Energy Efficient Transmissions in Cognitive MIMO Systems With Multiple Data Streams

We investigate energy-efficient communications for time-division multiple access (TDMA) multiple-input multiple-output (MIMO) cognitive radio (CR) networks operating in underlay mode. In particular, we consider the joint optimization over both the time resource and the transmit precoding matrices to minimize the overall energy consumption of a single cell secondary network with multiple secondary users (SUs), while ensuring their quality of service (QoS). The corresponding mathematical formulations turn out to be non-convex, and thus of high complexity to solve in general. We give a comprehensive treatment of this problem, considering both the cases of perfect channel state information (CSI) and statistical CSI of the channels from the SUs to the primary receiver. We tackle the non-convexity by applying a proper optimization decomposition that allows the overall problem to be efficiently solved. In particular, we show that when the SUs only have statistical CSI, the optimal solution can be found in polynomial time. Moreover, if we consider additional integer constraints on the time variable which is usually a requirement in practical wireless system, the overall problem becomes a mixed-integer non-convex optimization which is more complicated. By exploring the special structure of this particular problem, we show that the optimal integer time solution can be obtained in polynomial time with a simple greedy algorithm. When the SUs have perfect CSI, the decomposition based algorithm is guaranteed to find the optimal solution when the secondary system is under-utilized. Simulation results show that the energy-optimal transmission scheme adapts to the traffic load of the secondary system to create a win-win situation where the SUs are able to decrease the energy consumption and the PUs experience less interference from the secondary system. The effect is particularly pronounced when the secondary system is under-utilized.