Widely-linear transceiver design for amplify-and-forward MIMO relaying

This paper deals with the problem of transceiver optimization for amplify-and-forward multiple-inputmultiple-output (MIMO) cooperative networks with multiple relays. We consider the case where precoding at the source, forwarding at the relays, and decoding at the destination are all carried out by means of widely-linear (WL) structures. On the basis of the minimum-mean-square-error criterion with appropriate power constraints, we propose a closed-from design for the WL-MIMO source precoder, relaying matrices, and destination decoder. Numerical results, in terms of bit-error rate, demonstrate that, when the disturbance exhibits improper or noncircularity features, the proposed design ensures significant performance gain with respect to its linear counterpart.