Large system performance of power-constrained distributed detection with analog local processing

The problem of decentralized detection in a sensor network subjected to a total average power constraint is investigated assuming that local sensor decisions are based on analog relay amplifier processing. For both deterministic and stochastic Gaussian signals, asymptotic performance in a large sensor system is analyzed by deriving the error exponents. The large system analysis shows that, in the case of deterministic signals when the whole system is subjected to a total average power constraint it is better to combine as many not-so-good local decisions as possible rather than relying on a few very-good local decisions. However, in the case of stochastic signals there are an optimal number of local sensor decisions that should be combined at the fusion center in order to obtain the best performance. While up to this optimal limit it is better to divide the power among many not-so-good local decisions, beyond this value the performance starts to degrade as we increase the number of sensors. In other words, in the case of distributed detection of a stochastic signal there is a minimum power level that each node needs to maintain if they are to make a useful contribution to the final fusion decision.