Design and Analysis of In-Network Computation Protocols With Compressive Sensing in Wireless Sensor Networks

Compressive sensing (CS) provides a new paradigm for correlated data processing and transmission over wireless sensor networks (WSNs). In this paper, we take a new look to investigate the performance of CS for data gathering from the perspective of in-network computation. We formulate the problem of computing random projections for CS in WSNs as in-network function computation in random geometric networks. We focus on the design and performance analysis of the protocols that are efficient in terms of computation complexity. We first propose an efficient tree-based computation protocol with an optimal refresh rate and characterize the scaling laws of energy and latency requirements, which show that it can reduce energy consumption and latency compared with the traditional approach. Then, we present a more efficient block computation protocol by considering the correlations of temporal measurements in function computation to improve the performance in terms of refresh rate and energy consumption. We also devise a gossip-based scheme to improve the robustness of function computation, which is able to distribute computation results to all the nodes throughout the network. We show that the proposed protocol can improve upon the existing gossip-based schemes in terms of energy consumption. Finally, simulation results are also presented to demonstrate the effectiveness of the proposed protocols.