This paper introduces a Bayesian framework to detect multiple signals embedded in noisy observations, from an array of sensors. For various states of knowledge on the communication channel and the noise at the receiving sensors, a marginalization procedure based on random matrix theory techniques, in conjunction with the maximum entropy principle, is used to compute the Neyman-Pearson hypothesis testing criterion. Quite remarkably, although rather involved, explicit expressions for the Bayesian detector are derived which enable to decide on the presence of signal sources in a noisy wireless environment. Under the hypotheses that the true channel conditions adhere the maximum entropy model, the proposed detector is the optimal Neyman-Pearson detector; if so, the performance of the derived decision criteria can be used as an upper-bound for the performance of alternative detectors. In particular, simulation results are provided that suggest that the classical energy detector is close-to-optimal when the noise power is a priori known to the sensor array, especially when many sources simultaneously transmit, while the conditioning number-based detector, used classically when the noise power is unknown, is shown to perform poorly in comparison to the proposed optimal detector.