  We consider a wireless sensor network, consisting of N heterogeneous sensors
and a fusion center (FC), that is tasked with solving a binary distributed
detection problem. Each sensor is capable of harvesting randomly arrived energy
and storing it in a finite capacity battery. Sensors are informed of their
fading channel states, via a bandwidth-limited feedback channel from the FC.
Each sensor has the knowledge of its current battery state and its channel
state (quantized channel gain). Our goal is to study how sensors should choose
their transmit powers such that J-divergence of the received signal densities
under two hypotheses at the FC is maximized, subject to certain (battery and
power) constraints. We derive the optimal power map, which depends on the
energy arrival rate, the battery capacity, and the battery states probabilities
at the steady state. Using the optimal power map, each sensor optimally adapts
its transmit power, based on its battery state and its channel state. Our
simulation results demonstrate the performance of our proposed power adaptation
scheme for different system parameters.
