On the optimal power-distortion region for asymmetric Gaussian sensor networks with fading

We consider the estimation of a Gaussian source by a Gaussian sensor network where L distributed sensors transmit noisy observations of the source through a fading Gaussian multiple access channel (MAC) to a fusion center (FC). Since sensor power is usually limited, our goal is to characterize the optimal tradeoff between the transmission cost, i.e., the power vector P = (P₁, P₂, ..., P_L), and the average estimation distortion, D. We focus on asymmetric fading sensor networks in which the sensors have differing signal to noise ratios and transmission powers. We present necessary and sufficient conditions for the achievability of (L + 1)-tuples (P₁, P₂, ..., P_L, D). For a symmetric Gaussian sensor network with deterministic and equal-magnitude fading, we derive the optimal power-distortion tradeoff. We also provide an achievable power-distortion region for the asymmetric sensor network with deterministic fading by analyzing the transmission of scaled versions of vector-quantized observations. We show that some of the power-distortion tuples achievable by this scheme are not achievable via an uncoded system.