Abstract
In this paper, we present new relay precoder designs for two-way amplify-and-forward multiple-input multiple-output (MIMO) relay systems. We first derive the mean-squared error (MSE) matrices of the received signals at two terminals, and show that their behavior strongly depends on the singular values of the effective MIMO channels of the corresponding relay system. Motivated by this property, a set of relay precoders are constructed based on the singular vector subspaces of the MIMO channels, and one of them is selected for meeting a specific design criterion. Four design criteria are investigated, including the minimum sum of MSEs, the maximum sum of capacities, and the minimum or maximum sum of condition numbers, where the condition number is defined as the ratio of the largest to the smallest singular value of a MIMO channel. Compared to the conventional iterative methods, the proposed relay precoders based on minimizing the sum of MSEs or maximizing the sum of capacities achieve close performance while requiring much lower computational complexity. In contrast, the proposed designs based on minimizing or maximizing the sum of condition numbers provide further complexity reduction, with similar performance at high signal-to-noise ratios (SNRs) but a performance loss at low SNRs.