Energy and latency analysis for in-network computation with compressive sensing in wireless sensor networks

In this paper, we study data gathering with compressive sensing from the perspective of in-network computation in random networks, in which n nodes are uniformly and independently deployed in a unit square area. We formulate the problem of data gathering to compute multiround random linear function. We study the performance of in-network computation with compressive sensing in terms of energy consumption and latency in centralized and distributed fashions. For the centralized approach, we propose a tree-based protocol for computing multiround random linear function. The complexity of computation shows that the proposed protocol can save energy and reduce latency by a factor of Θ(√(n/log n)) for data gathering comparing with the traditional approach, respectively. For the distributed approach, we propose a gossip-based approach and study the performance of energy and latency through theoretical analysis. We show that our approach needs fewer transmissions than the scheme using randomized gossip.