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We consider a network, tasked with solving binary distributed detection,consisting of N sensors, a fusion center (FC), and a feedback channel from theFC to sensors. Each sensor is capable of harvesting energy and is equipped witha finite size battery to store randomly arrived energy. Sensors process theirobservations and transmit their symbols to the FC over orthogonal fadingchannels. The FC fuses the received symbols and makes a global binary decision.We aim at developing adaptive channel-dependent transmit power control policiessuch that J-divergence based detection metric is maximized at the FC, subjectto total transmit power constraint. Modeling the quantized fading channel, theenergy arrival, and the battery dynamics as time-homogeneous finite-stateMarkov chains, and the network lifetime as a geometric random variable, weformulate our power control optimization problem as a discountedinfinite-horizon constrained Markov decision process (MDP) problem, wheresensors' transmit powers are functions of the battery states, quantized channelgains, and the arrived energies. We utilize stochastic dynamic programming andLagrangian approach to find the optimal and sub-optimal power control policies.We demonstrate that our sub-optimal policy provides a close-to-optimalperformance with a reduced computational complexity and without imposingsignaling overhead on sensors.

On Distributed Detection in EH-WSNs With Finite-State Markov Channel and Limited Feedback