Signal Design for Multiple Antenna Systems With Spatial Multiplexing and Noncoherent Reception

We consider signal design for multiple-input multiple-output (MIMO) systems with spatial multiplexing and noncoherent reception in a flat Rayleigh fading environment. We obtain the symbol vector error probability (SEP) of noncoherent detection as a function of the signal amplitude levels and the effective precoder matrix, which depends on the precoder structure and the channel transmit covariance matrix. It is found that at high values of average signal-to-noise ratio (SNR) per symbol vector per diversity branch, the SEP tends to reach saturation. To obtain the best error performance, we need to find the optimal precoder and constellation parameters that minimize the saturation value of the SEP. Optimization of the saturation value of the SEP is carried out using the binary signal constellations {0,1} and {1, -r}, r > 1, two transmit antennas, a real valued transmit covariance matrix with equal diagonal elements, and a diagonal precoder. Results show that the optimal values of the parameters are almost independent of the number of receive antennas when the number of receive antennas is large. We also observe that the error performance of MIMO noncoherent reception is better than that of MIMO coherent reception with imperfect channel state information for a certain range of average SNR.