Performance analysis of zero-forcing precoding with signal space diversity under antenna correlation

We consider a multiantenna transmission system where the transmitter and receiver respectively have M and two antennas. Specifically, zero-forcing precoding is employed at the transmitter based on a possibly imperfect channel state information (CSI). The channel estimation is carried out at the transmitter using pilot signals sent from the receiver. Adopting a dual-stream transmission structure, the error performance of the system is enhanced by resorting to signal space diversity (SSD). The performance of the proposed system with binary phase shift keying modulation is studied under a slow flat Rayleigh fading scenario with uncorrelated transmit antennas and correlated receive antennas. We separately examine two cases: the perfect CSI and imperfect CSI at the transmitter. In the former scenario, we provide an exact closed-form expression on the bit error probability (BEP) of the proposed approach. A tight approximation on the BEP of the proposed scheme is presented for the latter scenario. The case with distinct channel estimation qualities for the two subchannels is also considered in the second scenario. The proper rotation angles for the BPSK signal constellation are analytically obtained such that the derived expressions on the BEP are minimized under both cases. We show that the inclusion of SSD into the original scheme yields a noteworthy improvement on the BEP performance with only an insignificant increase in complexity and no additional use of bandwidth/time slots. It is also shown that the proposed technique is more immune against the channel estimation errors as compared to the original method.