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  1. 1. Varinder Pal Sahni, AbhishekKaushik / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1388-13931388 | P a g eReview: PERFORMANCE EVALUATION OF CHANNELESTIMATION IN MIMO OFDMVarinder Pal Sahni*, AbhishekKaushik***(Department of Electronics and Communication,Punjab Technical University , Coimbatore-46)** (Department of Electronics and communication, Shri Krishan Institute of Engineering and Technology,Kurukshetra)ABSTRACTA multiple-input multiple-output(MIMO) communication system combined withthe orthogonal frequency division multiplexing(OFDM) modulation technique can achievereliable high data rate transmission high data ratetransmission over broadband wireless channels.The data rate and spectrum efficiency of wirelessmobile communications have been significantlyimproved over the last decade or so. Recently, theadvanced systems such as 3GPP LTE andterrestrial digital TV broadcasting have beensophisticatedly developed using OFDM andCDMA technologyChannel state information forboth single-input single-output (SISO) and MIMOsystems is investigated in this paper. Theestimation of channel at pilot frequencies withconventional Least Square (LS) and MinimumMean Square (MMSE) estimation algorithms iscarried out through Matlab simulation. Theperformance of MIMO OFDM and SISO OFDMare evaluated on the basis of Bit Error Rate (BER)and Mean Square Error (MSE) level. Furtherenhancement of performance can be achievedthrough maximum diversity Space Time BlockCoding (STBC) and Maximum LikelihoodDetection at transmission and reception endsrespectively. MMSE estimation has been shown toperform much better than LS but is more complexthan LS for the MIMO system using pilot carriers.Keywords:Channel Estimation, MIMO-OFDM,Pilot carriers, Diversity, Spatial Multiplexing,Space time codingI. INTRODUCTIONDuring the past few years, there has been anexplosion in wireless technology. This growth hasopened a new dimension to future wirelesscommunications whose ultimate goal is to provideuniversal personal and multimedia communicationwithout regard to mobility or location with high datarates. To achieve such an objective, the nextgeneration personal communication networks willneed to be support a wide range of services whichwill include high quality voice, data, facsimile, stillpictures and streaming video. These future servicesare likely to include applications which require hightransmission rates of several Mega bits per seconds(Mbps).The data rate and spectrum efficiency ofwireless mobile communications have beensignificantly improved over the last decade or so.Recently, the advanced systems such as 3GPP LTEand terrestrial digital TV broadcasting have beensophisticatedly developed using OFDM and CDMAtechnology. In general, most mobile communicationsystems transmit bits of information in the radiospace to the receiver. The radio channels in mobileradio systems are usually multipath fading channels,which cause inter-symbol interference (ISI) in thereceived signal. To remove ISI from the signal, thereis a need of strong equalizer which requiresknowledge on the channel impulse response [1].Equalization techniques which can combatand/or exploit the frequency selectivity of thewireless channel are of enormous importance in thedesign of high data rate wireless systems. Althoughsuch techniques have been studied for over 40 years,recent developments in signal processing, coding andwireless communications suggest the need forparadigm shifts in this area.On one hand, thedemonstrated efficiency of soft-input soft-outputsignal processing algorithms and iterative (turbo)techniques have fuelled interest in the design anddevelopment of nearly optimal joint equalization anddecoding techniques. On the other hand, thepopularity of MIMO communication channels,rapidly time varying channels due to high mobility,multi-user channels, multi-carrier based systems andthe availability of partial or no channel stateinformation at the transmitter and/or receiver bringnew problems which require novel equalizationtechniques [2].Hence, there is a need for thedevelopment of novel practical, low complexityequalization techniques and for understanding theirpotentials and limitations when used in wirelesscommunication systems characterized by very highdata rates, high mobility and the presence of multipleantennas.In radio channels, a variety of adaptiveequalizers can be used to cancel interference whileproviding diversity. Since the mobile fading channelis random and time varying, equalizers must track thetime varying characteristics of the mobile channel,and thus are called adaptive equalizers.The generaloperating modes of an adaptive equalizer includetraining and tracking. First, a known, fixed-length
  2. 2. Varinder Pal Sahni, AbhishekKaushik / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1388-13931389 | P a g etraining sequence is sent by the transmitter so that thereceiver’s equalizer may adapt to a proper setting forminimum bit error rate (BER) detection. The trainingsequence is typically a pseudorandom binary signalor a fixed, prescribed bit pattern. Immediatelyfollowing this training sequence, the user data (whichmay or may not include coding bits) is sent and theadaptive equalizer at the receiver utilizes a recursivealgorithm to evaluate the channel and estimate filtercoefficients to compensate for the distortion createdby multipath in the channel. The training sequence isdesigned to permit an equalizer at the receiver toacquire the proper filter coefficients in the worstpossible channel conditions( e.g., fastest velocity,longest time delay spread, deepest fades, etc.) so thatwhen the training sequence is finished, the filtercoefficients are near the optimal values for receptionof user data. As user data are received, the adaptivealgorithm of the equalizer tracks the changingchannel. As a consequence, the adaptive equalizer iscontinually changing its filter characteristics overtime. When an equalizer has been properly trained, itis said to have converged. The time span over whichan equalizer converges is a function of the equalizeralgorithm, the equalizer structure, and the time rate ofchange of the multipath radio channel.II. OBJECTIVESIn mobile communications systems, datatransmission at high bit rates is essential for manyservices such as video, high quality audio and mobileintegrated service digital network. When the data istransmitted at high bit rates, over mobile radiochannels, the channel impulse response can extendover many symbol periods, which leads to Inter-symbol interference (ISI). Orthogonal FrequencyDivision Multiplexing (OFDM) is one of thepromising technology to mitigate the ISI. In anOFDM signal the bandwidth is divided into manynarrow sub-channels which are transmitted inparallel. Each sub-channel is typically chosen narrowenough to eliminate the effect of delay spread. Bycombining OFDM with CDMA dispersive fadinglimitations of the cellular mobile radio environmentcan be overcome and the effects of co-channelinterference can be reduced. In this paper, theperformances of equalization techniques byconsidering 2 transmit 2 receive antenna case(resulting in a 2×2 MIMO channel). Assume that thechannel is a flat fading Rayleigh multipath channeland the modulation is BPSK.Spatially multiplexed MIMO (SM-MIMO) systems can transmit data at a higher speedthan MIMO systems using antenna diversitytechniques. However, spatial demultiplexing or signaldetection at the receiver side is a challenging task forSM MIMO systems. This also addresses signaldetection techniques for SM MIMO systems.Consider the NR*NT MIMO system in Fig 1. Let Hdenote a channel matrix with it ( j, i)thentry hji forthe channel gain between the ithtransmit antenna andthe jthreceive antenna, j=1, 2,..NR and i=1,2,.. NT.The spatially-multiplexed user data and thecorresponding received signals are represented byx = [x1; x2; . . . ; xNT ]Tandy =[y1; y2; . . . ; yNR ]T, (1)respectively, where xi and yj denote the transmitsignal from the ithtransmit antenna and the receivedsignal at the jthreceive antenna, respectively. Let zjdenote the white Gaussian noise at the jthreceiveantenna, and hi denote the ithcolumn vector of thechannel matrix H. Now, the NR*NT MIMO system isrepresented asy=Hx+z=h1x1 + h2x2+ ------- +hNT xNT +zWhere, z =[z1; z2; _ _ _ ; zNR]T. (2)Figure1:Spatially multiplexed MIMO systems.In the transmission of digital data over theMIMO communication systems, the signalpropagates from the transmitter to the receiverthrough different paths, each associated with a timedelay. As such each transmitted symbol is receivedseveral times, and each received symbol is disturbedby other symbols in the transmitted sequence,causing inter-symbol interference (ISI). While ideallyany multiple access schemes should provide eachtransmitter/receiver pair with an independentchannel, in practice this is often not the case. Due toinherent properties of the multiple access schemes inuse, different users interfere with each other, causingthe so-called inter-channel interference (ICI), alsoknown as multiple access interference (MAI). TheISI and ICI, due to the multi-path propagation andmulti-user impairment, if left uncompensated, will inturn, give rise to high error rate in symbol detection.A solution to this problem is to adopt a techniquewhich can compensate or reduce the ISI and/or ICI inthe received signal prior to detection. Such atechnique is called channel equalization.The ultimate goal is to minimize ornullify interference signals from other transmitantennas in the course of detecting the desired signalfrom the target transmit antenna.To achieve such anobjective we need strong equalization techniques tocompensate ISI.
  3. 3. Varinder Pal Sahni, AbhishekKaushik / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1388-13931390 | P a g e Zero Forcing (ZF) equalization Minimum Mean Square Error (MMSE)equalization Zero Forcing equalization with SuccessiveInterference Cancellation (ZF-SIC) MIMO with MMSE SIC and optimalordering.III. MIMO OFDM SYSTEMDeveloping high data rate technology with robust andseamless services is the main motivating factor behind bothfundamental and applied research in wirelesscommunications today. A key technique in fulfilling thistarget is the application of multiple transmit and multiplereceive antennas,Figure2: Block Diagram of MIMO OFDM systemWhich provide an additional spatial degreeof freedom. This spatial degree of freedom givesunique opportunities, e.g., for enhancing linkreliability, for interference suppression, and forsupporting high data rates. However, as the symboldata rate increases in broadband wirelessapplications, the underlying multiple-input multiple-output (MIMO) channel exhibit strong frequencyselectivity. As is well known, orthogonal frequencydivision multiplexing (OFDM) is a multicarriertransmission scheme that comes with low-complexity(de)modulation, equalization, and decoding tomitigate frequency-selective fading effects.Therefore, a combination of MIMO and OFDM(MIMO-OFDM) techniques appears particularlypromising for next generation broadband wirelesssystems. The block diagram of a MIMO-OFDMsystem is illustrated in Fig. 2.Various signal design methods for MIMOand MIMO-OFDM systems have been proposed. Acommon assumption in the signal design study ofMIMO/MIMO-OFDM systems is that the channelcoefficients between the pairs of transmit-receiveantennas are independent and identically distributed(i.i.d.) complex Gaussian process, which are perfectlyknown by the receiver. This is an idealistic situation.In practice, however, the channel coefficients arespatially correlated, where the degree of correlationdepends mainly on the antenna geometry, therichness of scattering, and the presence of dominantspecular components. Moreover, the channelcoefficients are in practice not perfectly known, andin some cases they are even unknown. Therefore, it isimportant to analyze and design signals forMIMO/MIMO-OFDM systems in the presence ofcorrelated channel coefficients on the condition ofimperfect channel state information (CSI) or evenwithout any CSI.Fig. 2 depicts a high level block diagram of theMIMO OFDM system. We consider MIMO–OFDMsystems with two transmit antennas and two receiveantennas. The total number of subcarriers is N.Basically, the MIMO-OFDM transmitter hasNtparallel transmission paths which are very similarto the single antenna OFDM system, each branchperforming serial-to-parallel conversion, pilotinsertion, N-point IFFT and cyclic extension beforethe final TX signals are up-converted to RF andtransmitted.The channel encoder and thedigitalmodulation can be done per branch, where themodulated signals are then space-time coded usingthe Alamouti algorithm [6] beforetransmitting frommultiple antennas [7] not necessarilyimplementedjointly over all the Nt branches. Subsequently atthereceiver, the CP is removed and N-point FFT isperformed perreceiver branch. Next, the transmittedsymbol per TX antenna iscombined and outputted forthe subsequent operations likedigital demodulationand decoding. Finally all the input binarydata arerecovered with certain BER.As a MIMO signalling technique, Nt different signalsare transmitted simultaneously over Nt XNrtransmission paths and each of those Nr receivedsignals is a combination of all the Nt transmittedsignals and the distorting noise. It brings in thediversity gain for enhanced system capacity as wedesire. Meanwhile compared to the SISO system, itcomplicates the system design regarding to channelestimation and symbol detection due to the hugelyincreased number of channel coefficients. The datastream from each antenna undergoes OFDMModulation. The Alamouti Space Time Block Coding(STBC) scheme has full transmit diversity gain andlow complexity decoder, with the encoding matrixrepresented as referred in [8] as
  4. 4. Varinder Pal Sahni, AbhishekKaushik / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1388-13931391 | P a g e(3)The vectors X1 and X2 are modulated usingthe inverse fast Fourier transform (IFFT) and afteradding a cyclic prefix as a guard time interval, twomodulated blocks Xg1and Xg2are generated and arethen transmitted by the first and second transmitantennas respectively. Assuming that the guard timeinterval is more than the expected largest delayspread of a multipath channel. The received signalwill be the convolution of the channel and thetransmitted signal. Assuming that the channel is staticduring an OFDM block, at the receiver side afterremoving the cyclic prefix, the FFT output as thedemodulated received signal can be expressed as inthe above equation [W1, W2……WNT] denotesAWGN and Hm,n is the (single-input single-output)channel gain between the mth receive and nth transmitantenna pair. The nth column of H is often referred toas the spatial signature of the nth transmit antennaacross the receive antenna array.Knowing the channelinformation at the receiver, Maximum Likelihood(ML) detection can be used for decoding of receivedsignals for two antenna transmission system, whichcan be written asIV. CHANNEL ESTIMATIONBased on those assumptions such as perfectsynchronization and block fading, we end up with acompact and simple signal model for both the singleantenna OFDM and MIMO-OFDM systems. Intraining based channel estimation algorithms, trainingsymbols or pilot tones that are known to the receiver,are multiplexed along with the data stream forchannel estimation. The idea behind these methods isto exploit knowledge of transmitted pilot symbols atthe receiver to estimate the channel. For a blockfading channel, where the channel is constant over afew OFDM symbols, the pilots are transmitted on allsubcarriers in periodic intervals of OFDM blocks.This type of pilot arrangement, depicted in Fig. 3(a),is called the block type arrangement. For a fast fadingchannel, where the channel changes between adjacentOFDM symbols, the pilots are transmitted at all timesbut with an even spacing on the subcarriers,representing a comb type pilot placement, Fig. 3(b)The channel estimates from the pilot subcarriers areinterpolated to estimate the channel at the datasubcarriers.Figure3: Block Pilot And Combo PilotV. SISO OFDM CHANNEL ESTIMATIONIn block-type pilot based channel estimation, OFDMchannel estimation symbols are transmittedperiodically, in which all subcarriers are used aspilots. If the channel is constant during the block,there will be no channel estimation error since thepilots are sent at all carriers. The estimation can beperformed by using either LS or MMSE [9], [10]. Incomb-type pilot based channel estimation, the Nppilot signals are uniformly inserted into X(k)according to the following equation:-(4)whereL = No. of subcarriers / Np and m is pilotcarrierindex. If inter symbol interference iseliminated by the guardinterval, we write (4) inmatrix notationWhere,(5)Is the DFT matric with(6)If the time domain channel vector h is Gaussian and
  5. 5. Varinder Pal Sahni, AbhishekKaushik / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1388-13931392 | P a g euncorrelated with the channel noise W, the frequencydomainMMSE estimate of is given by [3]:(7)where,(8)are the cross covariance matrix between h and Y andauto covariance matrix of Y respectively. Rhh is theautocovariance matrix of h, σ2represents the noisevariance E{│W(k)│2} and IN is the N X N Identitymatrix. To use LS (least square) method for channelestimation, we usually put those observationequations into a matrix form. LS is a well-knownmethod and widely used for estimation. We chooseLS rather than other methods like MMSE channelestimation for the simplicity of implementation. TheLS channel estimate is represented by:(9)the LS estimator is equivalent to what is also referredto as the zero-forcing estimator. In comb-type pilotbased channel estimation, an efficient interpolationtechnique is necessary in order to estimate channel atdata sub-carriers by using the channel information atpilot sub-carriers. In the linear interpolation methodthe channel estimation at the data-carrier k, mL<k <(m + 1) L, using linear interpolation is given by:(10)whereHp is channel estimation value at pilotfrequency. The low-pass interpolation is performedby inserting zeros into the original sequence and thenapplying a lowpass FIR filter that allows the originaldata to pass through unchanged and interpolatesbetween such that the mean-square error between theinterpolated points and their ideal values isminimized. The spline cubic interpolation produces asmooth and continuous polynomial fitted to givendata points.V. MIMO OFDM Channel EstimationSimilar to the SISO scenario, the LS channelestimation for MIMO-OFDM System between nthtransmitter and mthreceiver antenna is(11)and MMSE channel estimation for MIMO-OFDMSystem between nthtransmitter and mthreceiverantenna is(12)where(13)Where n = 1, 2….NT, m = 1, 2….NR and NT, NR arethe numbers of transmit and receive antennas,respectively, X(n)is an N X Ndiagonal matrix whosediagonal elements correspond to the pilots of thenthtransmit antenna and Y(m)is N length receivedvector at receiver antenna mVI. CONCLUSION AND FUTURERESULTSIn my work, I have compared channelestimation based on both block-type pilot and comb-type arrangements in both SISO and MIMO OFDMbased systemsThe work to be done in later stages is to perform theChannel estimation based on comb-type pilotarrangement is achieved by giving the channelestimation methods at the pilot frequencies and theinterpolation of the channel at data frequencies. Thisstudy can also be used to efficiently estimate thechannel in both OFDM systems given certainknowledge about the channel statistics in future.Also,the MMSE estimator assumes a prioriknowledge of noise variance and channel covarianceand discussed Space Time Block coding andmaximum likelihood decoding in the MIMO OFDMsystem to enhance its performance further. Wecanalso observe the advantage of diversity in MIMOsystemresults less BER than SISO system. It can alsocompares the performance of MMSE with LS, and isobserved that the former is more resistant to the noisein terms of the channel estimationREFERENCES[1] Ramjee Prasad, “OFDM for wirelesscommunications systems” Artech House, Inc.Publications.[2] Ezio Biglieri, Robert Calderbank, RobertCalderbank, Anthony Constantinides, AndreaGoldsmith, Arogyaswami Paulraj, H. VincentPoor, “MIMO wireless communications”Cambridge Press.[3] A. Petropulu, R. Zhang, and R. Lin, “BlindOFDM Channel Estimation Through SimpleLinear Pre-Coding" IEEE Transactions onWireless Communications, vol. 3, no.2, March2004, pp. 647-655.[4] Osvaldo Simeone, Yeheskel Bar-Ness,Umberto Spagnolini, “Pilot-Based ChannelEstimation for OFDM Systems by Trackingthe Delay-Subspace”, IEEE Transactions on
  6. 6. Varinder Pal Sahni, AbhishekKaushik / International Journal of Engineering Research andApplications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.1388-13931393 | P a g eWireless Communications, Vol. 3, No. 1,January 2004.[5] D. Mavares Terán, Rafael P. Torres, “ Space-time code selection for OFDM-MISO system”,ELSEVIER journal on ComputerCommunications, Vol. 32, Issue 3, 25February 2009, Pages 477-481.[6] Siavash M. Alamouti, “A Simple Transmitdiversity Technique for WirelessCommunications”, IEEE Journal on SelectAreas in Communications, Vol. 16, No. 8,October 1998.[7] PAN Pei-sheng, ZHENG Bao-yu, “Channelestimation in space and frequency domain forMIMO-OFDM systems” ELSEVIER journalof China Universities of Posts andTelecommunications, Vol. 16, No. 3, June2009, Pages 40- 44.[8] Mohammad Torabi, “Antenna selection forMIMO-OFDM Systems” ELSEVIER journalon Signal Processing, Vol. 88, 2008, Pages2431-2441.[9] J.-J. van de Beek, O. Edfors, M. Sandell, S. K.Wilson, and P. O. Borjesson, “On channelstimation in OFDM systems,” in Proc. IEEE45th Vehicular Tec D.A. Gore, R. W. Heath,Jr., and A. J. Paulraj, “Transmit Selection inSpatial Multiplexing Systems,” IEEECommun. Lett., vol. 6, no. 11, pp. 491-493,Nov. 2002.[10] G. J. Foschini, G. D. Golden, R. A.Valenzuela, P. W. Wolniansky, “SimplifiedProcessing for High Spectral EfficiencyWireless Communication Employing Multi-Element Arrays,” IEEE J. Select. AreasCommun., vol. 17, no. 11, pp. 1841-1852, Nov.1999.[11] A. Scaglione, P. Stoica, S. Barbarossa, G. B.Giannakis and H. Sampath, “Optimal Designsfor Space-Time Linear Precoders andEqualizers,” IEEE Trans. Signal Processing,vol. 50, no. 5, pp. 1051-164, May 2002.[12] Y. Ding, T. N. Davidson, Z.-Q. Luo, and K.M. Wong, “Minimum BER Block Precodersfor Zero-Forcing Equalization,” IEEE Trans.Signal Processing, vol. 51, no. 9, pp. 2410-2423, Sept. 2003.[13] L. Collin, O. Berder, P. Rostaing, and G.Burel, “Optimal minimum distance-basedprecoder for MIMO spatial multiplexing,”IEEE Trans. Signal Processing, vol. 52, no. 3,pp. 617-627, Mar. 2004.[14] D. J. Love and R. W. Heath Jr., “LimitedFeedback Precoding for Spatial MultiplexingSystems,” Proc. IEEE Globecom 2003, vol.4,pp. 1857-1861, San Francisco, CA, Dec. 2003.[15] N. Wang and S. D. Blostein, “Minimum BERPower Allocation for MIMO SpatialMultiplexing Systems,” Proc. IEEE ICC 2005,vol. 4, pp. 2282-2286, Seoul, Korea, May2005.[16] N. Wang and S. D. Blostein, “ApproximateMinimum BER Power Allocation for MIMOSpatial Multiplexing Systems,” IEEE Trans.Commun., accepted for publication, July 2005.[17] S. H. Nam, O.-S. Shin, and K. B. Lee,“Transmit Power Allocation for a Modified V-BLAST System,” IEEE Trans. Commun., vol.52, no. 7, pp. 1074-1079, July 2004.[18] N. Wang and S. D. Blostein, “Minimum BERTransmit Optimization for Two-InputMultiple-Output Spatial Multiplexing,” Proc.IEEE Globecom 2005, vol. 6, pp. 3774-3778,St. Louis, MO, Nov.-Dec. 2005.[19] J. Akhtar and D. Gesbert, “A Closed-FormPrecoder for SpatialMultiplexing overCorrelatedMIMO Channels,” Proc. IEEEGlobecom 2003, vol.4, pp. 1847-1851, SanFrancisco, CA, Dec.2003.[20] A. Abdi and M. Kaveh, “A Space-TimeCorrelation Model for Multielement AntennaSystems in Mobile Fading Channels,” IEEE J.Select. Areas Commun.,vol. 20, no. 3, pp. 550-560, Apr. 2002.[21] J. G. Proakis, Digital Communications, 4thed., New York: McGraw-Hill, 2001.[22] D. Gesbert, H. B¨olcskei, D. Gore, and A. J.Paulraj, “Outdoor MIMO Wireless Channels:Models and Performance Prediction,” IEEETrans. Commun., vol. 50, no. 12, pp. 1926-1934, Dec. 2002.[23] S. Zhou and G. B. Giannakis, “AdaptiveModulation for Multi- Antenna Transmissionswith Channel Mean Feedback,” Proc. Of IEEEICC 2003, vol. 4, pp. 2281-2285, Anchorage,AK, May 2003.