Low-Complexity Two-Way AF Relay Design for Millimeter Wave Communication Systems

In this paper, we consider the problem of hybrid multi-input multi-output (MIMO) transceiver design for a non regenerative hybrid two-way amplify-forward (AF) relay based millimeter wave (mmWave) communication system. We propose two low complexity mmWave system designs based on the quality of available channel state information (CSI). We first propose the design of transceivers and a two- way AF relay, by minimizing sum-mean square error (SMSE) under the constraint of total relay transmit power while assuming the perfect channel knowledge. We later extend it to a robust design under the assumption that the transceivers posses only imperfect information about the channel state, where the CSI error is assumed to follow the Gaussian distribution. In both the designs, reduced hardware complexity (introduced due to large number of antenna elements in mmWave system) is achieved by analog-digital hybrid processing by using orthogonal matching pursuit (OMP)-based sparse signal processing. We present numerical results on the performance of both the designs over various dictionaries. The comparison results show that robust design is resilient to the presence of CSI errors. Furthermore, we also demonstrate the convergence of both the proposed algorithms to a limit even though global convergence is hard to prove due to non convex nature of overall optimization problem.