Resource allocation optimization for distributed vector estimation with digital transmission

We consider the problem of distributed estimation of an unknown zero-mean Gaussian random vector with a known covariance matrix in a wireless sensor network (WSN). Sensors transmit their binary modulated quantized observations to a fusion center (FC), over orthogonal MAC channels subject to fading and additive noise. Assuming the FC employs the linear minimum mean-square error (MMSE) estimator, we obtain an upper bound on MSE distortion. We investigate optimal resource allocation strategies that minimize the MSE bound, subject to total bandwidth (measured in quantization bits) and total transmit power constraints. 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 are in agreement with our analysis and show that the proposed bit and power allocation scheme outperforms uniform bit and power allocation scheme.