International Journal of Applied Engineering Research, ISSN 0973-4562 Volume 12, Number 4 (2017) pp. 452–460 © Research India Publications, http://www.ripublication.com/ijaer.htm Exploiting Sparsity in Wireless Sensor Networks for Energy Saving: A Comparative Study Mohammed E. El-Telbany Computers and Systems Dept., Electronics Research Institute, Cairo, Egypt. Maha A. Maged Space Communincations Dept., NARSS, Cairo, Egypt. Abstract: To optimize the communication cost, data aggre- gation in wireless sensor networks (WSNs) is considered an effective technique for energy-saving. The data aggregation in large scale WSNs inevitably faces many challenging prob- lems such as: energy consumption. Fortunately, most sensing data are spatially and temporally correlated and compressible. Matrix completion, which is, an extension to compressive sensing, is considered as a promising reconstruction scheme to recover having missing with low-energy consumption. This paper proposes a data-recovery scheme which can be caste as a low-rank matrix completion framework. In the proposed methodology, the random access protocol is combined with low-rank matrix completion algorithm to minimize the nec- essary information that sensors transmit. The results indicate the superiority of the proposed algorithm over compressive sensing ones. AMS subject classification: Keywords: Wireless sensor networks, Compressed sens- ing, Matrix completion, Random access protocol, Energy consumption. 1. Introduction Maney researches in recent years are concerned with devel- oping energy efficient solutions to prolong the lifetime of Wireless Sensor Networks (WSNs). Some of these solutions are adjusting sensing ranges [1], sleep scheduling [2], clus- tering routing protocol [3], and data aggregation [4], [5], [6]. WSNs face a challenge that the information collected is incomplete due the limited energy availability to pro- duce samples and communication constraints. To solve this, many developers and researchers propose protocols and algo- rithms, including data compression and aggregation. On the other hand, compressive sensing(CS) [7] and matrix com- pletion(MC) [8]-[11] provide efficient ways to accurately recover the whole data from incomplete information. CS studies the process of acquiring and reconstructing a signal utilizing the prior knowledge that it is sparse. This sparse signal can be reconstructed from limited number of observa- tions [12], [13]. Similar to CS, MC allows the recovery of a randomly under-sampled low-rank matrix. This low-rank MC can be regarded as an extension to the concept of sparse vector to the matrix domain, which estimates the temporal and spatial subspaces simultaneously [14]. However, unlike CS-based methods, MC-based methods do not require the prior dictionary to sparsify the original signal. Actually, both CS and MC can recover the signal from fewer samples by solving an optimization problem to significantly reduce the number of transmissions over communication channel [15]. The low-rank MC, has been studied in many applications such as collaborative filtering [16], system identification [17], computer vision, video denoising [18], [19], machine learn- ing [20], pattern recognition and data mining [21]. In ref [22] studied the determination the location of sensors in WSN, where the Multi-Dimensional Scaling technique estimates their distances from a reference point which needs completion of this distance matrix. It is found that the pairwise distance matrix is low rank compared to its dimension [17]. The energy consumption of the WSN is proportional to the sampling rate