Optimal quantization and power allocation for energy-based distributed sensor detection

We consider the decentralized detection of an unknown deterministic signal in a spatially uncorrelated distributed wireless sensor network. N samples from the signal of interest are gathered by each of the M spatially distributed sensors, and the energy is estimated by each sensor. The sensors send their quantized information over orthogonal channels to the fusion center (FC) which linearly combines them and makes a final decision. We show how by maximizing the modified deflection coefficient we can calculate the optimal transmit power allocation for each sensor and the optimal number of quantization bits to match the channel capacity