Optimization of multi-antenna GLRT-based spectrum sensing for cognitive radio

This paper investigates the optimization of the generalized likelihood ratio test (GLRT) eigenvalue-based spectrum sensing detector in terms of decision thresholds and sensing time. In order to guarantee the interests of primary and secondary users simultaneously, the sensing performance is assessed using the total error rate, i.e., the summation of probabilities of false alarm and missed detection. Therefore, the generalized statistical distributions of the test statistic are derived under the absence and presence of primary users, assuming an arbitrary number of receive antennas. These distributions are necessary for the analyses of the total error rate performance and the optimization. The optimization consists of two parts. Firstly, the optimal decision threshold is numerically obtained, which can minimize the total error rate under the constraints of target probabilities of false alarm and missed detection. Secondly, the optimal sensing time is obtained when a target total error rate is guaranteed, so that the spectrum sensing process can be accelerated without the loss of sensing accuracy. Furthermore, the simulation and theoretical results reveal that the chosen optimal decision thresholds benefit the primary and secondary users simultaneously and the chosen optimal sensing time improves the speed of spectrum sensing.