Compressed Sensing Based Joint Rate Allocation and Routing Design in Wireless Sensor Networks

Hindawi Wireless Communications and Mobile Computing Volume 2018, Article ID 6261453, 11 pages https://doi.org/10.1155/2018/6261453 Research Article Compressed Sensing Based Joint Rate Allocation and Routing Design in Wireless Sensor Networks Jie Hao 1 ,1 Ran Wang,1 Baoxian Zhang ,2 Yi Zhuang ,1 and Bing Chen 1 Nanjing University of Aeronautics and Astronautics, Nanjing, China University of Chinese Academy of Sciences, Beijing, China 2 Correspondence should be addressed to Baoxian Zhang; Received 11 September 2017; Accepted 18 February 2018; Published 27 March 2018 Academic Editor: Paolo Barsocchi Copyright © 2018 Jie Hao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Compressed sensing for wireless sensor networks has attracted a lot of research attention in the last decade for its advantages in energy saving, robustness, and so on. Nevertheless, existing solutions mostly focus on the data compression performance while neglecting the energy efficiency. In this paper, we first present the joint resource allocation problem formulation based on compressed sensing. Then a distributed algorithm to compute the sampling rate and routes utilizing local network status is proposed. We conduct extensive experiments based on meteorological wireless sensor networks to verify the merit of our mechanism; it is shown that the proposed mechanism is able to achieve very high efficiency in terms of network lifetime and sensing quality compared with existing approaches. 1. Introduction Compressed sensing (CS, also known as compressive sensing) is an efficient tool to process data as it enables sparse sampling while guaranteeing high sampling quality in wireless sensor networks. With CS, the sink node only needs to collect the compressed measurements 𝑦𝑚×1 based on the sensing matrix Φ𝑚×𝑛 instead of the original measurements 𝑥𝑛×1 ; that is, 𝑦𝑚×1 = Φ𝑚×𝑛 𝑥𝑛×1 , 𝑚 < 𝑛. Φ𝑚×𝑛 is generally a Gaussian random matrix in which no entry is zero. The compressed sensing using this kind of nonsparse sensing matrix is referred to as dense compressed sensing. Typically, collection tree is by default used for supporting compressed data collection [1, 2]. Although the network performance is improved somehow, the communication cost needed to collect the compressed measurements caused by dense compressed sensing throughout the network is overlooked. Fortunately, sparse compressed sensing whose sensing matrix is sparse itself can achieve the same compression performance theoretically and experimentally with much less sampling and communication cost [3–6]. Figure 1 shows how sparse CS can reduce the communication consumption compared with dense CS. In this figure, a sensor network consisting of 𝑛 sensor nodes needs to collect all the measurements from the sensor nodes. Gaussian sensing matrix is used to compress the original measurement and we assume 𝑚 < 𝑛 compressed measurements are required and transmitted to sink by a routing tree. For a single compressed measurement 𝑦𝑗 , that is, the 𝑗th entry of 𝑦𝑚×1 , each node multiplies its own measurement 𝑥𝑖 with 𝜙𝑖𝑗 , adds it with the incoming weighted measurement, and then forwards the added measurement to its next hop until sink receives the compressed measurement 𝑦𝑗 = (𝜙1𝑗 , 𝜙2𝑗 , . . . , 𝜙𝑛𝑗 )(𝑥1 , 𝑥2 , . . . , 𝑥𝑛 )𝑇 . As 𝜙𝑖𝑗 ≠ 0, ∀1 ≤ 𝑖 ≤ 𝑚, 1 ≤ 𝑗 ≤ 𝑛, dense CS implies that each node gets involved in each single compressed measurement. As a result dense CS would generate 𝑂(𝑚𝑛) transmissions in total. In comparison, in sparse CS there is only a single 1 in each row of Φ and 0 elsewhere. It implies only 𝑚 nodes are chosen as the source nodes and hence the total transmission count is 𝑂(𝑚 log 𝑛) as the routing tree depth is 𝑂(log 𝑛). From the temporal perspective, sparse CS indicates each sensor node takes samples under different sampling schedules. Although more energy efficient than dense CS, most literature on sparse CS decouples the sampling and routing design and only concentrates on one side as it assumes either the sampling [5, 6] or the communication energy consumption with energy hungry sensors [3] is neglectable. However, in practice we 2 Wireless Communications and Mobile Computing 1 4 4 4 4 4 4 4 4 1 1 1 3 1 1 Sink Source node Non-source node Sink Source node Non-source node (a) Dense compressed sensing (b) Sparse compressed sensing Figure 1: Sparse sampling can reduce the communication cost compared with dense sampling. observe that the sampling or routing energy consumption could not be neglected in many cases. Take the typical radio module Semtech XE1205 radio transceiver [7] and SHT7x Humidity and Temperature Sensor [8] as examples. The typical TX power is around 62 mA, and the energy consumption for one byte is roughly 22 uJ at 76 kbps. The typical power in humidity measuring status is about 0.55 mA, and it takes a maximum of 20 ms for an 8-bit measurement. Thus the energy consumption for each measurement is 33 uJ. We can see that neither energy consumption for sampling nor routing should be ignored in this case for energy efficiency optimization. Therefore, this paper considers both sampling and routing energy consumption and aims at finding a joint design mechanism based on CS entitled Distributed Sampling Rate and Routing (DSRR) mechanism to optimize the overall energy consumption. The main contributions of this paper are summarized as follows: (i) We formulate a compressed sensing based joint design problem that tackles sampling and routing simultaneously. (ii) We propose a distributed algorithm that only utilizes local network status to achieve prolonged network lifetime and high sensing quality. (iii) We conduct extensive experiments based on real data set and network deployment from SensorScope [9], which demonstrate the effectiveness of the proposed joint design. The rest of this paper is organized as follows. A literature review of existing work is presented in Section 2. Section 3 describes the a priori knowledge of compressed sensing followed by Section 4 that presents compressed sensing based joint design formulation and the distributed algorithm. Section 5 reports our experimental results. Finally we make a conclusion in Section 6. for data compression. CDG (Compressive Data Gathering) [10] utilizes spatial correlation and uses CS for snapshot data gathering. Ji et al. [12] explore CS for both snapshot and continuous data gathering under channel interference model. Other than reducing the measurements, some research work explores the impact of routing on the CS performance. Quer et al. [1] combined geographical routing with CS and were surprised to observe that CS is not as good as expected. Luo et al. [2] explore the network throughput of tree based CS and conclude that the hybrid manner that only uses CS near the root of the tree can (...truncated)