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The problem of spectrum sensing in multi-frequency cognitive radio systems is addressed. The authors 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, they 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.
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