Robust peer-to-peer relay beamforming: A probabilistic approach

In this work, we design outage constrained collaborative relay beamforming (CRBF) vectors for a peer-to-peer amplify-and-forward (AF) relay network with imperfect channel state information (CSI) at the relays. Specifically, we model channel estimation error as a Gaussian random vector with known statistical distribution. The objective is to minimize the total transmit power at relays subject to probabilistic quality of service (QoS) constraints at each receiver. To solve the original non-convex problem, we utilize Bernstein-type inequalities and recast the original probabilistic constraints into conservative deterministic linear matrix inequalities (LMI). An alternative method is to replace the probabilistic constraint with a conservative one by applying S-procedure. Employing rank relaxation technique, the two convex reformulations are numerically solved with semidefinite programming (SDP). Simulation results are provided to corroborate our studies.