Source Optimization in MISO Relaying with Channel Mean Feedback: A Stochastic Ordering Approach

TL;DR

This paper develops a novel stochastic ordering approach to optimize source transmission in MISO relay channels with channel mean feedback, revealing that beamforming along the channel mean and eigenchannels maximizes capacity.

Contribution

It introduces a new method dividing the feasible set and compares nonnegative random variables to determine the optimal transmission strategy in nonconvex MISO relay channels.

Findings

Optimal strategy is to transmit along the channel mean and eigenchannels.

Rank-one precoding achieves capacity under certain conditions.

Results generalize traditional MISO precoding with mean feedback.

Abstract

This paper investigates the optimum source transmission strategy to maximize the capacity of a multiple-input single-output (MISO) amplify-and-forward relay channel, assuming source-relay channel mean feedback at the source. The challenge here is that relaying introduces a nonconvex structure in the objective function, thereby excluding the possible use of previous methods dealing with mean feedback that generally rely on the concavity of the objective function. A novel method is employed, which divides the feasible set into two subsets and establishes the optimum from one of them by comparison. As such, the optimization is transformed into the comparison of two nonnegative random variables in the Laplace transform order, which is one of the important stochastic orders. It turns out that the optimum transmission strategy is to transmit along the known channel mean and its orthogonal eigenchannels. The condition for rank-one precoding (beamforming) to achieve capacity is also determined. Our results subsume those for traditional MISO precoding with mean feedback.