A Survey on Channel Estimation Techniques in OFDM System

Transcription

1 A Survey on Channel Estimation Techniques in OFDM System Divya Pandey, Neelam Dewangan Chhatrapati Shivaji Institute of Technology, Durg Chhattisgarh, India Abstract Orthogonal Frequency Division Multiplexing (OFDM) breaks the carrier in to sub carriers which are orthogonal to one- another, and hence called as orthogonal frequency division multiplexing. It is an extension of conventional frequency division multiplexing (FDM ). The channel estimation techniques allow the receiver to approximate the behaviour of channel. In this paper various Channel Estimation Techniques of OFDM have been discussed. The channel estimation based on comb type pilot arrangement is studied through different algorithms for both estimating channel at pilot frequencies and interpolating the channel. The estimation of channel at pilot frequencies is based on LS and LMS while the channel interpolation is done using linear interpolation, second order interpolation, low-pass interpolation, spline cubic interpolation, and time domain interpolation. Furthermore, the channel estimation based on block type pilot arrangement is performed by sending pilots at every sub-channel and using this estimation for a specific number of following symbols. Further a brief introduction to blind and semi blind channel estimation is done. Keywords - OFDM, Channel Estimation, LS, LMS, MMSE, comb type pilot arrangement, block type pilot arrangement, blind channel estimation, semi blind channel estimation. I. INTRODUCTION Orthogonal frequency division multiplexing (OFDM) is a technique which divides the signal (carrier) in to several sub parts and transmits the signal with the help of those subcarriers. These subcarriers differ in terms of frequencies and they are orthogonal. Today OFDM is used in wired as well as wireless communication, such as the asymmetric digital subscriber line (ADSL) and the IEEE standard. OFDM was first introduced in 1960s and 1970s. Though all the subcarriers in an OFDM system is overlapped with the adjacent one but, the orthogonality can still be kept up by staggered QAM (SQAM) modulation technique. OFDM is similar to coded OFDM and is a multi tone modulation also called as multi carrier modulation. The term coded comes from the use of forward error correction (FEC). Motivation of OFDM is the problems that we faced in conventional FDM and TDM. FDM has a problem of bad spectrum usage where as TDM has a problem of multipath delay spread. The time spread between first and neighbouring signal in a multipath channel is called as multi path delay spread, which is seen by the receiver. These two problems were eliminated in OFDM. Problem faced in FDM was solved by efficient use of spectrum of subcarrier. Orthogonality of OFDM shows that, the subcarriers are orthogonal to oneanother. Frequency spectrum of subcarriers Figure 1 - subcarrier overlapping in OFDM OFDM is a dense multichannel system also called as multicarrier system. Sequential modulation is done in single carrier waveform. Let for example a signal of pulse width T is given then a single pulse occupies bandwidth of 1/T. Figure 2 - bandwidth for single carrier system Page 827

2 For multi carrier system, say for example for M number of signal the bandwidth required is 1/M th of total bandwidth 1/T. hence the OFDM reduces bandwidth requirement. Figure 3- bandwidth required for multi carrier system In conventional multichannel system the overlapping of adjacent channel is not there and also their two sided bandwidth is the separation between adjacent channels. Where as in OFDM multichannel system 50% overlapping of adjacent channel is there by which the available bandwidth is used twice and also channels are separated by twice of their two sided bandwidth. (LS) and minimum mean square error (MMSE) and comb type pattern has LS, LSM and interpolation. II. System model OFDM is basically a block process. It has signal generator, serial to parallel and parallell to serial convertors, modulator on transmitter side and demodulator, serial to parallel and parallel to serial convertor, signal detector on receiver side. Principal of modulation and demodulation is shown below through figures. Conventional multichannel signal OFDM multichannel signal Figure 5 - OFDM in block process Figure 4- Difference between conventional multichannel and OFDM multichannel Advantages of OFDM includes High spectral efficiency, immune to narrow-band co-channel interference, immune to inter symbol interference (ISI) and fading caused by multipath propagation, efficient use of available bandwidth Low sensitivity to time synchronization errors etc. No system is flaw free hence OFDM also have some drawbacks Sensitivity for Doppler shift, Sensitivity for problems related to frequency synchronization, High peak to average power ratio (PAPR), poor power efficiency of linear transmitter circuitry, Loss of efficiency caused by cyclic prefix. Benefits of OFDM system are higher data rates due to overlapping of subcarriers, Lower bandwidth than spread spectrum and Lower multi-path distortion. Channel estimation is a technique which guesses or evaluates the behavior of channel and gets a measure of their upshots on the signal. Hence channel estimation allows the receiver to approximate the effect of the channel on the signal. There are many channel estimation techniques in OFDM, that are pilot assisted, blind and semi blind. Pilot assisted technique consists of three patterns, block type pattern, comb type pattern and incline type pattern. Block type pattern has two estimators least squares Figure 6 - OFDM modulator An input signal is converted into N data streams by a serial to parallel port. The duration of the data is N-times elongated. Serial to parallel conversion is shown below. Page 828

3 Figure 7 - serial to parallel conversion The OFDM system based on pilot channel estimation is given in Figure[4] Mapping and grouping of binary data is done firstly with the help of modulation in signal mapper. After inserting pilots either as a block pattern or as a comb pattern IFDT block transforms the data sequence of length N{X(k)} into time domain signal {x(n)}. The subcarriers frequencies f 0, f 1, f 2.,f N-1 must be orthogonal to each other. The definition of the orthogonality was given in [3] as cos(2πfmt )x cos(2πfmt )dt = ϱ (n -m) (1) Where ϱ (n-m) = the Dirac-Delta function. In OFDM modulation, the subcarrier frequency f n is defined as f n = n f (2) Where f = = (3) Here f s = is the total bandwidth, and N is the number of subcarriers. Substituting equation (2) and (3) in (1), for all f 0, f 1, f 2.,f N-1 frequencies, orthogonality can easily be applied. At the receiver, the received signal is first made as base band signal by down conversion, then integration along with low pass filtering is done to separate out the sub carriers. All the subcarriers are separated successfully due to orthogonal property of OFDM. Transmitted signals and the received signals are alike. The OFDM demodulator is shown below. Figure 8 - OFDM Demodulator Figure 9 - OFDM system based on pilot channel estimation IFDT is followed by guard insertion block which provides guard time larger than the expected delay spread. This guard time removes ICI (inter carrier interference). The transmitted signal x(n) is passed through a channel with additive noise. The channel is frequency selective time varying fading channel. At receiver the guard time is removed and then y(n) is fed to the DFT block. Following DFT block, extraction of pilot channels is done and the estimated channel He(k) is gained for data sub-channel in channel estimation block. After the estimation of the transmitted data by: X e = ( ) ( ) k=0, 1... N (4) in signal demapper block the binary information data is obtained back [4]. III. Channel estimation Prior to demodulation dynamic channel estimation is necessary since for wideband mobile communication systems the radio channel is time-varying and frequency selective [4]. Channel estimation in OFDM has many techniques that are pilot assisted, blind and semi blind. Blind technique is nothing but estimation of channel without using pilot signal and the semi blind initially done estimation using pilots and then further it is done by channel tracking. The pilot technique is the most commonly used channel estimation technique. It basically has two patterns block and comb. We can perform cannel estimation either by reserving all the sub carriers for pilot tones with a specific period or by inserting pilot tones in each of the OFDM Page 829

4 symbol. The first one was introduced under slow fading channel and is block type pattern. It always assumes that transfer function is not moving very rapidly (even with decision feedback equalizer). For block type pilot pattern the channel estimation is based upon two estimators, least squares (LS) and MMSE. The MMSE estimate gives SNR of about10-15 db for the same mean square error of channel estimation over LS [5]. Comb type works on algorithms. It consists of algorithms to interpolate and estimate the pilot frequencies. The channel estimation in comb type pilot pattern is based on estimators LS, MMSE or least mean square (LMS). MMSE performs much better than LS. In [6]. Channel estimation principle The OFDM symbols pass through communication channel can be modelled as Y =XH + N n (5) Where Y is the received OFDM signal, X is the OFDM symbol at the transmitter, H is the channel frequency response or channel transfer matrix, N n is the complex zeromean Gaussian noise with the variance of (σ n 2 ). The noise is generally assumed uncorrelated with the channel frequency response H [7]. Channel Estimation Based On Block-Type Pilot Arrangement In block-type pilot-based channel estimation, as shown in Figure, periodic transmission of OFDM channel estimation is done and pilots are considered as sub carriers. Our aim here is to find out the channel conditions (specified by ḡ or ) given the pilot signals (specified by matrix or vector) and received signals (specified by ), with or without using certain knowledge of the channel statistics. To decode the received data the receiver uses the estimated channel conditions till the next pilot tone is not coming. The estimation can be based on least square (LS), minimum mean-square error (MMSE), and modified MMSE. LS Estimator Figure10 - block type pilot arrangement LS estimator maximizes the parameter { ( )}, where ( ) T shows conjugate transpose operation. The LS estimator of is given by = = [( )] (k= o N-1) (6) LS estimator has low complexity but high mean square error. MMSE Estimator The MMSE estimator employs the second-order statistics of the channel conditions to minimize the mean-square error. y =X (7) h =[h, h,.. h ] ( ) (8) n =[,,.. ], iff zero mean, Gaussian (9) h, =, y (10) Where F = ( ),,( ) ( )( ) (11) = (12) = y (13) = [ ] = (14) = [ ] = + [ ] (15) h = (16) The MMSE estimator performs better than LS and particularly in the case of low SNR it shows best result. The major disadvantage of MMSE estimator is its high computational complexity. Channel Estimation based on Comb Type Pilot Arrangement In comb-type pilot based channel estimation is an efficient interpolation technique which is necessary in order to estimate channel at data sub-carriers by using the channel information at pilot sub-carriers [4]. Interpolation at comb type pattern The adjacent pilot subcarriers channel estimation gives the transfer function for non pilot subcarriers via interpolation. Page 830

5 Various interpolation techniques are there which are basically algorithms and based on different pilot patterns. Linear Interpolation Second Order Interpolation Low pass Interpolation Spline Cubic Interpolation Time Domain Interpolation Linear interpolation is the most simple and most extensively used algorithm. In this algorithm we take same time slot of two adjacent or neighboring pilot frequencies of the same subcarrier and perform linear interpolation. Channel estimation using this at data rate k, ml < k < (m+1)l is given by ( ) = ( + ) 0 < = ( ( + 1) ( )) + ( ) (17) Second order interpolation is a bit better than linear interpolation. Channel estimation is given by -- (20) L=Number of Carriers/N p {H p (k) k=0,1,,n p }, channel at pilot sub-carriers X p input at the k th pilot sub-carrier Y p output at the k th pilot sub-carrier ( ) = ( + ) ( ), = 0 =. = 1,., 1 LS estimation ( ) = LMS estimation ( ) ( ) = 0,1,.., (21) ( ) = ( + ) = ( 1) + ( ) + ( + 1) (18) Where = ( ) = ( 1)( + 1), = = ( ) (19) The low-pass interpolation is performed by inserting zeros into the original sequence and then applying a lowpass FIR filter that allows the original data to pass through unchanged and interpolates between such that the meansquare error between the interpolated points and their ideal values is minimized [4]. Spline cubic interpolation gives plane or smooth response and continuous polynomial matched to data points that is given. Last interpolation i.e. time domain interpolation is a high resolution interpolation which is based on DFT/IDFT and zero padding. Figure shows time domain interpolation. Sometimes subcarriers are reserved for pilot frequency for each symbol and this done in comb type pilot pattern. Comb type pilot arrangement is shown in figure. Figure 11- comb type pilot arrangement N p pilot signals uniformly inserted in X(k) IV. Figure 12 - LSM estimator Blind and Semi blind Channel Estimation Blind channel estimation is done without using pilots. It does not depend on pilot tones and applied by channel statistics only hence training sequence is not necessary here. 2 nd or high order statistics give most blind channel estimation that has life. It has fast convergence rate and low complexity but has a disadvantage that it is hard to implement in real time systems. Semi-Blind as clear from name itself, initially channel estimation is done using pilot tones and then channel tracking. That is it relies partially on pilots and partially on the use of channel statistics. Hence semi blind technique is somewhat mixture of both pilot arrangement and blind channel estimation technique. V. CONCLUSION In this paper, a full review of OFDM and its channel estimation techniques are given. There are three main channel estimation techniques are there i.e. pilot arrangement, blind and semi blind. Pilot frequencies can be arranged in two manner i.e. block and comb. Channel estimation based on block-type pilot arrangement with or without decision feedback equalizer is described. Channel estimation based on comb-type pilot arrangement is presented by giving the channel estimation methods at the pilot frequencies and the interpolation of the channel at data Page 831

6 frequencies. Also we have described channel estimation techniques other than pilot arrangement. Those techniques are blind and semi blind technique. Blind channel estimation has complex structure and tedious for real time implementation. The comb type channel estimation with low pass interpolation performs the best among other techniques. Table: comparison of two channel estimation technique comes under comb and block type. Those estimators are LSE and MMSE. Parameter Carrier to interference ratio (CIR) Least square estimation (LSE) Not much affected. Minimum mean square error (MMSE) Not much affected. Complexity Lower than MMSE Higher than LSE Implementation Simple Hard Knowledge of Not needed Needed channel statistics Signal to noise ratio (SNR) VI. REFRENCES At low SNR lower than MMSE, but at high SNR same. At low SNR comparatively better, but at high SNR same. [1] R.W. Chang, Synthesis of band- limited orthogonal signals for multichannel data transmission, Bell Sys. Tech. Journal, vol. 45, Dec [2] Chi-Tsong Chen System and Signal Analysis Thomson, [3] Sinem Coleri, Mustafa Ergen,Anuj Puri, Ahmad Bahai A Study of Channel Estimation in OFDM Systems.2002 IEEE. [4] J.-J van de Beek, O. Edfors, M. Sandell, S.K. Wilson and P.O. Borjesson, On channel estimation in OFDM systems, in Proc. IEEE 45th Vehicular Technology Conference, Chicago, IL, Jul. 1995, pp [5] Xenofon G. Doukopoulos, student member, IEEE, and GeorgeV. Moustakides, Senior member, IEEE. Blind adaptive channel estimation in OFDM. IEEE transaction on wirelesscommunication, vol. 5, NO. 7,july 2006 [6] Bowie Song, Lin Gui, and Wenjun Zhang. Comb Type Pilot Aided Channel Estimation in OFDM system With Transit Diversity. IEEE TRANSECTION ON BROADCASTING, VOL.52, NO.1, MARCH [7] M. Hsieh and C. Wei, Channel estimation for OFDM systems based on comb-type pilot arrangement in frequency selective fading channels, in IEEE Transactions on Consumer Electronics, vol. 44, no.1, February [8] Lilong Liu, Xuelin Yang, Jun Li, Meihua Bi, Hao He, Wei sheng Hu State Key Laboratory of Advanced Optical Communication Systems and Networks Shanghai Jiao Tong University, Shanghai, , China, Experimental evaluation of pilot arrangement for channel estimation in OFDM systems. [9] Michele Morelli and Umberto Mengali, Fellow, IEEE A Comparison of Pilot Aided Channel Estimation Methods for OFDM Systems. IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 49, NO. 12, DEC 2001 [10] Saqib Saleem1, Qamar-Ul-Islam2. Department of Communication System Engineering, Institute of Space Technology Islamabad, Pakistan Performance and Complexity Comparison of Channel Estimation Algorithms for OFDM System. International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: 02. [11] Jan-Jaap, van de Beek, Ove Edfors, Magnus Sandell, Sarah Kate Wilsony, Per Ola BÄorjesson., On Channel Estimation in OFDM Systems. [12] Ye (Geoffrey) Li, Senior Member, IEEE, Nambirajan Seshadri, Senior Member, IEEE, and Sirikiat Ariyavisitakul, Senior Member, IEEE Channel Estimation for OFDM Systems with Transmitter Diversity in Mobile Wireless Channels, march [13] Ye (Geoffrey) Li, Senior Member, IEEE, july 2000, Pilot-Symbol-Aided Channel Estimation for OFDM in Wireless Systems. [14] Menng-Han and Che-Ho-Wei, department of electronics engineering national chiao tung university.channel estimation in OFDM systems based on comb type pilot arrangementin frequency selective fading Channels. Page 832

7 [15] Sinem Coleri, Mustafa Ergen, Anuj Puri, and Ahmad Bahai, Channel Estimation Techniques Based on Pilot Arrangement in OFDM Systems, SEPTEMBER [16] Sinem Coleri, Mustafa Ergen,Anuj Puri, Ahmad Bahai A Study of Channel Estimation in OFDM Systems. Page 833