Precoder Designs for the Relay-Aided X Channel Without Source CSI

In this paper, precoder designs are proposed for the wireless X networks aided by a relay and with no or very limited channel state information at the transmitters (CSIT). First, we derive the general feasibility conditions for interference alignment (IA) for a relay-aided symmetric multi-input-multi-output X channel (also called the X relay channel or XRC) without any CSI at the source transmitters. Next, we propose an IA-based joint beamforming approach with very limited feedback to the transmitters (referred to as "IA-LFB" in this paper), which can attain the maximum degrees of freedom (DoF) of the network under arbitrarily low relay power. Finally, we propose an iterative minimum-sum mean-square-error (MMSE) precoder design for the single-input-single-output XRC for throughput improvement in the finite signal-to-noise ratio (SNR) region. The proposed MMSE precoder also shows better bit error rate results than the IA precoder over a wide SNR range. Since the MMSE precoder can achieve only locally optimal solutions, we propose to initialize the iterative MMSE algorithm with the IA-LFB precoder which, unlike random initializations, not only improves the throughput in the finite SNR regions but also preserves the network DoF even under limited relay power.