Coherent fusion of information for optimal detection in sensor networks

In this work, we consider the problem of centralized detection in wireless sensor networks when the sensors transmit coherently through a multiple access channel. We derive the optimal weighting at each sensor that maximizes the error exponent. Firstly, the noiseless case is considered and a closed form solution to the problem is found. Secondly, we generalize the formulation to consider additive noise at the fusion center. For the noisy case, we propose a suboptimal approach which allows us to find a closed-form solution. Interestingly, the proposed approaches reduce to the extraction of a normalized eigenvector of a generalized eigenvalue problem. The performance of the proposed scheme is illustrated by means of numerical results, showing that the suboptimal approach has a similar performance to that of the optimal one; and that the proposed scheme outperforms other techniques, such as orthogonal transmissions or the maximization of the signal-to- noise ratio.