Optimal linear MIMO relay communication under a constraint on the condition number of relay transform matrix

In this paper, we consider a communication system employing a relay equipped with multi antennas. The relay transmits a linear transformation of its received signal vector to the destination node. We study the design of Relay Transformation Matrix (RTM) by maximizing the average and instantaneous SNR at the destination assuming a limited relay transmit power. To achieve the full multiplexing of such a MIMO system, we also study the problem of the SNR maximization under an additional constraint on the condition number of relay transform matrix. In addition, we derive the best RTM which achieves a certain condition number and has up to three different singular values.