Impact of the dimension of the observation space on the decision thresholds for GLRT detectors in spectrum sensing

The generalized likelihood ratio test (GLRT) detectors have been widely used for spectrum sensing in cognitive radio. However, due to difficulties in characterizing the exact distributions of the statistics, the decision thresholds obtained so far are based on the asymptotic assumption that the sample size is very large while the dimension of the observation space is very small. Not enough attention has been paid to the accuracy of the thresholds for the application with a moderate or large dimension, which usually occurs in the sensing scenarios with multiple antennas and/or multiple nodes. In this paper, we formulate the distributions in terms of a summation form of a series of chi-square distributions. Utilizing the series, the improved thresholds for GLRT detectors are then given by using the generalized inverse expansion of Cornish-Fisher type. The simulation results show that the improved thresholds are more robust to the dimension of the observation space, and can lead to higher spectrum utilization for the cognitive user and more reliable detection performance than the asymptotic ones.