Multi-Frequency GLRT Spectrum Sensing for Wideband Cognitive Radio

The problem of spectrum sensing in multi-frequency cognitive radio systems is addressed. We show that as the sensed bandwidth increases, the primary user detection is governed by a low signal-to-noise ratio (low-SNR) regime. By means of low-SNR approximations, we show that the optimal generalized likelihood ratio test (GLRT) only depends on the second order statistics of the observations and on a shaping kernel that highlights the relevant parameters required for detection. Furthermore, the ML estimates of the unknown model parameters are derived for multi-frequency systems, which allow closed-form expressions for the GLRT statistic. The detection performance and the kernel interpretation are supported with simulation results.