Unbalanced Expander Based Compressive Data Gathering in Clustered Wireless Sensor Networks

Conventional compressive sensing-based data gathering (CS-DG) algorithms require a large number of sensors for each compressive sensing measurement, thereby resulting in high energy consumption in clustered wireless sensor networks (WSNs). To solve this problem, we propose a novel energy-efficient CS-DG algorithm, which exploits the better reconstruction accuracy of the adjacency matrix of an unbalanced expander graph. In the proposed CS-DG algorithm, each measurement is the sum of a few sensory data, which are jointly determined by random sampling and random walks. Through theoretical analysis, we prove that the constructed <inline-formula> <tex-math notation="LaTeX">${M\times N}$ </tex-math></inline-formula> sparse binary sensing matrix is the adjacency matrix of a <inline-formula> <tex-math notation="LaTeX">$(k,\varepsilon )$ </tex-math></inline-formula> unbalanced expander graph when <inline-formula> <tex-math notation="LaTeX">${M=O\left ({k\log {N / k}}\right )}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${t = O\left ({ {{N_{c} / {\left ({ {kq} }\right )}}} }\right )}$ </tex-math></inline-formula> for WSNs with <inline-formula> <tex-math notation="LaTeX">$N_{c}$ </tex-math></inline-formula> clusters, where <inline-formula> <tex-math notation="LaTeX">${0\leq q\leq 1}$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">${N_{c}>k}$ </tex-math></inline-formula>. Simulation results show our proposed CS-DG has better performance than existing algorithms in terms of reconstruction accuracy and energy consumption. When hybrid energy-efficient distributed clustering algorithm is used, to achieve the same reconstruction accuracy, our proposed CS-DG can save energy by at least 27.8%.