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This paper investigates joint source and relay precoders design problem for a multi-input multi-output cognitive relay network (MIMO-CRN). A mathematical problem is formulated with the aim to maximize the energy efficiency (EE) of the secondary system, subject to transmit power constraints and interference constraints. The optimization is performed with respect to the source and relay precoding matrices. Such maximization problem is a challenging non-convex fractional programming problem, which is first divided into two sub-problems corresponding to each of the precoding matrices. Further, the tools of the fractional programming, augmented Lagrangian multiplier, and iterative optimization are employed to jointly design the source and relay precoding matrices. We also study the impact of minimum rate requirement of secondary user (SU) on the achievable EE by incorporating a quality-of-service (QoS …