We study the problem of joint quantization and power allocation in wireless sensor networks where spatially distributed sensors observe a Gaussian random source, quantize the resulting noisy observations, and transmit over orthogonal fading channels to a remote fusion center (FC). The role of the FC is to reconstruct the source with minimal distortion using linear minimum mean square error estimation rule. In this paper, we undertake the design of joint quantization and power allocation based on the following optimization problem: minimize the reconstruction distortion for a given total network power consumption. To address this problem, at each sensor node uniform scalar quantization is assumed. Moreover, assuming pseudo-quantization noise model we show that the problem can be solved using a block-coordinate descent type algorithm which iteratively optimizes the quantization bits and the power allocations. The algorithm takes into account the spatial correlation, the observation noise, and the channel quality of the sensors. Numerical and simulation examples corroborate the analytical results. The examples illustrate that the proposed design holds a considerable performance gain compared to a quantization scheme based on uniform power allocation to the sensors.
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