Abstract
Two-way multiple-input multiple-output (MIMO) relaying has attracted much attention for its capability to significantly improve the system performance and signal coverage in wireless communications, where an information exchange is realized through relays using the same amount of channel resources as that for direct transmission. In such systems, relay preocder designs play a key role to fully exploit spatial multiplexing and diversity gains. It should be noted that existing well-known diagonalization techniques for MIMO channels based on singular value decomposition cannot be directly applied to two-way MIMO relaying due to bidirectional transmission and reception at the relays. This limitation makes relay precoder designs in two-way MIMO relaying become a challenging issue. In this dissertation, we present new relay precoder designs for two-way amplify-and-forward MIMO relay systems with multiple relays and two terminals, where only a single relay is selected to participate in data transmission. For a given relay, we first derive the mean-squared error (MSE) matrices of the received signals at the two terminals, and then 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 subsequently 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. As compared with 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. Furthermore, we investigate antenna power allocation and relay selection algorithms based on the above-mentioned relay precoder designs for a multiple-relay case. Two antenna power allocation schemes are derived; one is based on minimizing the sum of asymptotic MSE lower bounds to approach the minimum sum of MSEs, and the other is obtained according to the distribution of singular values of both effective MIMO channels to approach the maximum sum of capacities, where more power is allocated to subchannels with larger singular values and less power is allocated to those with smaller singular values. It is demonstrated that, at high SNRs, the derived schemes contribute power gains as compared with equal power allocation among antennas. With these results, we then propose two joint algorithms to obtain the selected relays as well as the corresponding relay precoders with antenna power allocation for the minimum sum of MSEs and for the maximum sum of capacities, respectively. The proposed joint algorithms employ exhaustive search for the solutions, and achieve close performance to the conventional iterative methods with exhaustive-search relay selection at high SNRs. To reduce the search complexity, two simplified relay selection algorithms are also developed by utilizing the asymptotic MSE lower bounds, one based on the maximum sum of capacities and the other based on the minimum sum of MSEs. It is shown that the former still maintains close-to-optimal performance at high SNRs, while the latter has a small performance loss.