Distributed beamforming for cooperative networks with widely-linear processing at the relays and the receiver

This paper addresses the distributed beamforming problem, where widely-linear (WL) processing is employed at both the relays and the receiver to take advantage of strictly second-order (SO) noncircular source signals. We consider a single-antenna communication pair in a relay network, which suffers from strong interference. Assuming perfect channel state information (CSI), we design two algorithms based on the maximization of the signal-to-interference-plus-noise ratio (SINR) under a total relay power constraint. While the first algorithm jointly optimizes the weights at the relays and the receiver using semidefinite relaxation (SDR), the second algorithm performs a separate optimization in closed-form, requiring a substantially lower cost, but yielding almost the same performance. We show through simulations that the respective performance improvements associated with the WL processing at the relays and the receiver accumulate such that significant gains can be achieved compared to linear processing. Also, the complexity of the two algorithms is analyzed.