A Low-Complexity Hybrid Framework for Combining-Type Non-regenerative MIMO Relaying

Combining-type relay systems can benefit from distributed array gain if the signals retransmitted from different relays are superimposed coherently at the destination. For this purpose, we propose a low-complexity hybrid framework in which the non-regenerative multiple-input-multiple-output relaying matrix at each relay is generated by cascading two substructures, akin to an equalizer for the backward channel and a precoder for the forward channel. For each of these two substructures, we introduced two one-dimensional parametric families of candidate matrix transformations. The first family, non-cooperative by nature, depends only on the backward or forward channel of the same relay. The second (cooperative) family also makes use of information derived from the channels of other relays. This hybrid framework allows for the classification and comparison of all possible combinations of these substructures, including several previously investigated methods and their generalizations. The design parameters can be optimized based on individual channel realizations or on channel statistics; in the latter case, the optimum parameters can be well approximated by linear functions of the signal-to-noise ratios. The proposed methods achieve a good balance between performance and complexity: they outperform existing low-complexity strategies by a large margin in terms of both capacity and bit-error rate, and at the same time, are significantly simpler than previous near-optimal iterative algorithms.