Capacity and Delay Analysis for 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). In this paper, with the assumption that sensor data is sparse we apply the theory of CS to data gathering for a WSN where n nodes are randomly deployed. We investigate the fundamental limitation of data gathering with CS for both single-sink and multi-sink random networks under protocol interference model, in terms of capacity and delay. For the single-sink case, we present a simple scheme for data gathering with CS and derive the bounds of the data gathering capacity. We show that the proposed scheme can achieve the capacity Θ(\frac{nW}{M}) and the delay Θ(M\sqrtfrac{nlog n}), where W is the data rate on each link and M is the number of random projections required for reconstructing a snapshot. The results show that the proposed scheme can achieve a capacity gain of Θ (\frac{n}{M}) over the baseline transmission scheme and the delay can also be reduced by a factor of Θ(\fracsqrt{n\log n}{M}). For the multi-sink case, we consider the scenario where n_d sinks are present in the network and each sink collects one random projection from n_s randomly selected source nodes. We construct a simple architecture for multi-session data gathering with CS. We show that the per-session capacity of data gathering with CS is Θ(\frac{n\sqrt{n}W}{M n_d \sqrt{n_s \log n}}) and the per-session delay is Θ(M\sqrtfrac{{n}{log n}}). Finally, we validate our theoretical results for the scaling laws of the capacity in both single-sink and multi-sink networks through simulations.