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