  We consider a wireless sensor network, consisting of N heterogeneous sensors
and a fusion center (FC), tasked with detecting a known signal in uncorrelated
Gaussian noises. Each sensor can harvest randomly arriving energy and store it
in a finite-size battery. Sensors communicate directly with the FC over
orthogonal fading channels. Each sensor adapts its transmit symbol power, such
that the larger its stored energy and its quantized channel gain are, the
higher its transmit symbol power is. To strike a balance between energy
harvesting and energy consumption, we formulate two constrained optimization
problems (P1) and (P2), where in both problems we seek the jointly optimal
local decision thresholds and channel gain quantization thresholds. While in
(P1) we maximize the Jdivergence of the received signal densities at the FC, in
(P2) we minimize the average total transmit power, subject to certain
constraints. We solve (P1) and (P2), assuming that the batteries reach their
steady-state. Our simulation results demonstrate the effectiveness of our
optimization on enhancing the detection performance in (P1), and lowering the
average total transmit power in (P2). They also reveal how the energy
harvesting rate, the battery size, the sensor observation and communication
channel parameters impact obtained solutions.
