Frequency offset correction for space-time block coded OFDM systems based on maximum likelihood estimation Tim Zhong Mingqian 1 , A.S.Madhukumar 2 , A.B.Premkumar 3 , E.M-K.Lai 4 School of Computer Engineering Nanyang Technological Univerisity Singapore 639798 Email: tim@pmail.ntu.edu.sg 1 , {asmadhukumar 2 ,asannamalai 3 ,asmklai 4 }@ntu.edu.sg Abstract - This paper discusses the Maximum Likelihood (ML) frequency offset estimation and subsequent correction for a Space-Time Block Coded Orthogonal Frequency Division Multiplexing (STBC-OFDM) system. Carrier frequency offset in OFDM system destroys the orthogonality between subcar- riers resulting in performance deterioration. Also, it consider- ably reduces the diversity gain for STBC. Accurate frequency offset estimation and subsequent correction will significantly improve the performance of a STBC-OFDM system. This paper proposes an averaging approach for frequency offset estimation. The proposed scheme has been simulated with parameters in conformity with WLAN standards in a Rayleigh fading environment. Simulation results show that after the frequency offset correction, the STBC system may acquire the same level of performance as the system that possesses perfect frequency synchronization. Key Words - Maximum Likelihood Estimation (MLE), Multiple-Input Multiple-Output Orthogonal Frequency Divi- sion Multiplexing (MIMO-OFDM), Space-Time Block Coding (STBC), Frequency Offset Correction. I. I NTRODUCTION Multi-carrier systems such as OFDM-based WLAN can support high data rate transmission in multi-path fading chan- nel with the presence of large delay spread. This is due to the fact that a high data rate stream of information can be splitted into paralleled lower data rate stream, thus providing the stronger immunity against channel distortion caused mainly by Doppler shift in the context of wireless communication. Simultaneously, channel efficiency is obtained by overlapping subcarriers in the frequency domain [1]. Performance of wireless link can be further improved by introducing spatial diversity with the help of multiple antennae at both transmitters and receivers. A simple space-time block coding method is proposed in [2] as an approach of spatial-time diversity with two antennae at both ends of the link.This scheme has rela- tively low system complexity but results in good performance and therefore is attractive for practical implementation. The combination of OFDM and space-time block coding is the next logical step in obtaining further gain [3]. Cyclic Prefix(CP) has been exploited in OFDM systems to combat Inter-Symbol Interference (ISI), which is totally eliminated given this guard time is longer than the expected multi-path delay spread [4].On the other hand, OFDM is sensi- tive to frequency offset because the orthogonality is destroyed in such a case, leading to Inter-Carrier Interference (ICI). Consequently, estimation and correction of frequency offset is extremely important for OFDM systems. Many different frequency offset estimation schemes have been proposed in literature including both frequency-domain approach [5] and time-domain approach [6]. Maximum likelihood estimation is the key idea underlying these proposals and correlation operation is the common structure for most of them. It is in this context, this paper exploits the concept further for the frequency offset estimation and correction of space-time block coded OFDM. The rest of the paper is organized as follows: Section II describes a system model for STBC OFDM system with car- rier frequency offset. Section III introduces the proposed ML method for frequency offset correction. Section IV discusses the simulation result and shows the improvement brought by the novel approach. Section V concludes the paper. II. SYSTEM MODEL The OFDM system with two transmit and two receive antennae is shown in Figure 1. The system embeds an STBC module before the IFFT in the transmitter and a ML detector is added in the receiver. There exist two independent cyclic prefix (CP) appending/removing block in the two antenna branches just before and after the channel but are not shown in Figure 1 for simplicity. The received signal vector for k-th subcarrier can be expressed as, R(k) = • r 00 (k) r 01 (k) r 10 (k) r 11 (k) ‚ = • t 0 (k) t 1 (k) -t * 1 (k) t * 0 (k) ‚ * • h 00 (k) h 01 (k) h 10 (k) h 11 (k) ‚ + • n 00 (k) n 01 (k) n 10 (k) n 11 (k) ‚ (1) where * denotes convolution, t 0 (k) and t 1 (k) are the STBC- OFDM symbol, h 00 (k) through h 11 (k) denote the channel impulse response at the k-th subcarrier of the OFDM block corresponding to the i-th transmit and the j -th receive antenna (i =0, 1,j =0, 1) respectively. The channel state information (CSI) for at least two successive OFDM symbol remains fixed according to the traditional “quasi-static” channel model. The additive complex Gaussian noise plus the interference through