Wireless MIMO Switching With Imperfect CSI in Frequency and Time Division Duplex

This paper investigates the robust transceiver design in a wireless multiple-input multiple-output (MIMO) switching network in which multiple users exchange messages via a multi-antenna relay. Previous works assume that perfect channel state information (CSI) is known at the relay, which is intractable in practice. In this paper, channel uncertainty is considered in both frequency division duplex (FDD) and time division duplex (TDD) systems. Regarding different types of CSI imperfection of uplink and downlink transmission in FDD, a statistical and norm-bounded uncertainty models are adopted to characterize the imperfect CSI of uplink and downlink, respectively. In contrast to FDD, the uplink and downlink channels are reciprocal in TDD, and an identical statistical model is adopted for both uplink and downlink channel uncertainty. For each duplex system, an optimization problem is formulated by minimizing the worst-case mean square error (MSE) with respect to channel uncertainty in the constraint of the maximum transmit power of the relay. In FDD, since the problem is non-convex and difficult to solve, we divide the original problem into two subproblems in which the channel uncertainty of uplink and downlink are treated individually. For the uplink subproblem, we propose an iterative approach to determine a closed-form solution of the robust transceiver. In addition, a Sylvester equation is formulated which closed-form solution is provided explicitly for the downlink channel uncertainty subproblem. An overall iterative algorithm is proposed by combining the two algorithms for the subproblems, which can solve the original problem efficiently. Moreover, in TDD, the optimization problem is non-convex and difficult to solve as well. However, the involved channel uncertainty reduces to uplink only due to the reciprocity of uplink and downlink. We propose an iterative algorithm directly for the overall problem to determine the robust transceiver for TDD systems. The simulation results show that the proposed iterative algorithms reduce the sum MSE efficiently and outperform the existing schemes in the channel uncertain scenarios, which validate our conclusion.