Improved Channel Estimation in OFDM Systems with Synchronization Errors and Back-off Hisham A. Mahmoud and Huseyin Arslan Department of Electrical Engineering, University of South Florida 4202 E. Fowler Avenue, ENB-118, Tampa, FL, 33620 E-mail:{hmahmoud, arslan}@eng.usf.edu Abstract— In Orthogonal Frequency Division Multiplexing (OFDM) systems, synchronization errors in the receiver cause a linear phase rotation at the output of the Discrete Fourier Transform (DFT) block. The correlation between the channel coefficients at different subcarriers is weakened due to this phase rotation. As a result, the performance of Minimum Mean-Square Error (MMSE) channel estimation degrades significantly. In this paper, we propose two novel algorithms to improve MMSE channel estimation under synchronization errors. Theoretical analysis and simulation results are presented to compare the performance of the proposed algorithms with that of the conven- tional algorithm. I. I NTRODUCTION Wireless communication systems have evolved substantially over the last two decades. The explosive growth of the wireless communication market is expected to continue in the future, as the demand for all types of wireless services is increasing. Due to their ability to provide high data rates for multimedia appli- cations, Orthogonal Frequency Division Multiplexing (OFDM) is gaining a strong interest for wide-area, local area, and per- sonal area networks. In OFDM, carrier frequencies are chosen in such a way that there is no influence of other carriers in the detection of the information in the carrier of interest when the orthogonality of the carriers is maintained. Maintaining this orthogonality requires some special care for the frequency and symbol timing synchronizations. Cyclic extension of the symbols is usually used to relax the requirements for symbol synchronization. In wireless OFDM systems, channel estimation is an integral part of the coherent receiver design as the performance of the receiver is greatly affected by the quality of the channel estimation. Extensive studies on the topic can be found in the literature [1]-[6]. In OFDM systems, channel estimation is frequently employed in frequency domain after taking the Discrete Fourier Transform (DFT) of the time synchronized digital samples. There are numerous approaches of estimating the Channel Frequency Response (CFR) over the OFDM sub- carriers. The direct Least-Squares (LS) estimation assumes the channel over each subcarrier to be independent. However, in practice, the CFR is often oversampled over these subscarriers, and the estimated coefficients are correlated. On the other hand, the noise in these subcarriers can be independent. By exploiting the correlation of CFR over OFDM subcarriers, the noise can be reduced significantly, and hence the channel estimation accuracy can be improved. Assuming that the channel frequency correlation and noise variance are known, Minimum Mean-Square Error (MMSE) filtering of the LS estimates has been shown to provide optimal performance under Additive White Gaussian Noise (AWGN) [7]. However, other simple approaches can also be used to take advantage of the channel frequency correlation to reduce the noise variance effect [1]. Many of the channel estimation approaches proposed in the literature assume perfect symbol timing. However, in practice, the symbol timing used in OFDM systems is not perfect. As a matter of fact, the symbol timing is often intentionally shifted towards the Cyclic Prefix (CP) so that any possible error in symbol timing that might create the loss of orthogonality can be avoided [8]. Even though this intentional bias in synchronization avoids the loss of orthogonality of the carriers and inter-carrier-interference, it results in the effective CFR to be less correlated due to the additional carrier-dependent phase shift. As a result, the channel estimation performance will degrade since the noise averaging effect will be reduced. In this paper, we develop a novel MMSE channel estimation that takes the synchronization errors (intentional or not) into account. The proposed channel estimation improves the noise averaging capability and takes advantage of channel correla- tion fully by removing the effect of synchronization errors during the estimation process. The paper is organized as follows. We describe the system model in section II. The MMSE channel estimation is ex- plained in section III. In section IV, we present our proposed algorithms. Theoretical analysis and system performance is evaluated in section V. Section VI discusses the analytical and simulation results. Finally, we offer some conclusions in section VII. II. SYSTEM MODEL We consider an N subcarrier OFDM system with X k as the frequency domain transmitted symbol at the kth sub- carrier. The time domain complex baseband data sequence [x 0 x 1 ... x N-1 ] T is obtained at the output of the Inverse Dis- crete Fourier Transform (IDFT) block with [X 0 X 1 ... X N-1 ] T as the input. Before transmission, a CP of length N CP is added at the beginning of the data sequence to eliminate the Inter- Symbol Interference (ISI) and to preserve the orthogonality of the frequency subcarriers [9]. The data is then transmitted over a multipath channel. The time domain channel impulse 1-4244-0063-5/06/$20.00 ©2006 IEEE