetransmission of training sequence. But in the case of blindchannel shortening, the parameters of the channel shortening

pre-filter are derived directly from the received data.Channel shortening equalizers are used to shorten thechannel so that the main energy of the composite channel isconcentrated within a duration smaller than the guardinterval inserted while transmission. Thus by including

channel shortening equalizers at the receiver the intersymbol interference or the inter block interference can besuppressed.





Fig. 3: The system diagram with channel shortening at thereceiver

The system diagram with channel shortening at the receiveris given in figure 3 [5]. From the figure it is clear thatdifferent channel shortening algorithms can be applied at thereceiver for the correct reception of the transmitted

information.

IV. DIFFERENT CHANNEL SHORTENING ALGORITHMS

A. Cyclic PrefixThe existing method of blind channel shortening is theCyclic Prefix (CP) OFDM System [1]. Cyclic prefix refersto prefixing of a symbol with a repetition at the end. Thereare two purposes for doing so. The first and foremost

purpose is as a guard interval which can be used to eliminateISI and the second purpose is the channel estimation andequalization. An important fact to be kept in mind while

adding cyclic prefix is that the length of the cyclic prefixmust be equal to the length of the multipath channel.In this method, the CP length is assumed to be insufficientto counteract the multipath channel effects, i.e., Mcp < Lh,where, Mcp is the length of cyclic prefix and Lh is the orderof MIMO finite impulse response (FIR) which is likely tohappen in highly dispersive channels, and, thus, a MIMOchannel shortener is employed to jointly shorten all thechannel impulse responses. The major drawback of theexisting method is its large peak-to-mean power ratio due tothe superposition of all subcarrier signals. This can becomea distortion problem.

B. Eigen DecompositionEigen decomposition approach can be considered as a newlow-complexity method for the design of channel shorteningequalizers. The goal of this method is to minimize the delayspread of the effective channel. Eigen decomposition aims atthe spectral decomposition. The Eigen vectors are the non-zero vectors that when multiplied by the matrix yields avector that differs from the original vector at most by amultiplicative scalar. Eigen vectors and eigen values arenumbers and vectors associated to square matrices, andtogether they provide the eigen decomposition of a matrixwhich analyses the structure of this matrix. Eigen vectorsand eigen values are also referred to as characteristic vectors

and latent roots or characteristic equation (in German,“eigen” means “specific of” or “characteristic of”). The setof eigen values of a matrix is also called its spectrum.

C. Zero PaddingZero padding can be considered as an alternative to cyclic

prefixing. It is done to increase the sampling rates for betterresolution of signals. Zero padding in time domain givesspectral interpolation. Zero padding in frequency domain isdone at the Nyquist rate at N/2 samples because it is thehighest positive frequency and we can maintain spectral

symmetry in doing so. It is mainly done to ensure symbolrecovery regardless of the channel zero locations. ZP-OFDM context, exploits the signal redundancy in the formof guard zeros in the time domain, or null subcarriers in thefrequency domain, or both. As channel shortening mightlead to channels with undesirable frequency selectivity andcoloured noise, applying the generalized eigen filterapproach considerably improve the system performance.

V. EXPERIMENTAL RESULTS

In this experiment, the STFBC-OFDM symbols with zero padding are used to which eigen decomposition is applied atthe receiver. Zero padding at the end of a signal results inthe increase in spectral samples which are samples of trueFourier transform. This provides higher resolution.In the experiment, we evaluated the performance of the

proposed blind channel shortening algorithm. The values ofBER for different SNR values are studied. Theoversampling rate taken in the experiment is four and twoantenna systems are used for transmission and reception.

SNR (dB) BER1 0.18843 0.16065 0.13567 0.1216

9 0.119111 0.116313 0.111815 0.1103

Table. 1: Result of Blind Channel Shortening Using CyclicPrefix

Fig. 4: Average BER with oversampling for cyclic prefix





Fig 4 shows the BER versus SNR graph of STFBC-OFDMsystem using cyclic prefix. The values of BER aredecreasing uniformly as the values of SNR are incremented.But till 15 dB, the BER is never reaching zero .The value ofBER for different SNR is given in the table below.Zero padding at the end of a signal results in the increase inspectral samples which are samples of true Fourier

transform. This provides higher resolution.The table 2 shows the values of BER in the presence ofoversampling. The oversampling rate used in the experimentis four. In this case the BER is decremented more rapidlythan in the previous case. At 15 dB the BER is found to be0.0004 which is far less than that of cyclic prefix approach.The fig 5 shows the values of BER versus SNR in thesystem where oversampling is used.

SNR (dB) BER1 0.14263 0.08165 0.04927 0.02139 0.0101

11 0.004513 0.001215 0.0004

Table. 2: Result of Blind Channel Shortening Using ZeroPadding (With Oversampling)

Fig. 5: BER versus SNR with oversampling

SNR (dB) BER1 0.15133 0.10465 0.05817 0.01239 0.0056

11 0.001113 015 0

Table. 3: Result of Blind Channel Shortening Using ZeroPadding (With Oversampling)

The simulation results of blind channel shortening usingzero padding and eigen decomposition without

oversampling is found to be advantageous as compared tothe design with oversampling. The fig. 6 presents thesimulation result of proposed blind channel shorteningapproach in the absence of oversampling. The values ofBER for various SNR values are given in the table III. Inthis case, the BER is reaching zero at 13 dB and thus the

performance of the proposed approach is found to be better

in the absence of over sampling.

Fig. 6: BER versus SNR without oversampling

Fig. 7: Comparison of BER versus SNR

VI. CONCLUSION

The channel shortening blind design for MIMO-OFDMsystems employing STFBC have been proposed andanalysed. Simulations results show that the performance ofreceivers equipped with the proposed blind channelshortening pre-filters are better compared to that of theexisting algorithm. The design turns out to be especiallyadvantageous in the absence of oversampling. It is clearlydemonstrated that the generalized zero padding approachtogether with eigen decomposition are effective to improvethe performance of the system with channel shorteningfilters.





REFERENCES

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[2] Prafulla. D. Gawande and Sirddharth. A. Ladhake

BER Performance Of Ofdm System With CyclicPrefix & Zero Padding International Journal ofAdvances in Engineering & Technology, Mar. 2013.

[3] Berger,C.R.; Gomes, J.; Moura, Sea-trial results forcyclic-prefix OFDM with long symbol durationJ.M.F. OCEANS, 2011 IEEE – Spain

[4] Blind Channel Shortening for Zero-Padded OFDMWeian Chen, Jie Huang, Zhaohui Wang, and ShengliZhou Department of Electrical and ComputerEngineering, University of Connecticut, Storrs, CT06269

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blind channel shortening for mimo-ofdm system using zero padding and eigen decomposition approach

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