Linearly Combined Signal Energy based Spectrum Sensing Algorithm for Cognitive Radio Networks with Noise Variance Uncertainty

This paper proposes novel and simple linearly combined signal energy based spectrum sensing algorithm for cognitive radio networks. It is assumed that the transmitter pulse shaping filter is known to the cognitive receiver. And, flat fading channels with synchronous and asynchronous receiver scenarios are considered. For each of these scenarios, the proposed detector is explained as follows: First, by introducing a combiner vector, over-sampled signals with total duration equal to the symbol period are combined linearly. Second, for this combined signal, the Signal-to-Noise ratio (SNR) maximization and minimization problems are formulated as Rayleigh quotient optimization problems. Third, by using the solutions of these problems, the ratio of the energy of the combined signals corresponding to the maximum and minimum SNRs are proposed as the test statistics. For these test statistics, analytical probability of false alarm ($Pf$) and probability of detection ($Pd$) expressions are derived for additive white Gaussian noise (AWGN) channel. It is shown that these detectors are robust against noise variance uncertainty. Moreover, simulation results demonstrate that the proposed detectors achieve better detection performance compared to that of the well known energy detector in AWGN and Rayleigh fading channels with noise variance uncertainty. The proposed detectors also guarantee the prescribed $Pf(Pd)$ in the presence of adjacent channel interference signals.