An Investigation of the OFDM Channel Estimation

Transcription

1 An Investigation of the OFDM Channel Estimation Dr. ing. Dorina DRAGOMIR, Drd. ing. Cristina Gabriela GHEORGHE Rezumat. OFDM este o schemă de modulație digitală ce livrează sistemelor de comunicații de bandă largă volume mari de date și imunitate la interferența intersimbol și fading. Estimatorul de canal OFDM și egalizarea sunt robleme critice în dezvoltarea sistemului OFDM. Estimatorul de canal se bazează e ioteza sub-benzilor indeendente. Scoul acestui material este investigarea exhaustivă a schemelor de estimație entru a decide asura rofilului statistic al canalului. Cuvinte cheie: modulație digitală, zgomot, fading, multilexare cu divizare ortogonală de frecvență, estimarea canalului. Abstract: orthogonal frequency division multilexing (OFDM) is a digital modulation scheme which serve broadband communications systems with high volume of data and robust immunity to intersymbol interference and fading. Channel estimation and equalization issue are critical for the design of the OFDM system. he channel estimation relies on the subchannels correlations even if the receiver considers the subchannels indeendently. It is the urose of the resent aer to investigate estimation schemes in order to decide the aroriate channel statistics. Keywords: digital modulation, noise, fading, orthogonal frequency division multilexing, channel estimation.. INRODUCION A wireless communications channel is a medium enabling the information carriers to travel from the transmitters to the receivers under the ressure of disturbances and noise. Neither the erturbations nor the frequency characteristics of a band-limited channel are, usually, known a riori. he wireless communications channel could change its hysical roerties during the time so as its frequency characteristics are time-variant. Accordingly, the signals travelling the channel are distorted by multiath fading and corruted by noise. Fading, a multilicative effect which reduces the signal ower arriving at the receiver, can be stated as the con- Institutul Naţional de Studii şi Cercetări entru Comunicaţii I.N.S.C.C. volution of the transmitted signal with the channel imulse resonse. Since the electronic noise (at the receiver) and the transmitted signal are indeendently (statistically uncorellated) and the noise does not exerience fading, the fading degrades the signalto-noise ratio and decreases the channel caacity. he multiath signals originates from slitting mechanisms such as reflection, refraction, diffraction, and scattering caused by obstacles in the roagation ath of the wireless channel. If digital transmissions are emloyed, the multiath signals are reaching the receiver at different delays and different magnitudes. Both the delay and the magnitude are randomly distributed variables. In a frequency-selective (disersive) multiath channel (as a matter of fact the channel is frequency and time and even sace selective), each multiath ELECOMUNICAŢII Anul LXIX, nr

2 Dorina DRAGOMIR, Cristina Gabriela GHEORGHE signal (which is a coy of the transmitted signal) is sread out by disersion, with different delays and different amlitudes, causing the received signal get distorted by intersymbol interference []. If uncomensated, the intersymbol interference roduces high error rates [2]. Multicarrier modulation schemes, including OFDM techniques, are roviding high data rate transmisions with robustness against frequency selective fading and narrow band interference [3]. A multicarrier modulation system with a large number of subcarriers is exected to increase the link reliability because a very few subchannels could fail while exeriencing fading. he damaged subchannels could be restored by using error correction coding [4]. OFDM is used in digital audio broadcasting systems, digital video broadcasting systems, digital subscriber line standards, wireless LAN standards (IEEE 802.), and wireless broadband access standards (IEEE 802.6). he channel estimators for wireless OFDM are regarding the arrangement of the ilot information and the design of a low comlexity and high accuracy channel tracking [5]. he one dimensional channel estimations are block-tye ilot channel estimation and comb-tye ilot channel estimation [6]-[0]. he block-tye ilot arrangement uses the Least Square estimator, the Minimum Mean Square Error estimator, and the Modified Minimum Mean Square Error estimator. he comb-tye ilot arrangement uses the Least Square estimator, the Maximum Likelihood estimator, and the Parametric Channel Modelling-Based estimator [5]. 2. LEAS SQUARE CHANNEL ESIMAION he Least Square estimator is the minimum square distance between the received signal and the original signal. A schematic of a generic noise-corruted communications system is resented in Figure. he signal st () is transmitted to a frequency selective multiath fading channel with the comlex imulse resonse h(t). he signal st () is resulting from coding, interleaving and modulating (data maing) binary information data. Also, ilot (known) symbols are inserted into OFDM symbols after modulation. he modulated data are undertaking Inverse Fast Fourier ransform (IFF). Finally, a cyclic refix, usually longer than the maximum exected delay sread is added at the beginning of each OFDM symbol in order to remove intersymbol interference and intercarrier interference in the multiath fading channel. st () Multiath Channel h(t) Σ Filter rt () Detector st () Noise n(t) rt () () ht Channel estimation Figure. Model of a simle noise-corruted communications system with channel estimation. 6 ELECOMUNICAŢII Anul LXIX, nr. 2206

3 As OFDM scheme is slitting the broadband channel into narrowband subchannels, one subchannel for each subcarrier, every subchannel is stationary, slow-fading and quasi-flat frequency resonsively. More, the subchannels are indeendent each other. he imulse resonse of the multiath channel is (no Doler frequency shift): where of the L å ht () = ( t - ) () k= k () t is the comlex imulse resonse k k th k roagation ath in the channel, th () t is the delay time of the k ath, L is the k k number of aths, () t is the Dirac function. Let X X k and k0, N k k N k R R stand the inut data matrix of IDF (Inverse Discrete time Fourier ransform) at the transmitter and the outut data matrix of DF (Discrete time Fourier ransform) at the receiver, resectively. Let k k N k k N h h and n n be the samled channel imulse resonse matrix and the samled noise matrix, resectively. It can be roved that a block-tye ilot channel model is [2], [3]: where R R, R XH N (2) X diagx, N Fn, ( ) is the transose matrix of the ( ) matrix. æ 0,0 0, N- wn w ö N F = ç N-,0 N-, N- wn w çè N ø æ ö = ç çè N ø ik, w N - j 2 ik N, ik, = 0, N- H Fh ; (3) Equation (2) shows out that an OFDM transmission is sending data over arallel channels. ìï ïî LS estimation is min ï í( R -( XH) ) ( R-XH) * ü ï ý, ïþ where * denotes the comlex conjugate matrix of the matrix. he LS estimator of the channel, block-tye ilot channel is given by [6]: - LS k k é( ) ù H = X R = ë X Y û, k = 0, N- H LS, for a (4) he comutation of LS estimator in (4) is of a low comlexity but it suffers from high mean errors [5]. he comb-tye ilot estimation scheme interleaves eriodically ilot symbols and OFDM data symbols. he receiver learns the ilot locations [ ], P = Pk k = N -, where N is the number of the ilot symbols, and the ilot values X = éx ù ê k ú, k = 0, N -. Also, the receiver knows ë û the received signal R. he LS estimator of the comb-tye ilot channel is roved to be [5]: 0,, ù LS N - N - é ( ) ( ) ( ) H = ê R P X R P X R P X ë ú û (5) he channel estimation H (of length N) infers from the ilot symbols estimator H LS (of length N ) and received signals R. Estimation methods (which we will not resent herein) are D interolation, the maximum likelihood estimator, and the arametric channel modeling-base estimator [5], [8]-[0]. 3. MINIMUM MEAN-SQUARE ERROR CHANNEL ESIMAION 2 YX he Minimum Mean-Square Error (MMSE) is a second-order statistics estimate, namely the conditional variance of a conditional density function f y x []. YX ELECOMUNICAŢII Anul LXIX, nr

4 Dorina DRAGOMIR, Cristina Gabriela GHEORGHE he Minimum Mean-Square Error estimator for a block-tye ilot arrangement channel is [5]: H MMSE = FhMMSE = 2 * - - ( ( ) ) s = C C + XX H HH HH n where HH * * hh LS (6) C E HH FC F, C hh is the autocovariance matrix of the h matrix, 2 2 n E n is the noise variance. he Minimum Mean-Square Error estimator is erforming much better than the Least Square estimator, at the cost of a high comutation comlexity [5]. 4. CONCLUSIONS A free-error (in terms of intersymbol interference and inter-carrier interference) coherent detection of a received OFDM signal is imroved if roer multiath channel estimation schemes are erformed. Block-tye ilot arrangement andor comb-tye ilot arrangement are emloyed in order to estimate the fading channel. Block-tye ilot channel estimation fits a slow fading channel, while the comb-tye ilot channel estimation tailors fast fading channel. Least Square and Minimum Mean-Square Error channel estimators are described for both block-tye ilot and comb-tye ilot arrangements. he LS estimator is the best interolation method for the comb-tye ilot channel estimation. he Minimum Mean-Square Error estimator is much more aroriate to describe a block-tye ilot channel estimation, at the cost of a high comlexity comutation. Acronyms Acronym DF IDF IEEE IFF LAN MMSE OFDM Signification Discrete time Fourier ransform Inverse Discrete time Fourier ransform Institute of Electrical and Electronic Engineers Inverse Fast Fourier ransform Local Area Network Minimum Mean-Square Error Orthogonal Frequency Division Multilexing REFERENCES [] F. Xiong, Digital Modulation echniques, Artech House, Noorwood, MA, 2000 [2] J.G. Proakis, Digital Communications, 4th edition, McGraw-Hill, 200 [3] S. Hara, R. Prasad, Multicarrier echniques for 4G Mobile Communications, Artech House, Boston, 2003 [4] E. Krouk, S. Semenov, Modulation and Coding echniques in Wireless Communications, Wiley, U.K., 20 [5] Y. Shen, E. Martinez, Channel Estimation in OFDM Systems, Freescale Semiconductor, Alication Note AN3059, Jan [6] J-J Van de Beek, O.S. Edfors, M. Sandell, S.K. Wilson, On channel estimation in OFDM systems, 45th IEEE Vehicular echnology Conference, Chicago, Il., vol.2,.85-89, July, 995 [7] O. Edfors, M. Sandell, J-J. Van de Beek, S.K. Wilson, OFDM Channel Estimation by Singular Value Decomosition, IEEE ransactions on Communications, vol. 46, , July ELECOMUNICAŢII Anul LXIX, nr. 2206

5 [8] S. Coleri, M. Ergen, A. Puri, A. Bahai, Channel Estimation echniques Based on Pilot Arrangement in OFDM Systems, IEEE ransactions on Broadcasting, vol. 48, , Set [9] J. Wu, W. Wu, A Comarative Study of Robust Channel Estimators for OFDM Systems, Proceedings of ICC, , 2003 [0] B. Yang, K.B. Letaief, R.S. Cheng, Z. Cao, Channel Estimation for OFDM ransmission in Multiath Fading channels Based on Parametric Channel Modeling, IEEE ransactions on Communications, vol. 49, , March 200 [] R. Shiavi, Introduction to Alied Statistical Signal Analysis, 3rd edition, Academic Press, USA, 2007 ELECOMUNICAŢII Anul LXIX, nr