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Modeling and analysis of cooperative spectrum sensing is an important aspectin cognitive radio systems. In this paper, the problem of energy detection (ED)of an unknown signal over Nakagami-$m$ fading is revisited. Specifically, ananalytical expression for the local probability of detection is derived, whileusing the approach of ED at the individual secondary user (SU), a new fusionrule, based on the likelihood ratio test, is presented. The channels betweenthe primary user to SUs and SUs to fusion center are considered to beindependent Nakagami-$m$. The proposed fusion rule uses the channel statistics,instead of the instantaneous channel state information, and is based on theNeyman-Pearson criteria. Closed-form solutions for the system-level probabilityof detection and probability of false alarm are also derived. Furthermore, aclosed-form expression for the optimal number of cooperative SUs, needed tominimize the total error rate, is presented. The usefulness of factor graph andsum-product-algorithm models for computing likelihoods, is also discussed tohighlight its advantage, in terms of computational cost. The performance of theproposed schemes have been evaluated both by analysis and simulations. Resultsshow that the proposed rules perform well over a wide range of thesignal-to-noise ratio.

Another look in the Analysis of Cooperative Spectrum Sensing over Nakagami-$m$ Fading Channels