  We consider a wireless sensor network, consisting of N heterogeneous sensors
and a fusion center (FC), tasked with solving a binary distributed detection
problem. Sensors communicate directly with the FC over orthogonal fading
channels. Each sensor can harvest randomly arriving energy and store it in a
battery. Also, it knows its quantized channel state information (CSI), acquired
via a limited feedback channel from the FC. We propose a transmit power control
strategy such that the J-divergence based detection metric is maximized,
subject to an average transmit power per sensor constraint. The proposed
strategy is parametrized in terms of the channel gain quantization thresholds
and the scale factors corresponding to the quantization intervals, to strike a
balance between the rates of energy harvesting and energy consumption for data
transmission. This strategy allows each sensor to adapt its transmit power
based on its battery state and its qunatized CSI. Finding the optimal strategy
requires solving a non-convex optimization problem that is not differentiable
with respect to the optimization variables.We propose near-optimal strategy
based on hybrid search methods that have a low-computational complexity.
