Distributed Sensing with Orthogonal Multiple Access: To code or not to Code?

Abstract

We consider the estimation distortion of a distributed sensing system with finite number of sensor nodes, in which the nodes observe a common phenomenon and transmit their observations to a fusion center over orthogonal channels. In particular, we investigate whether the coded scheme (separate source-channel coding) outperforms the uncoded scheme (joint source-channel coding) or not. To this end, we explicitly derive the estimation distortion of a coded heterogeneous sensing system with diverse node and channel configurations. Based on this result, we show that in a homogeneous sensing system with identical node and channel configurations, the coded scheme outperforms the uncoded scheme if the number of nodes is $K=1$ or $K=2$. For homogenous sensing systems with $K\geq3$ nodes and general heterogeneous sensing systems, we also present explicit conditions for the coded scheme to perform better than the uncoded scheme. Furthermore, we propose to minimize the estimation distortion of heterogeneous sensing systems with hybrid coding, i.e., some nodes use the coded scheme and other nodes use the uncoded scheme. To determine the optimal hybrid coding policy, we develop three greedy algorithms, in which the pure greedy algorithm minimizes distortion greedily, the group greedy algorithm improves performance by using a group of potential sub-polices, and the sorted greedy algorithm reduces computational complexity by using a pre-solved iteration order. Our numerical and Monte Carlo results show that the proposed algorithms closely approach the optimal policy in terms average estimation distortion.