Precoder design for a three-input multiple-output spatial multiplexing system with noncoherent reception

In this paper, we consider the subject of diagonal precoder matrix design for a three-input multiple-output system using spatial multiplexing with binary symbols from the constellation {0,1} and noncoherent reception in flat Rayleigh fading having a uniform transmit covariance matrix. For this system, the symbol vector error probability (SEP) tends to saturate at high values of average signal-to-noise ratio per symbol vector per diversity branch. The saturation value of the SEP is minimized with respect to the precoder parameters to obtain the best error performance. It is found that when the number of receive antennas is large, the optimal values of the precoder parameters are almost independent of the number of receive antennas. Numerical results show the advantage of using noncoherent reception over coherent reception with imperfect channel state information.