Cooperative Transmission for Relay Networks Based on Second-Order Statistics of Channel State Information

TLDR

Cooperative beamforming in relay networks uses a source and cooperating nodes to transmit to a destination. The paper seeks to compute beamforming weights that maximize the destination SNR under total and individual relay power constraints, using only second‑order channel statistics. The source first transmits locally, then relays amplify‑and‑forward weighted copies; the weights are derived from second‑order CSI, with the total‑power problem reduced to a single‑variable Newton method and the individual‑relay problem cast as a homogeneous QCQP, which is solved via SDP relaxation for up to three relays or by coordinate descent or an infinity‑norm maximization with augmented Lagrangian when SDP fails. The authors show that for up to three relays the optimal weights can be obtained via SDP relaxation and rank‑one decomposition, while for larger networks they propose coordinate‑descent and smooth‑norm augmented‑Lagrangian methods to achieve near‑optimal solutions.

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.