OPTIMUM ENERGY ALLOCATION FOR DETECTION IN WIRELESS SENSOR NETWORKS Thesis

The problem of binary hypothesis testing in a wireless sensor network is studied in the presence of noisy channels and for non-identical sensors. We have designed a mathematically tractable fusion rule for which optimal energy allocation for individual sensors can be achieved. In this thesis we considered two methods for transmitting the sensor observations; binary modulation and M-ary modulation. In binary modulation we are able to allocate the energy among the sensors and protect the individual quantized bits where as the M-ary modulation provides optimum energy allocation only among the sensors. The goal is to design a fusion rule and an energy allocation for the nodes subject to a limit on the total energy of all the nodes so as to optimize a cost function. Two cost functions were considered; the probability of error and the J-divergence distance measure. Probability of error is the most natural criteria used for binary hypothesis testing problem. Distance measure is applied when it is difficult to obtain a closed form for the error probability. Results of optimal energy allocation and the resulting probability of error are presented for the two cost functions. Comparisons are drawn between the two cost functions regarding the fusion rule, energy allocations and the error probability.