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In this paper, the authors obtain approximations for the optimal Log-Likelihood Ratio (LLR) decision rule in cooperative detection when local energy detectors are assumed. Considering conditional independence, they also show under which bandwidth and sampling frequency regimes these approximations hold best. Furthermore, they present simulations where the performance of the approximated LLR decision rule is compared with other suboptimal decision rules given in the literature such as the optimal linear weighting. The simulations show that the density functions of the approximations exhibit negligible error in comparison with the exact ones, when conditions on bandwidth and sampling frequencies are met.
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