Low-Complexity Relay Precoder Designs for Two-Way AF MIMO Relay Systems

An eigenmode-selection approach was recently presented for relay precoding subject to the minimum/maximum sum of condition numbers of the effective multiple-input multiple-output (MIMO) channels in a two-way amplify-and forward (AF) MIMO relay system. Although this method can achieve close-to-optimal performance, it would involve high search complexity for the solution in a relay precoding set of size 2.M!, where M is the degrees of freedom of the MIMO relay system. In this paper, we propose low-complexity relay precoder designs based on eigenmode selection for two-way AF MIMO relay systems. We first exploit the properties of condition numbers of the effective MIMO channels, and then present two set-reduction methods accordingly for eigenmode-selection precoding to minimize/maximize the sum of condition numbers. As compared with the original eigenmode-selection precoding scheme, the proposed designs reach similar performance but reduce the search complexity by a factor of M(M-1).