Channel estimation in space and frequency domain for MIMO-OFDM systems

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1 June 009, 6(3): he Journal of China Universities of Posts and elecommunications Channel estimation in space and frequency domain for MIMO-OFDM systems PAN Pei-sheng ( ), ZHENG Bao-yu College of Communication and Information, Naning University of Posts and elecommunications, Naning 0003, China Abstract Multiple-input multiple-output (MIMO) systems can be combined with orthogonal frequency division multiplexing (OFDM) systems to improve the capacity and quality of wireless communications. In this article, a channel estimation technique in both space and frequency domain for MIMO-OFDM systems is proposed. It is shown that the proposed scheme with space-frequency pilot tones achieve optimal minimum mean square error (MME) channel estimation. imulation results indicate that the proposed method achieves good performance. Keywords channel estimation, MIMO, OFDM, space frequency pilot tones Introduction MIMO is superior to single-input single-output (IO) in terms of spectral efficiency [ ]. OFDM technology [3] turns a frequency-selective channel into a parallel set of frequency flat sub-channels suitable for high speed data transmission. Hence, the combination of MIMO systems with OFDM technology is a promising candidate for next generation fixed and systems mobile wireless systems. However, one problem is that accurate channel state information (CI) is required by the decoder. ince most MIMO-OFDM channel estimation methods [4 6] are based on space time processing, thus, to estimate the channel between each pair of antennas, each transmitter has to send pilot signals alternatively. his means that only one antenna sends pilot signals at a time, while the others stay silent. Another limitation for channel estimation carried out in space and time domain is that it requires the channel to maintain unchanged for duration of at least two OFDM symbols. Channel estimation methods for OFDM carried out in the frequency domain can be found in Refs. [7 0], in which only the frequency domain is concerned. For MIMO-OFDM systems, there are few references about channel estimation in both frequency domain and space domain. Because a mobile can carry multiple antennas, it is more difficult to estimate the CI for MIMO-OFDM systems than for Received date: Corresponding author: PAN Pei-sheng, panps@nupt.edu.cn DOI: 0.06/ (08)605-3 OFDM in which every mobile carries only one antenna. he proposed pilot structure is processed both in frequency domain and space domain, and different transmitter antennas can send pilot simultaneously. More importantly, this channel estimation technique can be carried out within one OFDM symbol duration, hence it does not require the channel to keep constant for duration of at least two OFDM symbols as those channel estimation methods processed in space and time domains do. It is shown that the proposed space frequency channel estimation technique achieves optimal minimum mean square error (MME) channel estimation. ystem model In MIMO-OFDM systems, at the nth OFDM symbol, the frequency response at the kth tone corresponding to the channel from the ith transmit antenna to the th receiving antenna is: L () l kl [, ] ( ) N l = 0 () l h ( ) H nk = h nw () where n is the lth channel impulse response from the ith transmit antenna to the th receiving antenna, i =,,..., N, =,,..., NR. WN = exp( π / N), and N is the total number of tones in an OFDM block, N is the number of transmitting antennas, N R is the number of receiving antennas, and is the sampling interval of the system, and / is the entire channel bandwidth of the system. = ( N + v) is the OFDM frame length where v is the F

2 Issue 3 PAN Pei-sheng, et al. / Channel estimation in space and frequency domain for MIMO-OFDM systems 4 number of cyclic prefix symbols. Let v L for the purpose of avoiding interference. Every channel between a transmitting antenna and a receiving antenna is assumed to be independent of each other. hus, the kth tone of the received signal at the th antenna can be expressed as N Y[ nk, ] = H [ nk, ] Xi[ nk, ] + W[ nk, ] () where k =,,..., N. W[ n, k ] denotes the additive complex Gaussian noise on the th receiving antenna and is assumed to be zero mean with variance σ n. Xi[ n, k ] denotes the kth tone of the transmitted signal at the ith transmitting antenna during the nth OFDM symbol. 3 Channel estimation Omitting the time index n, one can obtain the following from Eq. (): N Y[ p] = H [ p] Xi[ p] + W[ p] (3) where p denotes pilot tone index. Assume the channel frequency responses of two adacent tones are equal, that is: H [ p] = H [ p+ ] (4) he assumption above is reasonable when N is large enough, then: N i N H p Xi p W p Y [ p+ ] = H [ p+ ] X [ p+ ] + W [ p+ ] = [ ] [ + ] + [ + ] (5) From Eqs. (3) and (5), one can obtain: Y [ ] [ ] [ ] [ p] X p X p XN p Y[ p ] = + X[ p+ ] X[ p+ ] XN [ p+ ] H, [ p] W[ p] + W[ p+ ] (6) HN, [ p] Hence, ˆ + H = XY (7) where H ˆ is the estimation of the channel frequency + response corresponding to the th receiving antenna, and X is the pseudo-inverse of the training matrix X where Η ˆ ˆ ˆ ˆ = H, [ p] H, [ p] HN, [ p] X[ p] X[ p] XN [ p] X = X[ p+ ] X[ p+ ] XN [ p+ ] Y = Y( p) Y( p+ ) W[ p] W = W[ p+ ] he mean square error (ME) of the channel estimation is + H + H + E Η H = E ( WX ) WX = σ r{( XX ) } (8) { } { } Let H B = ( XX ) + be a matrix, then r( B ) = b, + b, b, b, (9) herefore, only when b, = b,, ME will reach its minimum. By Hardamard s inequality, b,b, det( B ) (0) with equality if and only if B is a diagonal matrix. hus, when B is a diagonal matrix and all elements in diagonal line are equal, the ME of the proposed method will be the minimum. It is easy to construct X to acquire the minimum ME according to the above condition. For simplicity in explanation, the authors let N =, N R =, and then one possible space frequency pilot structure is: i X[ p ] = + () i X[ p ] = () i X[ p+ ] = + (3) i X[ p+ ] = (4) where. hen i i + X = (5) i i Hence, i i i i + H XX = = i i i i + + i i i i + 0 = i i i i 0 = I + + (6) H B = ( XX ) + = Ι (7) where I is an identity matrix. hen the minimum ME equals 4σ. hus, the proposed space frequency pilot tones achieve optimal MME channel estimation. he estimation of channel frequency response of the other receiving antennas is the same as that of the th receiving antenna. It can be seen from the above analysis that the proposed channel estimation technique can be performed within one OFDM symbol; it then does not require the channel to keep unchanged within at least two OFDM symbols. It is noted that

3 4 he Journal of China Universities of Posts and elecommunications 009 [ n] [ n] h H = F = Fh (8) 0 [ ] (0) () ( ) [ ] where n [ ( ), ( ),..., L h = h n h n h ( n)] ; H n = { H [ n,0], H n H n N L denotes the maximum length of [,],..., [, ]}. the channel; h denotes channel impulse response from the ith transmitting antenna to the th receiving antenna; F denotes the N N discrete Fourier transform (DF) matrix. It can be seen that in the absence of noise, any L of the N tones can be used for training to recover the channel. Channel estimation based on comb-typed pilot arrangement is used in this design. L pilot tones are placed and equally spaced by N L in frequency domain. Pilot tones are divided into two groups for two transmitting antennas, respectively: N ( L ) N = 0,,..., L L N ( L ) N =, +,..., + L L he first transmitting antenna sends pilot tones X p = + on while sending pilot tones [ ] ( ) ( i ) X [ p+ ] = ( ) + ( i ) on and sending data on other tones. he second transmitting antenna sends pilot tones X p = on while sending pilot tones [ ] ( ) ( i ) X [ p+ ] = ( ) ( i ) on and sending data on other tones, as shown in Fig.. By comparison, the way in which the space time channel estimation, method which will be used in ect. 4, arranges its pilot tones is illustrated in Fig.. (a) Antenna (b) Antenna Fig. Pilot arrangement Within the nth OFDM symbol, the first transmitting antenna sends pilot tones on and the second transmitting antenna sends zero signals on. Within the (n+)th OFDM symbol, the second transmitting antenna sends pilot tones on, and the first transmit antenna sends zero signals on. he channel frequency responses of the L pilot tones can then be estimated under the assumption that the channel does not change within the duration of at least two OFDM symbols. (a) Antenna (b) Antenna Fig. Pilot arrangement 4 imulations Computer simulations are performed to demonstrate the performance of the proposed channel estimation technique. In the simulations, there are two transmitting antennas and two receiving antennas. he OFDM block size is N = 5, and a cyclic prefix (CP) with length of 8 is inserted at the beginning of each OFDM block. he four sub-channels are assumed to be independent of each other and have a maximum length of L = 8 each. hey are simulated by the Jakes model [] shown in able. he system bandwidth is MHz and QPK modulation is applied. he system performance is measured in terms of ME of the channel estimation, and the symbol

4 Issue 3 PAN Pei-sheng, et al. / Channel estimation in space and frequency domain for MIMO-OFDM systems 43 error rate (ER) versus the signal-to-noise ration (NR) of a maximum likelihood (ML) detector based on the channel estimation. able Channel model Path No. Delays/μs Fractional power In Fig. 3, the channel between the first transmitting antenna and the first receiving antenna is considered. he Doppler shift is 50 Hz and the curve marked with Known Channel serves as the performance bound as the channel state information in known exactly (which is, though unrealistic, assumed only for the purpose of simulation). It can be found that the curve generated by channel estimation based on the proposed pilot-tone design is close to the performance bound. Fig. 4 Performance comparison of the space time channel estimation and the space frequency channel estimation with Doppler shift 0 Hz Fig. 5 Performance comparison of the space time channel estimation and the space frequency channel estimation with Doppler shift 00 Hz Fig. 3 ymbol error rate versus NR with Doppler shift 50 Hz In Fig. 4, the performance of the proposed method is compared with the space time channel estimation method in which only one antenna sends pilot signals at a time while other antennas have to stay silent. imulation results indicate that the performance of the proposed method is superior to the space time method by over 5 db. In Fig. 5, the performance of the proposed method is compared with the space time channel estimation method at Doppler shift 00 Hz. imulation results show that in fast fading environments the performance of the space time method degrades significantly while the performance of the proposed method is only slightly worsened. hown in Fig. 6 are the MEs obtained using the proposed technique and the space time channel estimation method at Doppler shift 00 Hz. It can be seen from this figure that the proposed method here can achieve much lower MEs than the space time channel estimation. Fig. 6 he ME performance comparison of the space time channel estimation and the space frequency channel estimation with Doppler shift 00 Hz 5 Conclusions he proposed channel estimation method employs pilot structure in both space and frequency domain. By this method,

5 44 he Journal of China Universities of Posts and elecommunications 009 different transmitting antennas can send pilot simultaneously and can perform estimation within one OFDM symbol. Optimality of this method in terms of ME is verified. imulation results show that, compared with the space time channel estimation method, the proposed method is more effective in fast fading environments. Acknowledgements his work was supported by the National Natural cience Foundation of China (603707). References. Foschini G J. Layered space-time architecture for wireless communications in a fading environment when using multi-element antennas. Bell Laboratories echnical Journal, 996, (): Foschini G J, Gans M J. On limits of wireless communications in a fading environment when using multi-element antennas. Wireless Personal Communications, 998, 6(3): Cimini L Jr. Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing. IEEE ransactions on Communications, 985, 33(7): Li Y, eshadri N, Ariyavisitakul. Channel estimation for OFDM systems with transmitter diversity in mobile wireless channels. IEEE Journal on elected Areas in Communications, 999, 7(3): Barhumi I. Leus G. Moonen M. Optimal training design for MIMO OFDM systems in mobile wireless channels. IEEE ransactions on ignal Processing, 003, 5(6): Hu D, Yang L X, hi Y H, et al. Optimal pilot sequence design for channel estimation in MIMO OFDM systems. IEEE Communications Letters, 006, 0(): 3 7. Coleri, Ergen M, Puri A, et al. A study of channel estimation in OFDM systems. Proceedings of the 56th Vehicular echnology Conference (VC-Fall 0): Vol, ep 4 8, 00, Vancouver, Canada. Piscataway NJ, UA: IEEE, 00: Coleri, Ergen M, Bahai A. Channel estimation techniques based on pilot arrangement in OFDM systems. IEEE ransactions on Broadcasting, 00, 48(9): Negi R, Cioffi J. Pilot tone selection for channel estimation in a mobile OFDM system. IEEE ransactions on Consumer Electronics, 998, 44(3): 8 0. Yeh C, Lin Y. Channel estimation using pilot tones in OFDM systems. IEEE ransactions on Broadcasting, 999, 45(4): Jakes W C. Microwave mobile communications. New York, NY, UA: John Wiley and ons, 974 (Editor: ZHANG Ying) From p. 3 Compared with corresponding MPK or MQAM, the mapping constellation of OvCDM indeed is extended, but this is not the reason that contributes to the advantage of OvCDM. Its mapping constellation may be more preferable. 5 Conclusions he simulation results indicate that OvCDM can significantly improve spectrum efficiency. However, as the spectrum efficiency and constrained length increase, the number of states increases exponentially. Consequently, the decoding complexity increases rapidly. Future work may be focused on studying fast decoding algorithms to alleviate the problems discussed earlier. Also, other forms of configurations of OvCDM may be explored to further improve its performance. Acknowledgements Foundation of China ( ). References. Li D B. One time, space, frequency multi-address encoding method. PC International Patent Application: PC/CN006/ Li D B. A high spectral efficient multiple access code. Chinese Journal of Electronics, 999, 8(7): 3 3. Viterbi A J, Omura J K. Principle of digital communication and coding. New York, NY, UA: McGraw-Hill, Gallgager R G. Information theory and reliable communication. New York, NY, UA: John Wiley & ons, McEliece R J. he theory of inforamtion and coding. Reading, MA, UA: Addision-Wesley, Li D B. ignal statistical detection and estimate theory. Beiing, China: cience Press, 005 (in Chinese) 7. Yuan D F, Zhang H C. LDPC code theory and application, Beiing, China: Posts and elecommunications Press, 008 (in Chinese) 8. Wang W J, Lin Y W, Yan Y. Improved RB-HARQ scheme based on structured LDPC codes. he Journal of China Universities of Posts and elecommunications, 007, 4(4): Jin Y D, Wu W L. Reduced-complexity urbo equalization for urbo coded MIMO/OFDM systems. he Journal of China Universities of Posts and elecommunications, 006 3(): (Editor: WANG Xu-ying) his work was supported by the National Natural cience