Channel Estimation Schemes for OFDM-MIMO Systems and ... - iject

ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)IJECT Vo l. 2, Is s u e 2, Ju n e 2011Channel Estimation Schemes for OFDM-MIMO Systemsand their Performance Evaluation1 Naveen Rathee, 2 Dr. S.C.Gupta1Singhania University, Jhunjhunu, Rajasthan, India2RPIIT, Batsara, Karnal, Haryana, IndiaAbstractHigh data rates techniques in communication systems havegained considerable attraction in recent years. OrthogonalFrequency Division Multiplexing (OFDM) is a strong candidatefor these systems, which is a multi-carrier modulationtechnique. In OFDM systems, channel estimation is usuallyperformed by sending pilot symbols on sub carriers knownat the receiver. The quality of the estimation depends on thepilot arrangement. In this paper we compared the differentchannel estimation schemes by inserting pilot tones into allof the subcarriers of OFDM symbols with a specific period(Block-type) and (Comb-type). In this paper we also illustratethe minimum requirement of the number of pilots for channelestimation based on Sampling Theorem and other by the useof OFDM linear system.on sub-carriers known at the receiver. The estimation qualitydepends on the arrangements of pilots.II. Channel Estimation SchemesA. Block-type ArrangementThis scheme shown in Fig. 1(a) has been developed under theassumption of slow fading channel, where channel transferfunction is not changing rapidly. In this scheme of block-type pilot,OFDM channel estimation symbols are periodically transmitted,in which pilots are used for all sub-carriers. During the block ifthe channel is constant than there will be no channel estimationerror since pilots are sent at all carriers. The estimation canbe performed by using either LS or MMSE.KeywordsOFDM, MIMO, Channel Estimation, Pilot Symbols.I. IntroductionOrthogonal Frequency Division Multiplexing (OFDM) is apopular method for high-rate data transmission in wirelessenvironments. In OFDM the channel bandwidth is divided intoseveral narrow sub bands. The frequency response over each ofthese sub bands is flat. Hence a frequency - selective channelis transformed into several flat-fading sub-channels. The timedomainwaveforms of the subcarriers are orthogonal, yet thesignal spectra corresponding to different subcarriers overlapin frequency. Therefore, the available bandwidth is used veryefficiently. The data rate of the system is the aggregate ofthe data rate per sub channel. The other advantage of OFDMsystem is that they are less susceptible to various kind ofimpulse noise.Multiple Input Multiple Output (MIMO) systems use multipleantennas at both the transmitter and the receiver. Each antennasimultaneously transmits a small piece of data using the samefrequency band to the receiver. By taking advantage of thespatial diversity resulting from spatially separated antennas,the receiver can process the data flows and put them backtogether thereby, utilizing the bandwidth very efficiently.MIMO channels become frequency selective during highdata-rate transmission due to multipath characteristics ofthe environment. By combining the OFDM and MIMO, thesefrequency selective channels can be transformed to a set offrequency flat MIMO channels thereby, decreasing the receivercomplexity and overcoming the deteriorating effects of multipathfading and provide a high-performance transmission [1,2].In an OFDM-MIMO system, a coherent signal detection requiresa reliable estimate of the channel impulse responses betweentransmit and receiving antennas. The channel characteristicsmust be known to recover the transmitted signal afterdemodulation, so channel estimation is required. In OFDMchannel estimation is performed by sending pilot symbolswww.iject.orgFig. 1(a): Block-type Pilot ArrangementB. Comb-type ArrangementThis scheme shown in Fig. 1(b) has been introduced forsatisfying the need for equalizing when the channel changeseven in one OFDM block.Fig. 1(b): Comb-type Pilot ArrangementThis channel estimation scheme has algorithms for estimatingthe channel at pilot frequencies.This paper is based on a Comb-type arrangement, which is moreappropriate for the estimation of time varying channels [3, 4].The channel is frequency-selective invariant over each receivedblock, but allowed to vary from one block to another.There are two fundamental problems:• Number of pilot symbols to be transmitted.• Estimator complexityThe LS estimator has low complexity in comparison to MMSEestimator, but performance of MMSE estimator is good thanIn t e r n a t io n a l Jo u r n a l o f El e c t r o n ic s & Co m m u n ic a t io n Te c h n o l o g y 171

IJECT Vo l. 2, Is s u e 2, Ju n e 2011LS [5]. The OFDM transmission is robust to multi-path channeldelay, cyclic prefix is used to eliminate inter-symbol interference(ISI), but the inter-carrier interference is still a problem becauseof Doppler frequency. Orthogonality of the tones can’t bepreserved because of Doppler Effect [6] when the channelchanges even in one OFDM block in fast fading channels.In this paper we have studied the case of multipath fadingchannels with Orthogonality of tones being preserved alongwith optimal spacing of pilot symbols for OFDM-MIMO systems.The result of work based on channel capacity investigatingthis optimization problem [7] confirms the result of the studybased on the OFDM linear system (Y=HX+N), these studiesshow that in a multipath channel with L independent pathschannel estimation requires at least L symbols equally-spacedin the OFDM block.1. Estimation of Channel based on Comb-Type PilotArrangementThe received signal in an OFDM-MIMO system at the kth tonecan be expressed as:Y (k) = H (k) X (k) + I (k) + N (k), k = 0, 1 …N-1 (1)Where I (k) is the inter-carrier interference (ICI) because ofDoppler frequency.In case of multipath slowly fading channels, when channel isfrequency-selective invariant over each received block OFDMsymbol, the Orthogonality between subcarrier can be preservedand so we can writeISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)To fulfill the sampling theorem and avoid aliasing the pilotsymbols have to be close enough. Therefore, using piecewiseinterpolation we can reconstruct the channel impulseresponse. Whereas, if information about characteristics ofchannel is sufficient than the type of interpolation can bechoose even if pilot symbols are not close enough to fulfillsampling theorem.III. Minimum Pilot Tones RequirementIn this section we analyze the minimum requirement of pilotsfor channel estimation in OFDM-MIMO systems. Theoreticalanalysis shows that the channel estimation requires at least Lpilot symbols, and this statement can be proved by two differentmethods.• Sampling Theorem• OFDM linear system Y = HX+N.A. Sampling TheoremComb-type pilot arrangement channel estimation is based oninserting constant values (pilots) in some sub-carriers of theOFDM frame (Fig. 3). LS estimator gives estimation of channelat pilot sub-carriers after signal demodulation. The piecewiseconstant interpolation is used as shown in (Fig. 4). Hence,the process of estimation of channel based on pilot symbolswith piecewise constant interpolation is same as the samplingprocess. The bit-error-rate can be decreased if pilot symbols areplaced closer than that specified in the Sampling theorem.Y k,m= H k,mX k,m+ N k,m(2)Where Yk,m is the received signal; Xk,m is the transmitteddata and Nk,m is the AWGN noise. Because of the reason ofcomplexity there are several channel estimation criteria used,the estimation can be performed by using either linear MMSEcriterion (Wiener filtering) [8,9] and LS criterion. However LScriterion offers a good performance/complexity in high SNRregimes and when the noise level is low.2. InterpolationAn interpolation technique is necessary in order to estimatechannel at data sub-carriers by using the information of channelat pilot sub-carriers [10]. It is done using piecewise-constantinterpolation, linear interpolation, low-pass interpolation andother interpolation techniques. A comparison between threetypes of frequency channel response, Indoor A, Pedestrian Band Vehicular B is shown in Fig. 2 below.Fig. 3: Pilot InterpolationFig. 4: Sampling Process1. Modelling Multipath ChannelThe number of propagation paths determined by the ratio of themaximum delay spread τ maxand the sampling period T sis theparameter on which the complexity of an estimator depends.In the analog domain the multipath channel is given by thecomplex-valued impulse response [11]:Fig. 2: Rayleigh model 2GHz, ETSI TR101-102172 In t e r n a t io n a l Jo u r n a l o f El e c t r o n ic s & Co m m u n ic a t io n Te c h n o l o g y(3)where αl is the complex gain of the lth path, τl is the propagationdelay for the lth path. In digital transmission systems, symbolsare transmitted in regular time interval T s, called the samplingperiod. This period is smaller than the maximum delay timeτ max.For most of the wideband wireless systems, the discretewww.iject.org

ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)multipath model is regarded as the reference under anapproximation of constant number of multipath componentsL and slow variation of the delay values. The multipath channelis modeled as:Considering only the case whenplacement of pilot symbols.IJECT Vo l. 2, Is s u e 2, Ju n e 2011is an integer for equispacedThe path gains are given as samples which are taken at differentintervals Ts. The discrete signal spectrum is a periodic signal.Since inter-carrier spacing is ∆f and T=N.Ts is the duration ofan OFDM symbol, we have(5)In Comb-type pilot arrangement if it is assumed that pilots areplaced Nf subcarriers apart in every OFDM symbols and pilotsymbols are equally spaced and fe is the spacing between twoconsecutive pilot symbols then we have(6)Let He (f) be the frequency response of the channel constructedfrom the pilot symbols with a piecewise constant-interpolation.Then(4)Number _of_Pilot_Tones =Now knowing that is the number of pilot symbols in theOFDM frame, then the channel estimation requires at leastL pilot symbols.2. OFDM Linear System Y=HX+NWhen Orthogonality is preserved in the OFDM system, thesystem equation is expressed asY k,m= H k,mX k,m+ N k,m(13)Where N k,mis AWGN noise.Let there be the set of L tones used for transmitting pilotsymbols {k 1 , k 2 ,-----, k L }.If there is no noise, then from (13) we have:Y pl = H pl X pl (14)Where(7)(8)Inverse Fourier transform of this distribution is he(t) and iswritten as:(9)(10)(11)Since Q is a Vandermonde matrix with L parameters distinct,h can be found by inverting Q.From equation 13 we have L unknowns h 1 , ---h L . If L is thenumber of pilot symbols then the number of equations equalsthe number of unknowns, then the system can be solved. Ifthe symbols are less than L then number of equations willbe less than the number of unknowns and we will have anunder-determined system of linear equations, and hence anon-unique solution h.Therefore in both the cases (in the absence of noise) theminimum number of pilot symbols is L for exact channelestimation.IV. Results of Simulation(12)Thus h(t) can be reconstructed from h e(t).Sampling period Temust be greater than channel impulse response for samplesto be close enough to fulfill sampling theorem and avoidaliasing.i.e. Te ≥ L.Ts where L.Ts is the length of the multipath channelimpulse response. Using equation 6 we have.A. Multipath Channel EffectFor analysis, an OFDM 16 QAM transmission over a multipathchannel in the absence of noise (4 paths, 6 paths and 10 paths)was tested with N = 256 subcarriers, and cyclic prefix lengthequal to CP =32 was taken which is greater than the maximumdelay spread to avoid inter-symbol interference.In the Fig. 5 below it is seen that as the multipath channellength increases, the error rate increases. So, for correctingthe OFDM symbols Channel estimation is necessary.www.iject.orgIn t e r n a t io n a l Jo u r n a l o f El e c t r o n ic s & Co m m u n ic a t io n Te c h n o l o g y 173

IJECT Vo l. 2, Is s u e 2, Ju n e 2011Fig.5: Multipath Channel EffectB. Pilot Symbols Based Channel EstimationA typical OFDM system with N=256 subcarrier, CP=32 cyclicprefix length and 16 QAM transmission over a multipath channelin the absence of noise with 8 paths was considered.Equally spaced pilot symbols (1+ j) inserted with the receiverusing an LS estimator and interpolation.• First we insert 16 pilot symbols in every OFDM frame, thenthe number of pilot symbols is greater than the channellength (L=8 paths).• Secondly we insert 8 pilot symbols in every OFDM frame,then the number of pilot symbols is equal to the channellength (L=8 paths).The simulation results are shown below in Fig. 6 and Fig. 7. Itis found that the estimation of channel with 16 pilot symbolsper OFDM frame have good performance as compared to 8pilot symbols/OFDM frame.Fig. 6: Signal Constellation before CorrectionChannel estimation Channel Estimation8 pilot/OFDM block 16 pilots/OFDMblockISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)of OFDM linear system. We studied the minimum spacing ofOFDM pilot symbols in the multipath slowly fading channel. Itis shown that estimation of channel requires at least L pilotsymbols equally-spaced. Also we have analyze that one has tochoose the number of pilot symbols greater than the length ofthe multipath channel and for that we inserted pilot symbols(1 + j), since pilot symbols are not equally spaced in the OFDMframe. The number of pilot symbols was varied in OFDM blockswith receiver using an LS estimator.References[1] M. Engels, “Wireless OFDM Systems”, Kluwer AcademicPublishers, New York, 2002.[2] R.S.B.Ahmad, R.S.Burton, “Multi-Carrier_Digital_Communications: Theory and Application of OFDM,”Kluwer Academic Publishers, New York, 2002.[3] S.Coleri, M.Ergen, A.Puri, A.Bahai, “Channel EstimationTechniques based on Pilot Arrangement in OFDM-MIMOSystems,” IEEE Transactions on, Vol. 48, No. 3, September2002, pp. 223-229.[4] M.S.Akram, “Pilot-based Channel Estimation in OFDMSystems,” Master Dissertation, Technical University ofDenmark, Denmark, 2007.[5] J.J.VAN DE Beek, O.Edfors, M.Sandell, “On ChannelEstimation in OFDM Systems,” Vehicular TechnologyConference, IEEE 45th, Vol. 2, 1995, pp. 815-819.[6] H.Hijazi, L.Ros, “Rayleigh Time-varying Channel ComplexGains Estimation in OFDM Systems,” EuropeanTransactions on Telecommunications, Vol. 20, No. 1,2009, pp. 782-796.[7] S. Ohno, G.B.Giannakis, “ Capacity Maximizing MMSE-Optimal Pilots for wireless OFDM over Frequency-selectiveBlock Rayleigh Fading Channels,” IEEE Transactions onInformation Theory, Vol. 50, No. 9, 2004, pp. 2138-2145.[8] P.Hoecher, S.Kaiser, P.Roberston, “Pilot-Symbol-AidedChannel Estimation in Time and Frequency,” KluwerAcademic Publishers, USA,1997.[9] M.Sandell, O.edfors, “A Comparative Study of Pilot-basedChannel Estimators for Wireless OFDM,” Division of SignalProcessing, Lulea University of Technology, Lulea, Sweden,September 1996.[10] P.Y.Tsai, T.D.Chiueh, “Frequency-Domain InterpolationBased Channel Estimation in Pilot-Aided OFDM Systems,”Vehicular Technology Conference, IEEE 59th, Vol. 1, 2004,pp. 420-424.[11] D.Tse, P.Viswanath, “Fundamentals of WirelessCommunication,” Cambridge University Press, UK,2005.[12] Xiaoguang Wu, Guixia Kang, “Pilot Sequence Design Schemefor MIMO-OFDM Systems under Time-varying Channels,”Beijing University of Posts and Telecommunications,Beijing, China, IEEE Transactions, 2008, pp. 777-781.Fig. 7: Constellation after correctionV. ConclusionsIn this paper we have studied and compared the differentchannel estimation schemes by inserting pilot tones into allof the subcarriers of OFDM symbols with a specific period(Block-type) and (Comb-type). In this paper we also illustratethe minimum requirement of the number of pilots for channelestimation based on Sampling Theorem and other by the use174 In t e r n a t io n a l Jo u r n a l o f El e c t r o n ic s & Co m m u n ic a t io n Te c h n o l o g ywww.iject.org

ISSN : 2230-7109(Online) | ISSN : 2230-9543(Print)IJECT Vo l. 2, Is s u e 2, Ju n e 2011Er. Naveen Rathee received his B.E.degreein Electronics and Telecommunicationfrom Marathwada University Aurangabad,Maharashtra, India in 1991 and M.Techfrom IASE University, Rajasthan, India in2006. He is a research scholar pursuing hisdoctorate from Department of Electronicsand Communication Engineering,Singhania University, Rajasthan, India. Hehas an experience of 19 years working as Associate Professorand R&D Project manager to his credit. His major areas ofthrust includes VLSI signal Processing, Digital Communication,Digital System Design and Reconfigurable Fabric. At present heis holding the position of Dean (Academics) in SBIT, Sonepat,Haryana, India.Dr.S.C.Gupta received his Doctorof Philosophy from the Faculty ofEngineering and Technology in thedepartment of Electrical Engineeringin 1988 from Kurukshetra University,Kurukshetra, Haryana, India. Hehas worked as the Chairman ofElectrical Engineering Department inKurukshetra University for almost hisentire tenure for many years. He alsoprovided consultancy to Government of Haryana in ElectricalTransmission and Distribution in State Electricity board. Hehas guided many Research Scholars and PG students. He isan erudite academician with an experience of establishingmany reputed technical universities and Engineering collegesof repute in India. Presently, he is spearheading the postof Executive director at RPIIT, Batsara, Gharounda, Karnal,Haryana, India.www.iject.orgIn t e r n a t io n a l Jo u r n a l o f El e c t r o n ic s & Co m m u n ic a t io n Te c h n o l o g y 175