Constellation Design for Energy-Based Noncoherent Massive SIMO Systems Over Correlated Channels

This letter concerns the constellation design problem in energy-based noncoherent massive single-input multiple-output (SIMO) systems over correlated channels. Thanks to the large number of receiving antennas, we approximate the detection error minimization problem by the maximization of the minimum Kullback-Leibler (KL) divergence of the received signal vectors corresponding to different transmitted symbols. However, the max-min KL divergence problem is still difficult to solve. This is because the KL divergence expression involves summations of nonlinear functions of the transmitted signal powers induced by the channel correlation. We then resort to the Szegö’s theorem on large Hermitian Toeplitz matrices to simplify the formulated problem, which subsequently can be optimally solved by a one-dimensional bisection search. Simulation results demonstrate that the constellation designed by our approach outperforms its counterpart without considering the channel correlation, and the performance gain enlarges as the degree of correlation increases.