In this paper, cooperative spectrum sensing under perfect and imperfect feedback channels is investigated. In particular, the optimal number of cognitive radios (CRs) required to minimize the total error of the sensing process when a perfect/imperfect reporting channels is derived. We show that the total error is always greater than zero regardless of the number of cooperating nodes. Furthermore, we derive a general formula that represents the boundaries of false alarm probability, and demonstrate that tightening the value of this boundary alone will not result in an improvement of system performance. Additionally, we show that errors in the reporting feedback channels can easily be mitigated when the optimal number of CRs participating in the sensing process is used; therefore, the overall detection probability is improved. Interestingly, results show that errors in the feedback channels can improve the detection probability at a low signal to noise ratio (SNR) link between the primary users (PUs) and the CRs.
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