Optimal Non-regenerative Linear MIMO Relay for Orthogonal Space Time Codes

We consider a multi-input multi-output (MIMO) communication system in which a linear non-regenerative MIMO relay assists the data transmission between a source and a destination node using orthogonal space time block codes (OSTBC). We derive the relay transformation matrix (RTM) by minimizing the symbol error rate (or maximizing the capacity) of the system under a constraint on the relay´s transmitted power. The RTM is derived in the presence of the direct source-destination path and for spatially-correlated additive noise vectors. We show that the proposed RTM can significantly enhance the performance of the system in terms of the capacity/symbol error rate. Interestingly, our simulation results, in various conditions, reveal that the proposed method provides close to the optimum data rate even for the system without OSTBC. This suboptimal approach is justified, as the complexity of computing the proposed RTM is significantly less than the computation complexity of the RTM which maximizes the non-regenerative capacity.