Robust filter and forward relay beamforming with spherical channel state information uncertainties

Most of the beamforming designs that have been proposed in literature for relay networks often assume flat fading channels with perfect channel state information. However, in practice, the channel is likely to be frequency selective. On the other hand, in many cases, having the perfect channel state information is impossible. In this paper, we investigate the robust filter and forward beamforming for a relay network consisting a transmitter, a receiver and R relay nodes. All channels between the transmitter, relays and the receiver are assumed to be frequency selective with imperfect channel state information and it is also assumed that the channel uncertainty is bounded by a spherical region. Our aim in this paper is to minimize the total transmit power of the relays subject to a constraint on the worst signal-to-interference-plus-noise ratio (SINR). To solve the resulting non convex problem, we use a two-stage approach that considers the channel error. The robust beamforming can be obtained by KKT conditions, an auxiliary variable and S-procedure. Simulation results demonstrate the efficiency of the proposed method.