  We consider a network, tasked with solving binary distributed detection,
consisting of N sensors, a fusion center (FC), and a feedback channel from the
FC to sensors. Each sensor is capable of harvesting energy and is equipped with
a finite size battery to store randomly arrived energy. Sensors process their
observations and transmit their symbols to the FC over orthogonal fading
channels. The FC fuses the received symbols and makes a global binary decision.
We aim at developing adaptive channel-dependent transmit power control policies
such that J-divergence based detection metric is maximized at the FC, subject
to total transmit power constraint. Modeling the quantized fading channel, the
energy arrival, and the battery dynamics as time-homogeneous finite-state
Markov chains, and the network lifetime as a geometric random variable, we
formulate our power control optimization problem as a discounted
infinite-horizon constrained Markov decision process (MDP) problem, where
sensors' transmit powers are functions of the battery states, quantized channel
gains, and the arrived energies. We utilize stochastic dynamic programming and
Lagrangian approach to find the optimal and sub-optimal power control policies.
We demonstrate that our sub-optimal policy provides a close-to-optimal
performance with a reduced computational complexity and without imposing
signaling overhead on sensors.
