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.

[1]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[2]  Donald F. Towsley,et al.  Data gathering capacity of large scale multihop wireless networks , 2008, 2008 5th IEEE International Conference on Mobile Ad Hoc and Sensor Systems.

[3]  Athanasios V. Vasilakos,et al.  Compressed data aggregation for energy efficient wireless sensor networks , 2011, 2011 8th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.

[4]  Kannan Ramchandran,et al.  Distributed Sparse Random Projections for Refinable Approximation , 2007, 2007 6th International Symposium on Information Processing in Sensor Networks.

[5]  David L Donoho,et al.  Compressed sensing , 2006, IEEE Transactions on Information Theory.

[6]  Chiara Santi,et al.  On the data gathering capacity and latency in wireless sensor networks , 2010, IEEE Journal on Selected Areas in Communications.

[7]  Soummya Kar,et al.  Gossip Algorithms for Distributed Signal Processing , 2010, Proceedings of the IEEE.

[8]  Stavros Toumpis Asymptotic Capacity Bounds for Wireless Networks with Non-Uniform Traffic Patterns , 2008, IEEE Transactions on Wireless Communications.

[9]  Jack K. Wolf,et al.  Noiseless coding of correlated information sources , 1973, IEEE Trans. Inf. Theory.

[10]  R. Srikant,et al.  The multicast capacity of large multihop wireless networks , 2010, TNET.

[11]  Xinbing Wang,et al.  On the Capacity and Delay of Data Gathering with Compressive Sensing in Wireless Sensor Networks , 2011, 2011 IEEE Global Telecommunications Conference - GLOBECOM 2011.

[12]  Muriel Médard,et al.  A power efficient sensing/communication scheme: Joint source-channel-network coding by using compressive sensing , 2011, 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[13]  Siyuan Chen,et al.  Order-optimal data collection in wireless sensor networks: Delay and capacity , 2009, 2009 6th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks.

[14]  Martin J. Wainwright,et al.  Information-Theoretic Limits on Sparse Signal Recovery: Dense versus Sparse Measurement Matrices , 2008, IEEE Transactions on Information Theory.

[15]  Michele Zorzi,et al.  On the interplay between routing and signal representation for Compressive Sensing in wireless sensor networks , 2009, 2009 Information Theory and Applications Workshop.

[16]  Jun Sun,et al.  Compressive data gathering for large-scale wireless sensor networks , 2009, MobiCom '09.

[17]  Antonio Ortega,et al.  Spatially-Localized Compressed Sensing and Routing in Multi-hop Sensor Networks , 2009, GSN.

[18]  Shaojie Tang,et al.  Multicast capacity for large scale wireless ad hoc networks , 2007, MobiCom '07.

[19]  Richard J. Barton,et al.  Toward Optimal Data Aggregation in Random Wireless Sensor Networks , 2007, IEEE INFOCOM 2007 - 26th IEEE International Conference on Computer Communications.

[20]  Hesham El Gamal On the scaling laws of dense wireless sensor networks: the data gathering channel , 2005, IEEE Trans. Inf. Theory.

[21]  Jun Sun,et al.  Efficient Measurement Generation and Pervasive Sparsity for Compressive Data Gathering , 2010, IEEE Transactions on Wireless Communications.

[22]  Muriel Médard,et al.  Compressive sensing over networks , 2010, 2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[23]  Panganamala Ramana Kumar,et al.  RHEINISCH-WESTFÄLISCHE TECHNISCHE HOCHSCHULE AACHEN , 2001 .

[24]  Mingyan Liu,et al.  On the Many-to-One Transport Capacity of a Dense Wireless Sensor Network and the Compressibility of Its Data , 2003, IPSN.

[25]  Panganamala Ramana Kumar,et al.  The Number of Neighbors Needed for Connectivity of Wireless Networks , 2004, Wirel. Networks.