Contents I. Introduction
Multiple-input multiple-output (MIMO) communications systems using multi-antenna arrays simultaneously during transmission and reception have generated significant interest in recent years. Under the assumption that the fading channel coefficients between different antenna elements are statistically independent and known at the receiver (coherent detection), theoretical work of [1] and [2] revealed that the channel capacity of multiple-antenna array communication systems scales linearly with the smaller of the number of transmit and receive antennas. Motivated by these works, [3] – [5] have proposed several modulation and coding schemes, namely space-time trellis codes and space-time block codes, to exploit the potential increase in capacity and diversity gain using multi antenna arrays with coherent detection. The effectiveness of these schemes heavily relies on the accuracy of the channel estimation at the receiver. Therefore, differential space-time coding schemes make an attractive alternative to combat inaccuracy of channel estimation in above schemes. With differential space-time coding schemes channel state information is not required at either end of the channel. Several differential space-time coding schemes for multi-antenna systems have been proposed in [6] – [8] and the error performance of some of these schemes have been investigated in [9] – [11]. In [9], a closed form expression of bit error probability of DSTBCs based on Alamouti's scheme was derived assuming fading channels are statistically independent. By applying the theory of Gaussian quadratic forms, an upper bound for the PEP of DSTCs was derived in [10] for arbitrary correlated channels. Following a similar approach, [11] has derived a closed form expression of the exact pairwise error probability (exact-PEP) at asymptotically high signal-to-noise ratios (SNR) of the DSTC in spatially correlated fading channels.
