Sum-rate maximization for filter-forward relay network using virtual WMMSE algorithm

Filter-and-forward (FF) relay protocols can combat the impact of frequency-selective fading. This paper studies filter design for FF multicast multi-relay networks. We formulate the sum-rate maximization problem with individual relay power constraints. Different from the sum-rate maximization problems of general channel setups, the studied sum-rate problem cannot be directly tackled using the popular WMMSE technique. Based on the special structure of the sum-rate maximization problem at hand, we introduce virtual parallel flat-fading channel and establish an equivalent problem of the sum-rate maximization problem. The equivalent problem can be addressed using block coordinate descent (BCD) algorithm, which leads to virtual WMMSE algorithm. We show that the virtual WMMSE algorithm can monotonically converge to a stationary point of the sum-rate maximization problem. Simulations demonstrate the effectiveness of the proposed virtual WMMSE algorithm.