Bandwidth And Power Constrained Distributed Vector Estimation In Wireless Sensor Networks

We address bandwidth and power constrained distributed vector estimation problem in a wireless sensor network where sensors observe a common unknown zero-mean Gaussian random vector with a known covariance matrix. Sensors transmit their quantized and digitally modulated correlated observations to a fusion center (FC), over orthogonal channels subject to fading and additive white Gaussian noise (AWGN). We assume the FC employs the linear mean square error (LMMSE) estimator to estimate the unknown vector and the WSN is subject to total bandwidth (measured in quantization bits) and total transmit power constraints. We provide an upper bound on the mean square error (MSE) distortion at the FC and investigate the optimal quantization bit and transmit power allocation among sensors such that this bound is minimized. The bound consists of two terms, where the first and second terms, respectively, account for the MSE distortion due to quantization and communication channel errors. Therefore, we find the bit allocation that minimizes the first distortion term. Given the optimal bit allocation, we obtain the power allocation that minimizes the second distortion term. Our simulation results corroborate our analysis and show that our proposed bit and power allocation scheme outperforms uniform bit and power allocation scheme