On Cooperative Beamforming Based on Second-Order Statistics of Channel State Information

TL;DR

This paper develops methods for cooperative beamforming in relay networks using second-order channel statistics to optimize SNR under power constraints, providing solutions for small relay sets and approaches for larger networks.

Contribution

It introduces novel optimization techniques for beamforming weights based on second-order statistics, including SDP relaxation and alternative methods for larger relay networks.

Findings

Optimal beamforming weights maximize SNR under power constraints.

SDP relaxation yields global solutions for up to three relays.

Coordinate descent and norm maximization methods effectively solve larger problems.

Abstract

Cooperative beamforming in relay networks is considered, in which a source transmits to its destination with the help of a set of cooperating nodes. The source first transmits locally. The cooperating nodes that receive the source signal retransmit a weighted version of it in an amplify-and-forward (AF) fashion. Assuming knowledge of the second-order statistics of the channel state information, beamforming weights are determined so that the signal-to-noise ratio (SNR) at the destination is maximized subject to two different power constraints, i.e., a total (source and relay) power constraint, and individual relay power constraints. For the former constraint, the original problem is transformed into a problem of one variable, which can be solved via Newton's method. For the latter constraint, the original problem is transformed into a homogeneous quadratically constrained quadratic programming (QCQP) problem. In this case, it is shown that when the number of relays does not exceed three the global solution can always be constructed via semidefinite programming (SDP) relaxation and the matrix rank-one decomposition technique. For the cases in which the SDP relaxation does not generate a rank one solution, two methods are proposed to solve the problem: the first one is based on the coordinate descent method, and the second one transforms the QCQP problem into an infinity norm maximization problem in which a smooth finite norm approximation can lead to the solution using the augmented Lagrangian method.