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On the Probability of False Alarm of the Power Spectral Density Split Cancellation Method

The cooperative power spectral density split cancellation (CPSC) method was recently proposed for cooperative spectrum sensing, with the novelties of being robust against noise uncertainty and having low computational complexity. The probability of false alarm has been derived in the related paper, but under assumptions that make it inaccurate. In this letter, we derive the correct cumulative distribution functions of the main random variables that form the decision statistic of the CPSC model. We also derive the correlation coefficient between sub-band decisions, necessary information that was neglected in the reference paper, leading to an expression for the final probability of false alarm that is more accurate than the original one. Our theoretical results are validated with simulations.