On performance of the zero forcing receiver in presence of transmit correlation

Spatial multiplexing (SM) is an emerging spatial signaling technique that achieves high spectral efficiency in MIMO wireless communication links. We study the performance of the zero forcing receiver (used to recover the transmitted data stream) in flat fading channels with transmit correlation. The results for interference rejection in i.i.d. environments presented by Salz, Winters and Gitlin (1994) may be interpreted in a MIMO single user context to conclude that the zero forcing receiver achieves M _r -M_t + 1 order diversity on each stream. We provide an alternative derivation based on Wishart matrix analysis for the same result. In addition our formulation allows the inclusion of transmit correlation in the channel. We show that the SNR on each decoded strewn is a weighted Chi-squared variable with 2(M_r $M_t + 1) degrees of freedom. The weight characterizes the degradation in SNR and is accurately quantified by the corresponding diagonal element of the inverse of the transmit correlation matrix.