Compressive sensing meets unreliable link: sparsest random scheduling for compressive data gathering in lossy WSNs

Compressive Sensing (CS) has been recognized as a promising technique to reduce and balance the transmission cost in wireless sensor networks (WSNs). Existing efforts mainly focus on applying CS to reliable WSNs, namely, each wireless link is 100% reliable. However, our experimental results show that traditional compressive data gathering (CDG) could result in arbitrarily bad recovery performance, when the wireless links are lossy. In this paper, we study the impact of packet loss on compressive data gathering and ways to improve its robustness using sparsest random scheduling (SRS). The key idea of our scheme is to treat each sampling value as one CS measurement, which helps us to reduce the impact of packet loss on the recovery accuracy. Our scheme also outperforms the tradition CDG in reliable WSNs in that our scheme has significantly lowered transmission cost. To achieve this, we present a sparsest measurement matrix where each row has only one nonzero element. More importantly, we propose a representation basis to sparsify the gathering data, and prove that our measurement matrix satisfies the restricted isometric property (RIP) with high probability. Extensive experimental results show our scheme can recover the data accurately with packet loss ratio up to $15\%$, while traditional CDG can hardly recover the data under similar or even better conditions.