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In this paper we analyze the performance of the distributed power detection algorithm operating in a shadowing environment and with communication constraints. A well performing detection algorithm is critical for detecting a primary user's signal for dynamic spectrum allocation purposes. Dynamic spectrum allocation allows a secondary user to use a spectrum chunk provided that the primary user is not disturbed. In a shadowing environment one secondary user could not guarantee a reliable detection of primary user's signal with acceptable false detection probability. The detection performance can be greatly enhanced by combining measurements from secondary users at a fusion centre. Such combining requires communication bandwidth. We provide equations and numerically compute the bounds for two extremes of communication requirements. In the first scheme the secondary users send a full loglikelihood ratio, which in principle would require infinite amount of communication capacity. In the second scheme the secondary users send to the fusion centre only one bit, describing the hard decision made based on the loglikelihood ratio. These two cases provide performance bounds for possible practical implementations.