An iterative beamforming optimization algorithm for generalized MIMO Y channels

We consider a K-user multiple-input multiple-output (MIMO) relay channel, where each user sends K - 1 independent messages to the other K - 1 users via a common relay. All users and the relay are assumed to have multiple antennas. The communication happens in two time slots, the multiple access (MA) stage and the broadcast (BC) stage. A linear transmit beamforming and receive combining scheme is proposed based on signal subspace alignment and physical layer network coding. The optimization of the beamforming and combining vectors is addressed with an iterative suboptimal algorithm based on orthogonal projection optimization in the signal subspaces. Suboptimal power allocation is also considered to maximize the effective signal-to-noise ratios (SNRs). The bit error rate (BER) performance of the proposed scheme in various channel configurations is verified by simulation, which shows that the proposed scheme produces significant improvement over existing one.