Detection of Gaussian sources using dumb wireless sensors

We consider the signal detection problem using a large wireless sensor networks (WSN) . In our WSN, each sensor transmits a single linear combination of the data sample it receives to a fusion center (FC). We wish to design an optimal choice of these linear precoders for the signal detection problem. The detection performance is evaluated using the error exponent approach. We provide an optimal solution in the following cases: 1) when the sensors reception is free of noise 2) when an orthogonality constraint is imposed on precoders.