On Optimal Input and Capacity of Non-Coherent Correlated MISO Channels under Per-Antenna Power Constraints

Abstract

This paper investigates the optimal input and capacity of non-coherent correlated multiple-input singleoutput (MISO) channels in fast Rayleigh fading under per-antenna power constraints. Toward this end, we first establish the convex and compact properties of the feasible sets, and demonstrate the existence of the optimal input distribution and the uniqueness of the optimal effective magnitude input distribution. By exploiting the solutions of a quadratic optimization problem, we show that the Kuhn-Tucker condition (KTC) on the optimal inputs can be simplified to a single dimension. As a result, we can apply the Identity Theorem to show the discrete and finite nature of the optimal effective magnitude distribution. By using this distribution, we then construct a finite and discrete optimal input vector distribution. The use of this input allows us to determine precisely the capacity gain of MISO over SISO via the phase solutions of a non-convex constrained quadratic optimization problem on a sphere. These phase solutions can be calculated effectively via a proposed penalized optimization algorithm.