Performance Analysis of Space-Time Block Codes in Flat Fading MIMO Channels with Offsets

Use of space-time codes with multiple transmit antennas has generated a lot of interest for increasing spectral efficiency as well as improved performance in wireless communications. Although, the literature on space-time coding is quite rich now, the orthogonal designs of Alamouti [1], Tarokh et al. [2, 3], Naguib and Seshádri [4] remain popular. The strength of orthogonal designs is that these lead to simple, optimal receiver structure due to the possibility of decoupled detection along orthogonal dimensions of space and time. Presence of a frequency offset between the transmitter and receiver, which could arrive due to oscillator instabilities, or relative motion between the two, however, has the potential to destroy this orthogonality and hence the optimality of the corresponding receiver. Several authors have, therefore, proposedmethods based on pilot symbol transmission [5] or even blind methods [6] to estimate and compensate for the frequency offset under different channel conditions. Nevertheless, some residual offset remains, which adversely affects the code orthogonality and leads to increased symbol error rate (SER). The purpose of this paper is to analyze the effect of such a residual frequency offset on performance of MIMO system. More specifically, we obtain a general result for calculating the SER in the presence of imperfect carrier offset knowledge (COK) and compensation, and the resulting imperfect CSI (due to imperfect COK and noise). The results of [7–12] which deal with the cases of performance analysis of OSTBC systems in the presence of imperfect CSI (due to noise alone) follow as special cases of the analysis presented here. The outline of the paper is as follows. Formulation of the problem is accomplished in Section 2. Mean square error (MSE) in the channel estimates due to the residual offset error (ROE) is obtained in Section 3. In Section 4, we discuss the decoding of OSTBC data. In Section 5, the probability of error analysis in the presence of imperfect offset compensation is presented and we discuss the analytical and simulation results in Section 6. Section 7, contains some conclusions and in the appendix we derive the total interference power in the estimation of OSTBC data.