A Unified Approach to Optimal Transceiver Design for Nonregenerative MIMO Relaying

We propose a unified approach to transceiver optimization for nonregenerative multiple-input-multiple-output (MIMO) relay networks. This approach leads to new transceiver designs and reduces algorithmic complexity with adaptive implementations. First, we formulate a generic system model that accommodates various network topologies by imposing structural constraints on the source precoder, the relaying matrix, and the destination equalizer. Based on the minimum-mean-square-error (MMSE) criterion, we derive the optimal relaying matrix as a function of the other two matrices, thereby freeing the optimization problem from this matrix and its associated power constraint with no loss of optimality. Subsequently, we study how to optimize either the precoder or the equalizer under different structural constraints and propose an alternating algorithm for the joint design. When optimizing the equalizer, the optimum from the previous transmission block is chosen as the initial search point to speed up convergence and, hence, to reduce computational complexity. The proposed framework is further explained and numerically validated within the context of different system configurations.