On the Capacity and Delay of Data Gathering with Compressive Sensing in Wireless Sensor Networks

Compressive sensing (CS) provides a new paradigm for efficient data gathering in wireless sensor networks (WSNs). The theory of CS allows to reconstruct all sensor data of the network, while only collecting a small number of measurements at a sink. In this paper, we consider a scenario where a sink collects spatially correlated sensor data from n sensor nodes randomly deployed in a region. We investigate the fundamental limitation of data gathering with CS in such a scenario, in terms of capacity and delay. We construct a scheduling and routing scheme based on CS for data gathering in WSNs. We show that the proposed scheme can achieve a per-node transport capacity of Θ(1/ log n) under physical interference model. Furthermore, we also study the delay performance of the proposed scheme and show that the delay for collecting a snapshot with CS is Θ(√n log n). In particular, our results demonstrate that the proposed scheme can achieve a capacity gain of Θ(n/log n) over the case without CS and the delay can also be reduced by a factor of Θ(√n/log n).