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The authors consider centralised cooperative spectrum sensing under correlated shadowing in this study. Formulating the spectrum sensing problem as a Gauss-Gauss hypothesis test, they use a linear quadratic rule and show that it is the optimal detector under Bayesian criterion. They derive the upper and lower Bhattacharyya bounds and investigate the error performance of spectrum sensing by studying the behaviour of these upper and lower bounds. They also study the asymptotic error performance in two different scenarios of finite and infinite area networks. They show that by increasing the number of nodes the sensing error probability approaches zero in both cases but with different decay rates. The lower the correlation between nodes or the larger the network area, the faster the decay.