In this paper we tackle distributed detection of a non-cooperative target with a Wireless Sensor Network (WSN). When the target is present, sensors observe an unknown random signal with amplitude attenuation depending on the distance between the sensor and the target (unknown) positions, embedded in white Gaussian noise. The Fusion Center (FC) receives sensors decisions through error-prone Binary Symmetric Channels (BSCs) and is in charge of performing a (potentially) more-accurate global decision. The resulting problem is a one-sided testing with nuisance parameters present only under the target-present hypothesis. We first focus on fusion rules based on Generalized Likelihood Ratio Test (GLRT), Bayesian and hybrid approaches. Then, aimed at reducing the computational complexity, we develop fusion rules based on generalizations of the well-known Locally-Optimum Detection (LOD) framework. Finally, all the proposed rules are compared in terms of performance and complexity.