OFDM Comb-Type Channel Estimation Using A MMSE Estimator
OFDM Comb-Type Channel Estimationusing a MMSE EstimatorSonali Sahu & A.B. NandgaonkarDept. Electronics & Telecommunication, Dr.Babasaheb Ambedkar Technological University,Raigad,Maharashtra,IndiaE-mail : act–Orthogonalfrequencydivisionmultiplexing (OFDM) is a keytechnique for wirelesscommunication because of its robustness for narrowband interference, frequency selective fading andspectral efficiency. Channel estimation andequalization in OFDM is necessary in order to nullifythe effect of impairments induced by the frequencyselective fading channel. A frequency domain combtypepilot assisted channel estimation has beenimplemented for the channel estimation purpose.Modified Minimum Mean Square Error (MMSE)estimator is considered for estimation of the channelat pilot subcarriers. The performance andcomplexity comparison is made between themodified MMSE and MMSE estimator for fastfading Rayleigh channel. Linear, Low Pass andspline cubic interpolation techniques have been usedwith the proposed modified MMSE estimator. Theeffect of increase in number of channel taps on theperformance of both estimators has been studied.Video Broadcasting-terrestrial (DVB-T) are usingOFDM [2]. In OFDM, frequency selective fadingchannel is transformed to flat fading channel by thedivision of the available channel bandwidth into severalsub channels.Improvisationin the performance of theOFDM system can be done in the presence of frequencyselective fading channel through the use of channelestimation and equalization. In single hniques are used for inter symbol interference (ISI)cancellation; however OFDM uses cyclic prefix for ISImitigation [3].Semi-blind, blind and pilot-aided channelestimation is the three categories of channel estimation.The information about the channel state is estimatedthrough the use of received signal statistics. Pilot tonesare used in pilot-aided channel estimation for theestimation of the channel impulse response. Semi-blindchannel estimation is the combination ofpilot aided bilityof blind estimation can be enhancedthrough the use of pilots [4]. In [5], comb-type pilotassisted channel estimation over Rayleigh fadingchannel is used. The interpolation technique proposed in[5] has been compared with time domain [6] and secondorder interpolation technique. Minimum mean squareerror (MMSE) estimator outperforms least square (LS)estimator [7][8].MMSE estimator uses prior informationabout the channel statistics.Keywords – Co-channel interference, munication, frequency division multiplexing,frequency domain analysis, time domain analysis,time-varying channels.I.INTRODUCTIONBandwidth efficiency and robustness to channelimpairments have made orthogonal frequency divisionmultiplexing (OFDM) technique an attractive feature forwireless communication standards. OFDM is usedwidely in applications i.e. Wi-Fi, Wi-MAX and powerline communications [1]. Broadcasting standards i.e.Digital Multimedia Broadcasting (DMB) and Digital1D comb-type channel estimation is consideredbecause of its low computational complexity ascompared to 2D channel estimation. Modified MMSEchannelestimator is used for estimation of channel atpilot sub-carriers. The performance comparison betweenthe modified MMSE estimator and conventional MMSEISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201337
ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)estimator is made for channels of different number oftaps. Sofar, the performance of the modified MMSEestimator remains fine for an increase in number of taps,however performance degradation occurs forconventional MMSE estimator with an increase inchannel taps.Notation : Ip stands for 𝑃 𝑋 𝑃identity matrix.Subscripts 1𝑇 and 1𝐻 represents the transpose andHermitian transpose.Fig.2 : Arrangement of PilotsA. CHANNELESTIMATIONFREQUENCIESII. SYSTEM OVERVIEWThe OFDM system model with channel estimationis shown in fig.1 below. The input bits are mapped andparallelized. To nullify the effects of the multipathfading channel, it is necessary to effectively estimate thechannel frequency response. A MMSE estimator toestimate the channel impulse response at pilotsubcarriers has been used. Finally after channelestimation and equalization, the signal is de-mapped toyield the output bits.ATPILOTIn comb-type pilot based channel estimation, the′𝑁𝑝 ′ pilot signals are uniformly inserted into X(k)according to the following equation:X(k) X(mL l) (1)Where L number of carriers / Np and xp (m) is thenth pilot carrier value. It is defined { Hp(k) 0, 1, .Np } as the frequency response of the channel at pilotsub-carriers. The estimate of the channel at pilot subcarriers based on LS estimation is given by(2)Where, Yp(k) and Xp(k) are output and input at thekth pilot sub-carrier respectively.Fig.1: OFDM System with Comb-type ChannelEstimationSince LS estimate is susceptible to noise and ICI,MMSE is thought about while compromisingcomplexity. Since MMSE includes the matrix inversionat each iteration, the simplified linear MMSE estimatoris suggested in [12]. In this simplified version, theinverse is only need to be calculated once. In [13],thecomplexity is further reduced with a low-rankapproximation by using singular value decomposition.III. CHANNEL ESTIMATION ANDINTERPOLATION TECHNIQUESOne dimensional (1D) Channel estimation inOFDM has two common types i.e. block-type andcomb-type;based upon the arrangement of pilots. Blocktype channel estimation is used for slow fading channelswhile comb-type is best suited for fast fading channels.Arrangement of pilots for comb-typeand block-typechannel estimation is shown in fig.2. A comb-typechannel estimation has been used because of the use ofthe fast fading Rayleigh channel for performanceanalysis of the OFDM system. Equi-spaced pilotinsertion is adopted because of optimum performance[10]. The channel frequency response at pilot subcarrieris estimated by using MMSE estimator because of itssuperior performance as compared to least square (LS)estimator [7][8].B. INTERPOLATION TECHNIQUESThechannel estimation based on comb type pilotinsertion, an interpolationtechnique is necessary in orderto estimate channel at data sub-carriers by using thechannel information at pilot sub-carriers.The linear interpolation method gives better results thanthe piecewise-constant interpolation in [7]. The channelestimationatthedata-carrier„k‟,mL k (m 1)L,usinglinear interpolation is given by:ISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201338
ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)The estimate of the channel at all frequencies is obtainedby:𝑁 1𝐺𝑁 𝑛 𝑒 𝑗𝐻 𝑘 (3)2𝜋𝑛𝑘𝑁,0 𝑘 𝑁 1𝑛 0(7)The second-order interpolation results to be betterthan the linear interpolation [13]. The channel estimatedby second-order interpolation is given by:IV. SIMULATIONA. Description of Simulation(i) System Parameters:OFDM system parameters used in the simulationare indicated in Table I.It is assumed to have perfectsynchronization since the aim is to observe channelestimation performance. Moreover, the guard intervalhas been chosenin such a way that it is greater than themaximum delay spread in order to avoid inter-symbolinterference. Simulations are carried out for differentsignal-to-noise (SNR) ratios and for different Dopplerspreads.where,(4)The low-pass interpolation is performed byinserting zeros into the original sequence and thenapplying a lowpass FIR filter (interp function inMATLAB) that allows the original data to pass throughunchanged and interpolates betweensuch that the meansquare error between the interpolated points and theirideal values is minimized. The spline cubic interpolation(spline function in MATLAB) produces a smooth andcontinuous polynomial,fitted to given data points. Thetime domain interpolation is a high-resolutioninterpolation based on zero-padding and DFT/IDFT[8].After obtaining the estimated channel {𝐻𝑃 𝑘 0,1, . 𝑁𝑝 -1},it is first converted to time domain byIDFT:Table I.Simulation Parameters𝑁𝑝 1𝐺 𝑛 𝐻𝑝 𝑒𝑗 (2𝜋𝑘𝑛 /𝑁𝑝 ), 𝑛 0,1, . . 𝑁𝑝 1𝑘 0(5)Then, by using the basic multi-rate signal processingproperties [9], the signal is interpolated bytransformingthe 𝑁𝑝 points into N points with the following method:𝑀 𝑁𝑝2ParametersSpecificationsFFT size1024No.of activecarriers(N)128Pilot Ratio1/8Guard Interval256Guard TypeCyclic extensionSample Rate44.1 kHzBandwidth17.5 KHzSignalConstellationBPSK,QPSK,DQPSK,16QAMChannel ModelRayleigh Fading,AR Model(ii) Channel Model:Two multi-path fading channel models are used inthe simulations. The 1st channel model is the ATTC(Advanced Television Technology Center) and theGrande Alliance DTV laboratory‟s ensemble E model,whose static case impulse response is given by: 1𝐺𝑝 , 0 𝑛 𝑀 2𝑁𝑃𝐺(𝑁) 0, 𝑁 𝑚2𝐺𝑝 𝑛 𝑁 2𝑀 1 , 𝑀 𝑛 𝑁 1h(n) α(n) 0.3162α(n-2) 0.1995α(n-17) 01296α(n-36) 0.1α(n-75) 0.1α(n-137)(6)(8)ISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201339
ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)The 2nd channel model is the simplified version ofDVB-T channel model, whose static impulse response isgiven in Table II. In the simulation, Rayleigh fadingchannel has been used. In order to see the effect offading on comb type based and LMS based channelestimation,a channel has been modeled which is timevarying according to the followingautoregressive (AR)model:h(n 1) αh(n) w(n)Fig. 4. LMS scheme(9)where „α‟ is the fading factor and w(n) is AWGNnoise vector which is chosen to be close to 1 in order tosatisfy the assumption that channel impulse responsedoes not change within one OFDM symbol duration. Inthe simulations, changes from 0.90 to 1 is taken in toconsideration.(iii) Channel Estimation Based on Block-Type PilotArrangement:Two types of block-type pilot basedchannelestimation has been modeled. Each block consists of afixed number of symbols, which is 30 in the simulation.Pilots are sent in all the sub-carriers of the first symbolof each block and channel estimation is performed byusing LS estimation. According to the first model, thechannel estimation is done at the beginning of the block, used for all the symbols of the block and according tothe second method, the estimation is done at thedecision feedback equalizer, which is used for to trackthe channel.Table II.Channel Impulse Response for channel 41870.3170.20550.1846-0.1545-2.4592.83722.8641(iv) Channel Estimation Based on Comb-Type PilotArrangement:Both LS and LMS estimators to estimate thechannel at pilot frequencies has been used.The LMSestimator uses one tap LMS adaptive filter at eachpilotfrequency. The first value is found directly throughLS and the rest of the values are calculated based on theprevious estimation and the current channel output asshown in fig. 4.Fig. 3. Time domain interpolationFig. 5. BPSK modulation with Rayleigh fading (channel1, Doppler freq. 70 Hz).ISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201340
ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)The channel estimation at pilot frequencies isperformed by using either LS or LMS. Then all of thepossible interpolation techniques (linear interpolation,second order interpolation, low-pass interpolation,spline cubic interpolation, and time domaininterpolation) are applied to LS estimation results, toinvestigate the interpolation effects and linearinterpolation is applied to LMS estimation results tocompare with the LS overall estimation results.B. Simulation ResultsThe words “linear, second-order, low-pass, spline,time domain” denotes the interpolation schemes ofcomb-type channel estimation with the LS estimate atthe pilot frequencies, “block type” shows the block typepilot arrangement with LS estimate at the pilotfrequencies and without adjustment, “decisionfeedback” means the block type pilot arrangement withLS estimate at the pilot frequencies and with decisionfeedback, and “LMS”is for the linear interpolationscheme for comb-type channel estimationwith LMSestimate at the pilot frequencies.Fig. 6. QPSK modulation with Rayleigh fading (channel1, Doppler freq. 70 Hz).Figs. 5–8 gives the BER performance of channelestimation algorithms for different modulations and forRayleigh fading channel, with static channel responsegiven in (8), Doppler frequency70 Hz and OFDMparameters given in Table I. These results shows that theblock-type estimation and decision feedback BER is 10–15 dB higher than that of the comb-type estimation type.This is because the channel transfer function changessofast that there are even changes for adjacent OFDMsymbols. The comb-type channel estimation with lowpass interpolation achieves the best performance amongall the estimationtechniques for BPSK, QPSK, and16QAM modulation. The performance among combtype channel estimation techniques usually ranges fromthe best to the worst as follows: low-pass, spline, timedomain, second-order and linear. The results wereexpected since the low-pass interpolation used insimulation does the interpolation such that the meansquare error between the interpolated points and theirideal values isminimized. Theseresults are alsoconsistent with those obtained in [13] and [14].Fig. 7. 16QAM modulation with Rayleighfading(channel 1, Doppler freq.70 Hz).Fig. 8. DQPSK modulation with Rayleigh fading(channel 1, Doppler freq.70 Hz).ISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201341
ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)simulation results shows that the comb-type pilot basedchannel estimation with low-pass interpolation performsthe best among all channel estimation algorithms. Thiswas expected since, the comb-type pilot arrangementallows the tracking of fast fading channel and low-passinterpolation does the interpolation such that the meansquare error between the interpolated points and theirideal values gets minimized. In addition, for lowDoppler frequencies, the performance of decisionfeedback estimation is observed to be slightly worsethan that of the best estimation. Therefore, someperformance degradation can be tolerated for higher databit rate for low Doppler spread channels although lowpass interpolationcomb-type channel estimation is morerobust for the increase in Doppler frequency.VI. REFERENCESFig.9: 2x2 uncoded QPSK systemDQPSK modulation based channel estimationshows almost the same performance for all channelestimation techniques except the decision-feedbackmethod. This is expected because dividing twoconsecutive data sub-carriers in signal de-mapper,eliminates the time varying fading channel effect. Theerror in estimation techniques result from the additivewhite noise. The BER performance of DQPSK for allestimation types ismuch better than those withmodulations QPSK and 16QAM and worse than thosewith the BPSK modulation for high SNR.The generalcharacteristics of the channel estimation techniquesperforms the same as fig. 7 for Rayleigh fading channel,whose static impulse response is given in Table II for16QAM.The general behavior of the plots is that BERincreases as the Doppler spread increases. The reason isthe existence of severe ICI caused by Doppler shifts.Another observation from this plot is that decisionfeedback block type channel estimation performs betterthan comb-type based channel estimation for lowDoppler frequencies as suggested in [14] except lowpass and spline interpolation.It is alsao observed thattime-domain interpolation performance is improvedcompared to other interpolation techniques as Dopplerfrequency increases.[1]Armstrong, Jean, “Tutorial on optical OFDM,"Transparent OpticalNetworks (ICTON), 201214th International Conference on , 2-5 July2012.[2]Adarsh B. Narasimhamurthy, Mahesh K. Banavarand CihanTepedeleniogly, OFDM Systems forWireless Communications, Morganand Claypoolpublishers, 2010[3]Yang, Z. Bai, W. Liu, Z., "A Decision-AidedResidual ISI CancellationAlgorithm for OFDMSystems," Signal Processing, 2006 8thIEEEInternational Conference on , vol.3, pp.1620, 2006.[4]Hu Feng. Li Jianping, Cai Chaoshi, "A novelsemi-blind channelestimation algorithm forOFDM systems," Wireless Communications&Signal Processing, 2009. WCSP 2009.International Conference on ,pp.1-4, Nov. 13-15,2009.[5]Chunlong He, Zhenming Peng, Qi Zeng and YingZeng, “A NovelOFDM Interpolation ations,NetworkingandMobile Computing, 2009. WiCom'09. 5thInternational Conference on, pp. 1-4, Sept. 24-26,2009.[6]He Chunlong and Hao li. “Pilot-Aided ChannelEstimation Techniquesin OFDM System,” inProc. International Conference onCommunicationSoftware and Networks, China, February 2009,pp.143–146.[7]Morelli, M., Mengali, U., "A comparison of pilotaided channelestimation methods for OFDMsystems," Signal Processing, IEEETransactionson , vol.49, no.12, pp.3065-3073, Dec 2001.V. CONCLUSIONIn this paper, a full experimental study of blocktype and comb-type pilot based channel estimation isdone. Channel estimation based on comb-type pilotarrangement is presented by giving the channelestimation methods at the pilot frequencies and theinterpolation of the channel at data frequencies. TheISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201342
ITSI Transactions on Electrical and Electronics Engineering (ITSI-TEEE)[8][9][10]Bowei Song, Lin Gui, Wenjun Zhang, "Combtype pilot aided channelestimation in E Transactions on , vol.52,no.1, pp. 50- 57, March 2006.Sinem Coleri, Mustafa Ergen, Anuj Puri, andAhmad Bahai, “ChannelEstimation IEEE trans.Broadcasting, Vol.48, no. 3,pp.223-229,September 2002.S. Ohno and G. B. Giannakis, “Optimal trainingand redundant precodingfor block transmissionswith application to wireless OFDM,”IEEE Trans.Comm., vol. 50, pp. 2113–2123, Dec. 2002.[11]S. T. Kay, Fundamentals of Statistical SignalProcessing. Volume I:Estimation Theory. NewJersey: Prentice-Hall, 1993.[12]M. Hsieh and C.Wei, “Channel estimation forOFDM systems based on comb-type pilotarrangement in frequency selective fadingchannels,”IEEE Trans. Consumer Electron., vol.44, no. 1, Feb. 1998.[13]R. Steele, Mobile Radio Communications.London, England: PentechPress Limited, 1992.[14]Y. Li, “Pilot-symbol-aided channel estimation forOFDM in wirelesssystems,” IEEE Trans.Vehicular Technol., vol. 49, no. 4, Jul. 2000. ISSN (PRINT) : 2320 – 8945, Volume -1, Issue -4, 201343
analysis of the OFDM system. Equi-spaced pilot insertion is adopted because of optimum performance [10]. The channel frequency response at pilot subcarrier is estimated by using MMSE estimator because of its superior performance as compared to least square (LS) estimator [7][8]. Fig.2 : Arrangement of Pilots
simulations, BER v/s E b /N o curves are simulated to analyze the performance of OFDM using 4 PSK, 8 PSK and 16 PSK modulation techniques. MATLAB software is used for programming and realizing the OFDM system. modulation techniques are called M Index Terms -OFDM, BER, OFDM using MPSK, MPSK, 4 PSK, 8 PSK, 16 PSK. 1.
the statistical subspace methods. Channel identifiability condi-tions are developed that guarantee perfect channel retrieval in the absence of noise using only a single OFDM block. These conditions are derived for the general case when virtual carriers are present, which is compatible with most practical wireless OFDM systems.
approach and focuses on the design of a control channel that is tailor-made for an NC-OFDM-based data plane. In particular, we discuss the design and implementation of a low-power CDMA-like underlay control channel (UCC) for each link that is designed specifically with the needs of NC-OFDM in mind. Control channel design for cognitive networks .
the BER performance of the MIMO (Multi-Input Multi-Output) OFDM system for AWGN (Additive White Gaussian Noise) Channel, Rayleigh Fading Channel along with a simulation channel using different modulation technique. Also the result of the analysis suggest for the better technique in order to improve the BER characteristic of the MIMO-OFDM .
the massive MIMO system for symbol synchronization. For OFDM-based massive MIMO systems, both channel estimation and frequency synchronization are considered. For feasible channel estimation for the massive MIMO system, the time-division duplex (TDD) is assumed, in which case, the standard least-square (LS) channel estimation is applied in the .
A survey on the contribution of OFDM techniques on RF and LiFi systems is an initial, but it is an indispensable stage to our contributions among many research directions. The benefits of OFDM technology to show an overview of the advantages of OFDM technique with RF syste
channel impulse response in all OFDM symbols are sent. Two channel estimates obtained from the adjacent pilot symbols used for channel estimation on the data between them. There are various types of such one-dimensional interpolation, linear interpolation, cubic spine -interpolation, low pass interpolation, ond -order interpolation.
Your river will be somewhere on a spectrum from very low energy to high energy. You can use Figure 3 below to help you identify the type of techniques likely to perform best depending on where your river is on this spectrum. In general, the higher the river’s energy, the larger the diameter of stems, roots and branches that you will need to use to cushion the bank from the force of the river .
