Abstract
Recently, an eigenmode-selection approach was suggested for relay precoding in a two-way amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system, where a finite set of relay precoders are constructed based on the eigenspaces of the effective MIMO channels and one of them with appropriate eigenmodes is selected to meet a specific design criterion. To design a relay precoder subject to the minimization/maximization of the sum of the condition numbers of the effective MIMO channels, this method needs to search for the solution in a relay procoding set of size 2K!, where the condition number is defined as the ratio of the largest to the smallest singular value of a MIMO channel and K denotes the degrees of freedom of the system. Although the eigenmode-selection precoding scheme can achieve close-to-optimal performance, the required search complexity would become prohibitively high when K is large. In this thesis, we propose some low-complexity relay precoder designs based on eigenmode selection for a two-way AF MIMO relay system. We first exploit properties of the condition numbers of the effective MIMO channels, and then present two set-reduction methods based on these properties to reduce the search complexity in selecting appropriate eigenmodes for the minimization/maximization of the sum of the condition numbers. As compared to the original eigenmode-selection precoding scheme, the proposed approaches reach similar performance but reduce the search complexity by a factor of K(K-1).