Designing of a relay precoding matrix using singular value decomposition

In this paper, a relay precoder matrix is designed for an underlay multi-input multi-output cognitive relay network (MIMO-CRN), where a secondary system communicates through a non-regenerative relay. An optimization problem is formulated such that the energy efficiency of the secondary system is maximized subject to a transmit power and an interference threshold constraint at the relay. The formulated problem is a non-convex fractional programming problem, which is solved by using the singular value decomposition method combined with the fractional programming theory. Numerical results are provided to show the effectiveness of the proposed scheme.