Information Rate Optimization for Non-Regenerative MIMO Relay Networks with a Direct Link

TL;DR

This paper optimizes the capacity of a MIMO relay network with a direct link by deriving explicit solutions for the relay transform matrix, considering perfect channel knowledge and different coding schemes, extending previous work.

Contribution

It provides a convex optimization framework with explicit solutions for relay matrix design, including a water-filling-like algorithm, for networks with a direct link.

Findings

Explicit solutions for relay transform matrix under capacity criteria

Extension of previous models to include direct link effects

Simulation results demonstrating the impact of direct link SNR

Abstract

We consider the optimization of a two-hop relay network based on an amplify-and-forward Multiple-Input Multiple-Output (MIMO) relay. The relay is assumed to derive the output signal by a Relay Transform Matrix (RTM) applied to the input signal. Assuming perfect channel state information about the network at the relay, the RTM is optimized according to two different criteria: {\bf\em i)} network capacity; {\bf\em ii)} network capacity based on Orthogonal Space--Time Block Codes. The two assumptions have been addressed in part in the literature. The optimization problem is reduced to a manageable convex form, whose KKT equations are explicitly solved. Then, a parametric solution is given, which yields the power constraint and the capacity achieved with uncorrelated transmitted data as functions of a positive indeterminate. The solution for a given average power constraint at the relay is amenable to a \emph{water-filling-like} algorithm, and extends earlier literature results addressing the case without the direct link. Simulation results are reported concerning a Rayleigh relay network and the role of the direct link SNR is precisely assessed.