Power scheduling of distributed estimation in sensor networks with repetition coding

This paper considers the optimal power scheduling for the distributed estimation of a source parameter using quantized samples of noisy sensor observations in a wireless sensor network (WSN). Repetition codes are used to transmit quantization bits of sensor observations to achieve unequal error protection, and a quasi-best linear unbiased estimate is constructed to estimate the source parameter at the fusion center (FC). Based on the adopted distributed estimation scheme (DES), we optimize the power scheduling among sensors to minimize the L^1-norm of the power vector subject to the desired tolerance, which implies minimizing the total transmission power. Since the optimization problem is not convex, we propose a low-complexity alternative, which minimizes the L^2-norm of the power vector while insuring the desired tolerance. We derive the closed form solution of the L^2-norm power scheduling scheme. Simulation results show that the total power consumption of the L^2-norm power scheduling scheme is close to that of the L^1-norm power scheduling scheme, while complexity analysis demonstrates that the L^2-norm power scheduling scheme has very low complexity.