Sensors 2014, 14, 16766-16784; doi:10.3390/s140916766 OPEN ACCESS
sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article
WSNs Data Acquisition by Combining Hierarchical Routing Method and Compressive Sensing Zhiqiang Zou 1,2,3,*, Cunchen Hu 1,†, Fei Zhang 1,†, Hao Zhao 1 and Shu Shen 1,2,3 1
2
3
†
Nanjing University of Posts and Telecommunications, Nanjing 210003, China; E-Mails: [email protected] (C.H.); [email protected] (F.Z.); [email protected] (H.Z.); [email protected] (S.S.) Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing 210003, China Department of Geography, University of Wisconsin-Madison, Madison, WI 53706, USA These authors contributed equally to this work.
* Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +608-422-9099; Fax: +86-25-8586-6433. Received: 8 June 2014; in revised form: 22 August 2014 / Accepted: 26 August 2014 / Published: 9 September 2014
Abstract: We address the problem of data acquisition in large distributed wireless sensor networks (WSNs). We propose a method for data acquisition using the hierarchical routing method and compressive sensing for WSNs. Only a few samples are needed to recover the original signal with high probability since sparse representation technology is exploited to capture the similarities and differences of the original signal. To collect samples effectively in WSNs, a framework for the use of the hierarchical routing method and compressive sensing is proposed, using a randomized rotation of cluster-heads to evenly distribute the energy load among the sensors in the network. Furthermore, L1-minimization and Bayesian compressed sensing are used to approximate the recovery of the original signal from the smaller number of samples with a lower signal reconstruction error. We also give an extensive validation regarding coherence, compression rate, and lifetime, based on an analysis of the theory and experiments in the environment with real world signals. The results show that our solution is effective in a large distributed network, especially for energy constrained WSNs.
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Keywords: compressive sensing; wireless sensor networks; sparse representation; hierarchical routing method; energy efficiency
1. Introduction Wireless sensor networks (WSNs) are used in a variety of applications, such as environmental data collection, dangerous event monitoring, and disaster prevention [1,2]. However, they have some performance limits (e.g., energy consumption). Conventional WSNs protocols, like location-based protocols [3] and hierarchical protocols [4], are helpful in reducing bandwidth requirements. The theory of compressive sensing (CS) [5,6], a novel sensing/sampling paradigm that goes against common wisdom in data acquisition, can further reduce the bandwidth requirements and save more energy. Candès and Wakin [5] provided an introduction to compressive sampling, which is usually used in the field of efficient digital image compression. If a signal is known to be compressible, Donoho [6] found that the number of measurements M for this signal is dramatically smaller than the size of signal N (M i≠ j
(8)
The values of μ depend on a column in the CS matrix, where H i = ΦΨ i , H j = ΦΨ j , and T
< H i , H j >= Ψ i Φ T ΦΨ j . From the large number of experiments carried out, we find two methods are
able to decrease μ and increase the stability of CS recovery: (1) Adopting the Gaussian random measurement matrix, i.e., the RS scheme. This is because occurrence probability of 0’s and 1’s in a row of the Gaussian random measurement matrix is relatively fixed so that the coherence being relatively stable; (2) Increasing the number of cluster-head nodes at some extent. This is because that the measurement matrix based on the HRM is built by setting the value of the local head node to “1” and that of the other nodes in this cluster to “0”. Therefore, with an increasing number of cluster-head nodes, both the number of non cluster-head nodes within each new cluster and the total number of occurrences of the value “1” in a row decrease. This leads to the coherence μ decreasing.
3.4. Optimization of HRM_CS Model The HRM_CS objective is to provide a data acquisition method with longer lifetime and higher recovery accuracy under the real WSN environment. In this section, three performance metrics, namely, recovery accuracy (Error), communication cost and compression rate are analyzed. Based on this analysis, the optimized model from the two variant models of HRM_CS, i.e., HRM_CS1 with BCS and HRM_CS2 with L1-minimization can be obtained. Detailed experimental results are shown in Table 1, where the raw AD values denote the values from the card of Analog signals conversion Digital signals in a real WSN scenario GreenOrbs [18].
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Recovery Method
Threshold
Number of Cluster Heads M
L1 BCS L1 BCS L1 BCS L1 BCS L1 BCS L1 BCS
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40 40 56 56 68 68 84 84 100 100 140 140
Coherence
μ 1.950 1.950 1.495 1.495 1.085 1.085 0.658 0.658 0.556 0.556 0.388 0.388
Success Recovery Rate (%)
Error (%)
Variance
20 100 20 100 25 100 33 100 60 100 100 100
0.262 0.327 0.247 0.329 0.224 0.326 0.250 0.326 0.209 0.326 0.222 0.326
298.748 466.902 265.394 472.804 218.526 463.506 272.964 463.182 191.134 462.999 55.810 462.787
Error: recovery error; Variance: variance of raw AD values between original signal and recovery signal; L1: the recovery method based on L1-minimization; BCS: the recovery method based on BCS.
First, we investigate recovery accuracy (Error). The max Error is less than 1%, which meets the system demands. Although the HRM_CS1 is a little inferior to the HRM_CS2 with respect to recovery accuracy, HRM_CS1 is superior to the HRM_CS2 with respect to much more stability, i.e., the recovery method based on BCS has greater success than L1-minimization (hereafter called L1). Moreover, the number M of head nodes does not have a large effect on the error and variance of recovery in a BCS scenario. This is because BCS estimates the most probable value by maximizing a posteriori without depending on the particular WSN topology considered. Second, we analyze communication cost. Here we compute the total number of packets in the HRM_CS. The main steps are as follows: (1) N − M nodes in the cluster send their own sensor readings to M cluster-head nodes with an associated cost O(N ‒ M); (2) Next, superposition of the signal is carried out at the cluster-head node. In addition, the M cluster-head nodes transmit their own sensor readings to the sink along a routing path that minimizes the number of transmissions. On this path the packet is not processed but simply forwarded with the longest path O(N½); (3) The total cost of delivering packets to the sink from M cluster-head nodes is O(MN½). Last, we consider compression rate. From a sink point of view, compression rate is defined as M (1 − ) × 100 % . It is related to the number M of head nodes and increases as M decreases, where N is the N
total number of sensor nodes. From the above analysis, it can easily been seen that the WSN based on the HRM_CS has longer lifetime, compared with the classic approaches given by Equations (3) and (4), where the data are not well compressed. In particular, it can also been seen that the HRM_CS1 with M = 40 is our optimal choice since the higher compression rate and stability can be gotten at a little cost of recovery error, compared with the HRM_CS2.
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4. HRM_CS Framework
In this section we present our framework for implementing the HRM_CS, which performs well for fully distributed compression in WSNs and centralized recovery of an N-dimensional signal from a compressed M-dimensional signal at the sink. We first present the HRM_CS framework from a holistic viewpoint, and then, we describe WSNs deployment and clustering scenarios. Finally, we introduce the preprocessing for monitoring data, which can optimize the HRM_CS performance.
4.1. HRM_CS Framework for WSNs To implement the model in Equation (5) described in Section 2, we present our framework for WSNs data acquisition in detail. From Figure 1, we can see that the monitoring region is mapped with N = I × J nodes into two-dimensional matrix U in the first step. Note that U corresponding to the one-dimensional vector X in Equation (1). Then, in the next step, we logically re-organize U to build a clustering structure based on the hierarchical routing method, by randomly selecting cluster-heads and nodes within their clusters to evenly distribute the energy load among the sensors in the network. Each sensor node selected sends its data to local cluster base stations and then these data are transferred to the sink node. In the final step the superposition of the signal is completed and the original signal is recovered at the central sink node based on the optimization techniques. Figure 1. HRM_CS framework.
1≤ n ≤ N
CM YK = wk ,c xk ,c + z k ,c c = C1 M Y = Yk + Z k k =1 wk ,c ~ Gaussian N (0,1) −1 z k ,c , Z k ~ Gaussian N (0, β )
4.2. WSN Deployment We consider the deployment in GreenOrbs [18], which is a real WSN scenario set up for long-term monitoring of temperature and humidity in a forest without human supervision. We depict these nodes with their ID and location as shown in Figure 2. The operation of HRM_CS is broken up into rounds, where some node becomes a cluster-head for the current round while each non-cluster-head node decides the cluster to which it will belong for this round. Furthermore, according to the path of the message transmission in one round, we obtain the corresponding screen-shot of hierarchical cluster topology as shown in Figure 3.
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sensors relative position under a real WSN scenario in Y direction
Figure 2. Deployment in a real WSN scenario.
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4.3. Monitored Data Preprocessing In this section, we discuss the preprocessing of the monitored data. As the first step, based on the hierarchical cluster topology as shown in Figure 3, we select the top right region with the most densely distributed nodes as the experimental data. Let the relative position be depicted on the X- and Y-axis according to the grid structure preprocessing, while the raw AD values from the sensors corresponding to the monitored temperature are given on the Z-axis, as displayed in 3D in Figure 4. As is known, the AD raw values from the sensor must be converted into a natural signal temperature by the formula: temperature = −39.60 + 0.01 × (AD raw value) [18].
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Then, in order to optimize the compression rate, we compared two cases: sorted and unsorted monitored data values during the preprocessing. The X-axis depicts the 256 nodes while the Y-axis gives the raw AD values from the sensors corresponding to the monitored temperature as shown in Figure 5. Note that the compression rate for the “Sorted” case (Figure 5b) is superior to that for the “Unsorted” case (Figure 5a) in the preprocessing since it is affected by a discrete signal characteristic in the frequency domain. To demonstrate the effectiveness of the preprocessing, we create a sparse representation of the “Unsorted” (Figure 6a) and “Sorted” (Figure 6b) monitored data values by DCT. As shown in Figure 6, the X-axis depicts the 256 nodes while the Y-axis gives the AC components of the DCT transformation coefficients. The “Sorted” case is superior to the “Unsorted” case with respect to compression rate during the preprocessing since “Sorted” case decreases the total communication cost, which coincides with the conclusion in reference [12].
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Figure 6. (a) Sparsity of unsorted monitored data values during the preprocessing; (b) Sparsity of sorted monitored data values during the preprocessing. 350 AC components of the DCT transformation coefficients
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5. Performance Comparison
To extensively validate our HRM_CS, we focus on recovery error, energy consumption, and lifetime, compared with other classic WSNs [3,13,25]. As for the limited computational power and communication bandwidth in WSNs, the lifetime of WSNs is the most important metric.
Energy Consumption
As the analysis in the previous section shows, compared with the traditional clustering method, the energy consumption of the HRM_CS is substantially reduced by introducing compressive sampling. To analyze the energy consumption, we focus on the sending and receiving phase although there are multiple other phases, such as the sensor computation during the data acquisition. We adopt the energy model given as Equations (6) and (7) in Section 3. For further details refer to [4,26]. Lifetime
Assume that each sensor is a tiny powered sensing unit with a finite amount of energy that determines its lifetime. According to the computation energy consumed, when the energy left is lower than zero, we refer to this sensor as dead; otherwise it is alive. Recovery Error (err)
~ Assume an original signal X ∈ R N , and recovery signal X ∈ R N , then: err =
~ X −X X
2 2
N
2 2
=
(x
i
−~ xi ) 2
i =1
N
x i =1
2 i
(9)
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First, let us consider the effects of preprocessing on L1-minimization recovery [27]. Figure 7a shows the referenced values after subtracting the minimum value from the original signal. Figure 7b shows the recovery effects with preprocessing and applying a DCT, while Figure 7c shows the recovery effects without preprocessing but applying a DCT. Figure 7d depicts the recovery effects without preprocessing and using PCA. From this experiment, we find that the following results: (1) the recovery error in Figure 7b is smaller than those in Figure 7c,d; (2) the recovery errors in Figure 7c,d are of the same magnitude, however, from the viewpoint of varying trends, the method using PCA in Figure 7d is inferior to that using DCT in Figure 7c since the DCT transform can characterize the original signal using more coefficients with low and middle frequency. Next, we consider the performance of variants of the B HRM_CS model. Figure 8 shows the experimental results of the HRM_CS1, i.e., jointly using CS as the recovery algorithm and LEACH as the hierarchical routing method. Figure 9 depicts the experimental results with high recovery accuracy for the HRM_CS2, i.e., combining L1-minimization as the recovery algorithm and LEACH as the hierarchical routing method. Under the HRM_CS2 scenario, if there are too few 1’s when creating the measurement matrix, i.e., there are too few nodes to participate in the measurement, it will lead to failure during the recovery operation since the coherence between the measurement and sparsity matrices increases, as shown in Figure 10. Based on the above experiments, as for the stability of information recovery, we find that the applying CS naively like L1-minimization may be not proper under the real scenario of WSNs and HRM_CS1 is superior to HRM_CS2.
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In Figure 11, we demonstrate the recovery accuracy by comparing the HRM_CS1 with the GM_CS [13] based on the same recovery method, BCS. Figure 11 depicts the experimental results for the original and recovered signals, for which the error is less than 1 °C. Furthermore, the mean error of our HRM_CS1 0.0101 is slightly greater than the mean error of the GM_CS 0.0084 while HRM_CS1 has much longer lifetime than that of the GM_CS, as shown in Figure 13. Figure 11. Experimental results of the original and recovered signals with HRM_CS1 and GM_BCS. (a) HRM_CS1 mean error = 0.0101; (b) GM_BCS mean error = 0.0084. Temperature Diffrence between Original and Recovery Signals Based on GM+BCS 1.5
Temperature Diffrence between Original and Recovery Signals Based on LEACH+BCS 1.5
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As for the number of measurements M , i.e., the number of clusters in HRM_CS model, it is a vital parameter and has an influence on the lifetime of WSNs. Based on the basic compressive sensing theory [5], we know that M ³ 4 K , K is the number of significant components in original signal X while K varies with the different threshold value during the process of signal, which can be seen in Table 2. As a result, it can be seen from the Figure 12 that the lifetime of WSNs with different number of clusters also take the corresponding changes and the maximal lifetime is obtained at M = 40 . Table 2. Relationship of M, K and threshold value. Threshold Value
Number of Significant Components K
Number of Clusters M
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In the last graph, Figure 13, we show the impact of different data acquisition methods on the lifetime of WSNs. We compared four different methods, namely, HRM_CS, one_hop method [3], traditional LEACH [25] and GM_CS [13]. Here GM_CS means that we use the Gaussian random matrix as the routing matrix jointly with CS. As described in Table 1, L1-minimization is more unstable than BCS in this real WSN scenario. Therefore, here we use the BCS as CS recovery
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algorithm in our experiment. As shown in Figure 13, our solution HRM_CS, is superior to the other methods since the HRM_CS adopts compressive sampling, which decreases the number of communication packets and prolongs the lifetime as a consequence. Figure 12. Lifetime of WSNs with different number of clusters. Lifetime of WSNs No. No. No. No. No. No.
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6. Conclusions
In this paper, we proposed the HRM_CS, a model for data acquisition in WSNs by jointly applying the hierarchical routing method and compressive sensing, which minimizes global energy usage by decreasing the number of samples. HRM_CS outperforms conventional LEACH by introducing the sparse representation technology of PCA and DCT to capture the similarities and differences of the original signal. We studied an approximate recovery of the original signal from this smaller number of WSNs samples with a lower signal reconstruction error, such as L1-minimization or Bayesian compressed sensing. Thereafter we compared the performance of these two signal reconstruction
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techniques combining a different measurement matrix. The extensive validation demonstrates that our solution is effective in reducing energy dissipation and enhancing system lifetime, although it is not necessarily the most accurate. Other supervised WSNs routing algorithms, such as the multicast tree, even for arbitrary topology [12] and routing-free [14], also have attractive features and should be compared when applied jointly with CS in our future work. Supplementary Materials
Supplementary materials can be accessed at: http://www.mdpi.com/1424-8220/14/9/16766/s1. Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 61170065, 61373137, 61171053, 61103195, 61203217), Six Industries Talent Peaks Plan of Jiangsu Province (No. 2013-DZXX-014), the Natural Science Foundation of Jiangsu Province (No. BK2012436, No. BK20141429), the Scientific and Technological Support Project (Society) of Jiangsu Province (No. BE2014718, No. BE2013666), Natural Science Key Fund for Colleges and Universities in Jiangsu Province (No. 11KJA520001, No. 12KJA520002), Scientific Research & Industry Promotion Project for Higher Education Institutions (No. JHB2012-7), the NJUPT Natural Science Foundation (No. NY213157 and No. NY213037), and the State University Student STITP of China (No. 0700412017). In addition, we are grateful to the anonymous reviewers for their insightful and constructive suggestions. Author Contributions
Zhiqiang Zou is responsible for designing the model HRM_CS for data acquisition while Cunchen Hu and Fei Zhang is responsible for implementing this model. Hao Zhao and Shu Shen is responsible for verifying this model by doing extensive experiments. Glossary
The table of the key letters and abbreviations in the paper. Symbol HRM_CS
L1 HRM_CS1 HRM_CS2
χˆ
Explanation
Symbol
Model of combining
μ
HRM and CS Recovery algorithm L1minimization Model of combining the HRM and the BCS Model of combining the HRM and the L1 Estimated value of χ
Explanation
Symbol
Coherence between the measurement and sparsity
PCA
matrices
Φ
Measurement matrix
BCS
Ψ
Transform Matrix
X
wk ,c
Random Coefficients of
xk ,c
Sensor value of cth node
cth node of kth cluster of kth cluster
Y χ
Explanation Principal Component Analysis Bayesian Compressed Sensing One-dimensional data vector
M random projec-tions vector X K-sparse value of the original signal X
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Conflicts of Interest
The authors declare no conflict of interest. References
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sensors ISSN 1424-8220 www.mdpi.com/journal/sensors Article
WSNs Data Acquisition by Combining Hierarchical Routing Method and Compressive Sensing Zhiqiang Zou 1,2,3,*, Cunchen Hu 1,†, Fei Zhang 1,†, Hao Zhao 1 and Shu Shen 1,2,3 1
2
3
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Nanjing University of Posts and Telecommunications, Nanjing 210003, China; E-Mails: [email protected] (C.H.); [email protected] (F.Z.); [email protected] (H.Z.); [email protected] (S.S.) Jiangsu High Technology Research Key Laboratory for Wireless Sensor Networks, Nanjing 210003, China Department of Geography, University of Wisconsin-Madison, Madison, WI 53706, USA These authors contributed equally to this work.
* Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +608-422-9099; Fax: +86-25-8586-6433. Received: 8 June 2014; in revised form: 22 August 2014 / Accepted: 26 August 2014 / Published: 9 September 2014
Abstract: We address the problem of data acquisition in large distributed wireless sensor networks (WSNs). We propose a method for data acquisition using the hierarchical routing method and compressive sensing for WSNs. Only a few samples are needed to recover the original signal with high probability since sparse representation technology is exploited to capture the similarities and differences of the original signal. To collect samples effectively in WSNs, a framework for the use of the hierarchical routing method and compressive sensing is proposed, using a randomized rotation of cluster-heads to evenly distribute the energy load among the sensors in the network. Furthermore, L1-minimization and Bayesian compressed sensing are used to approximate the recovery of the original signal from the smaller number of samples with a lower signal reconstruction error. We also give an extensive validation regarding coherence, compression rate, and lifetime, based on an analysis of the theory and experiments in the environment with real world signals. The results show that our solution is effective in a large distributed network, especially for energy constrained WSNs.
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Keywords: compressive sensing; wireless sensor networks; sparse representation; hierarchical routing method; energy efficiency
1. Introduction Wireless sensor networks (WSNs) are used in a variety of applications, such as environmental data collection, dangerous event monitoring, and disaster prevention [1,2]. However, they have some performance limits (e.g., energy consumption). Conventional WSNs protocols, like location-based protocols [3] and hierarchical protocols [4], are helpful in reducing bandwidth requirements. The theory of compressive sensing (CS) [5,6], a novel sensing/sampling paradigm that goes against common wisdom in data acquisition, can further reduce the bandwidth requirements and save more energy. Candès and Wakin [5] provided an introduction to compressive sampling, which is usually used in the field of efficient digital image compression. If a signal is known to be compressible, Donoho [6] found that the number of measurements M for this signal is dramatically smaller than the size of signal N (M i≠ j
(8)
The values of μ depend on a column in the CS matrix, where H i = ΦΨ i , H j = ΦΨ j , and T
< H i , H j >= Ψ i Φ T ΦΨ j . From the large number of experiments carried out, we find two methods are
able to decrease μ and increase the stability of CS recovery: (1) Adopting the Gaussian random measurement matrix, i.e., the RS scheme. This is because occurrence probability of 0’s and 1’s in a row of the Gaussian random measurement matrix is relatively fixed so that the coherence being relatively stable; (2) Increasing the number of cluster-head nodes at some extent. This is because that the measurement matrix based on the HRM is built by setting the value of the local head node to “1” and that of the other nodes in this cluster to “0”. Therefore, with an increasing number of cluster-head nodes, both the number of non cluster-head nodes within each new cluster and the total number of occurrences of the value “1” in a row decrease. This leads to the coherence μ decreasing.
3.4. Optimization of HRM_CS Model The HRM_CS objective is to provide a data acquisition method with longer lifetime and higher recovery accuracy under the real WSN environment. In this section, three performance metrics, namely, recovery accuracy (Error), communication cost and compression rate are analyzed. Based on this analysis, the optimized model from the two variant models of HRM_CS, i.e., HRM_CS1 with BCS and HRM_CS2 with L1-minimization can be obtained. Detailed experimental results are shown in Table 1, where the raw AD values denote the values from the card of Analog signals conversion Digital signals in a real WSN scenario GreenOrbs [18].
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Recovery Method
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Coherence
μ 1.950 1.950 1.495 1.495 1.085 1.085 0.658 0.658 0.556 0.556 0.388 0.388
Success Recovery Rate (%)
Error (%)
Variance
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0.262 0.327 0.247 0.329 0.224 0.326 0.250 0.326 0.209 0.326 0.222 0.326
298.748 466.902 265.394 472.804 218.526 463.506 272.964 463.182 191.134 462.999 55.810 462.787
Error: recovery error; Variance: variance of raw AD values between original signal and recovery signal; L1: the recovery method based on L1-minimization; BCS: the recovery method based on BCS.
First, we investigate recovery accuracy (Error). The max Error is less than 1%, which meets the system demands. Although the HRM_CS1 is a little inferior to the HRM_CS2 with respect to recovery accuracy, HRM_CS1 is superior to the HRM_CS2 with respect to much more stability, i.e., the recovery method based on BCS has greater success than L1-minimization (hereafter called L1). Moreover, the number M of head nodes does not have a large effect on the error and variance of recovery in a BCS scenario. This is because BCS estimates the most probable value by maximizing a posteriori without depending on the particular WSN topology considered. Second, we analyze communication cost. Here we compute the total number of packets in the HRM_CS. The main steps are as follows: (1) N − M nodes in the cluster send their own sensor readings to M cluster-head nodes with an associated cost O(N ‒ M); (2) Next, superposition of the signal is carried out at the cluster-head node. In addition, the M cluster-head nodes transmit their own sensor readings to the sink along a routing path that minimizes the number of transmissions. On this path the packet is not processed but simply forwarded with the longest path O(N½); (3) The total cost of delivering packets to the sink from M cluster-head nodes is O(MN½). Last, we consider compression rate. From a sink point of view, compression rate is defined as M (1 − ) × 100 % . It is related to the number M of head nodes and increases as M decreases, where N is the N
total number of sensor nodes. From the above analysis, it can easily been seen that the WSN based on the HRM_CS has longer lifetime, compared with the classic approaches given by Equations (3) and (4), where the data are not well compressed. In particular, it can also been seen that the HRM_CS1 with M = 40 is our optimal choice since the higher compression rate and stability can be gotten at a little cost of recovery error, compared with the HRM_CS2.
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4. HRM_CS Framework
In this section we present our framework for implementing the HRM_CS, which performs well for fully distributed compression in WSNs and centralized recovery of an N-dimensional signal from a compressed M-dimensional signal at the sink. We first present the HRM_CS framework from a holistic viewpoint, and then, we describe WSNs deployment and clustering scenarios. Finally, we introduce the preprocessing for monitoring data, which can optimize the HRM_CS performance.
4.1. HRM_CS Framework for WSNs To implement the model in Equation (5) described in Section 2, we present our framework for WSNs data acquisition in detail. From Figure 1, we can see that the monitoring region is mapped with N = I × J nodes into two-dimensional matrix U in the first step. Note that U corresponding to the one-dimensional vector X in Equation (1). Then, in the next step, we logically re-organize U to build a clustering structure based on the hierarchical routing method, by randomly selecting cluster-heads and nodes within their clusters to evenly distribute the energy load among the sensors in the network. Each sensor node selected sends its data to local cluster base stations and then these data are transferred to the sink node. In the final step the superposition of the signal is completed and the original signal is recovered at the central sink node based on the optimization techniques. Figure 1. HRM_CS framework.
1≤ n ≤ N
CM YK = wk ,c xk ,c + z k ,c c = C1 M Y = Yk + Z k k =1 wk ,c ~ Gaussian N (0,1) −1 z k ,c , Z k ~ Gaussian N (0, β )
4.2. WSN Deployment We consider the deployment in GreenOrbs [18], which is a real WSN scenario set up for long-term monitoring of temperature and humidity in a forest without human supervision. We depict these nodes with their ID and location as shown in Figure 2. The operation of HRM_CS is broken up into rounds, where some node becomes a cluster-head for the current round while each non-cluster-head node decides the cluster to which it will belong for this round. Furthermore, according to the path of the message transmission in one round, we obtain the corresponding screen-shot of hierarchical cluster topology as shown in Figure 3.
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sensors relative position under a real WSN scenario in Y direction
Figure 2. Deployment in a real WSN scenario.
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Figure 6. (a) Sparsity of unsorted monitored data values during the preprocessing; (b) Sparsity of sorted monitored data values during the preprocessing. 350 AC components of the DCT transformation coefficients
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To extensively validate our HRM_CS, we focus on recovery error, energy consumption, and lifetime, compared with other classic WSNs [3,13,25]. As for the limited computational power and communication bandwidth in WSNs, the lifetime of WSNs is the most important metric.
Energy Consumption
As the analysis in the previous section shows, compared with the traditional clustering method, the energy consumption of the HRM_CS is substantially reduced by introducing compressive sampling. To analyze the energy consumption, we focus on the sending and receiving phase although there are multiple other phases, such as the sensor computation during the data acquisition. We adopt the energy model given as Equations (6) and (7) in Section 3. For further details refer to [4,26]. Lifetime
Assume that each sensor is a tiny powered sensing unit with a finite amount of energy that determines its lifetime. According to the computation energy consumed, when the energy left is lower than zero, we refer to this sensor as dead; otherwise it is alive. Recovery Error (err)
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First, let us consider the effects of preprocessing on L1-minimization recovery [27]. Figure 7a shows the referenced values after subtracting the minimum value from the original signal. Figure 7b shows the recovery effects with preprocessing and applying a DCT, while Figure 7c shows the recovery effects without preprocessing but applying a DCT. Figure 7d depicts the recovery effects without preprocessing and using PCA. From this experiment, we find that the following results: (1) the recovery error in Figure 7b is smaller than those in Figure 7c,d; (2) the recovery errors in Figure 7c,d are of the same magnitude, however, from the viewpoint of varying trends, the method using PCA in Figure 7d is inferior to that using DCT in Figure 7c since the DCT transform can characterize the original signal using more coefficients with low and middle frequency. Next, we consider the performance of variants of the B HRM_CS model. Figure 8 shows the experimental results of the HRM_CS1, i.e., jointly using CS as the recovery algorithm and LEACH as the hierarchical routing method. Figure 9 depicts the experimental results with high recovery accuracy for the HRM_CS2, i.e., combining L1-minimization as the recovery algorithm and LEACH as the hierarchical routing method. Under the HRM_CS2 scenario, if there are too few 1’s when creating the measurement matrix, i.e., there are too few nodes to participate in the measurement, it will lead to failure during the recovery operation since the coherence between the measurement and sparsity matrices increases, as shown in Figure 10. Based on the above experiments, as for the stability of information recovery, we find that the applying CS naively like L1-minimization may be not proper under the real scenario of WSNs and HRM_CS1 is superior to HRM_CS2.
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In Figure 11, we demonstrate the recovery accuracy by comparing the HRM_CS1 with the GM_CS [13] based on the same recovery method, BCS. Figure 11 depicts the experimental results for the original and recovered signals, for which the error is less than 1 °C. Furthermore, the mean error of our HRM_CS1 0.0101 is slightly greater than the mean error of the GM_CS 0.0084 while HRM_CS1 has much longer lifetime than that of the GM_CS, as shown in Figure 13. Figure 11. Experimental results of the original and recovered signals with HRM_CS1 and GM_BCS. (a) HRM_CS1 mean error = 0.0101; (b) GM_BCS mean error = 0.0084. Temperature Diffrence between Original and Recovery Signals Based on GM+BCS 1.5
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As for the number of measurements M , i.e., the number of clusters in HRM_CS model, it is a vital parameter and has an influence on the lifetime of WSNs. Based on the basic compressive sensing theory [5], we know that M ³ 4 K , K is the number of significant components in original signal X while K varies with the different threshold value during the process of signal, which can be seen in Table 2. As a result, it can be seen from the Figure 12 that the lifetime of WSNs with different number of clusters also take the corresponding changes and the maximal lifetime is obtained at M = 40 . Table 2. Relationship of M, K and threshold value. Threshold Value
Number of Significant Components K
Number of Clusters M
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In the last graph, Figure 13, we show the impact of different data acquisition methods on the lifetime of WSNs. We compared four different methods, namely, HRM_CS, one_hop method [3], traditional LEACH [25] and GM_CS [13]. Here GM_CS means that we use the Gaussian random matrix as the routing matrix jointly with CS. As described in Table 1, L1-minimization is more unstable than BCS in this real WSN scenario. Therefore, here we use the BCS as CS recovery
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algorithm in our experiment. As shown in Figure 13, our solution HRM_CS, is superior to the other methods since the HRM_CS adopts compressive sampling, which decreases the number of communication packets and prolongs the lifetime as a consequence. Figure 12. Lifetime of WSNs with different number of clusters. Lifetime of WSNs No. No. No. No. No. No.
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of cluster is of cluster is of cluster is of cluster is of cluster is of cluster is
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Figure 13. Lifetime of WSNs under different methods. Lifetime of WSNs LEACH One_hop GM_CS HRM_CS
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6. Conclusions
In this paper, we proposed the HRM_CS, a model for data acquisition in WSNs by jointly applying the hierarchical routing method and compressive sensing, which minimizes global energy usage by decreasing the number of samples. HRM_CS outperforms conventional LEACH by introducing the sparse representation technology of PCA and DCT to capture the similarities and differences of the original signal. We studied an approximate recovery of the original signal from this smaller number of WSNs samples with a lower signal reconstruction error, such as L1-minimization or Bayesian compressed sensing. Thereafter we compared the performance of these two signal reconstruction
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techniques combining a different measurement matrix. The extensive validation demonstrates that our solution is effective in reducing energy dissipation and enhancing system lifetime, although it is not necessarily the most accurate. Other supervised WSNs routing algorithms, such as the multicast tree, even for arbitrary topology [12] and routing-free [14], also have attractive features and should be compared when applied jointly with CS in our future work. Supplementary Materials
Supplementary materials can be accessed at: http://www.mdpi.com/1424-8220/14/9/16766/s1. Acknowledgments
This work is supported by the National Natural Science Foundation of China (Nos. 61170065, 61373137, 61171053, 61103195, 61203217), Six Industries Talent Peaks Plan of Jiangsu Province (No. 2013-DZXX-014), the Natural Science Foundation of Jiangsu Province (No. BK2012436, No. BK20141429), the Scientific and Technological Support Project (Society) of Jiangsu Province (No. BE2014718, No. BE2013666), Natural Science Key Fund for Colleges and Universities in Jiangsu Province (No. 11KJA520001, No. 12KJA520002), Scientific Research & Industry Promotion Project for Higher Education Institutions (No. JHB2012-7), the NJUPT Natural Science Foundation (No. NY213157 and No. NY213037), and the State University Student STITP of China (No. 0700412017). In addition, we are grateful to the anonymous reviewers for their insightful and constructive suggestions. Author Contributions
Zhiqiang Zou is responsible for designing the model HRM_CS for data acquisition while Cunchen Hu and Fei Zhang is responsible for implementing this model. Hao Zhao and Shu Shen is responsible for verifying this model by doing extensive experiments. Glossary
The table of the key letters and abbreviations in the paper. Symbol HRM_CS
L1 HRM_CS1 HRM_CS2
χˆ
Explanation
Symbol
Model of combining
μ
HRM and CS Recovery algorithm L1minimization Model of combining the HRM and the BCS Model of combining the HRM and the L1 Estimated value of χ
Explanation
Symbol
Coherence between the measurement and sparsity
PCA
matrices
Φ
Measurement matrix
BCS
Ψ
Transform Matrix
X
wk ,c
Random Coefficients of
xk ,c
Sensor value of cth node
cth node of kth cluster of kth cluster
Y χ
Explanation Principal Component Analysis Bayesian Compressed Sensing One-dimensional data vector
M random projec-tions vector X K-sparse value of the original signal X
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Conflicts of Interest
The authors declare no conflict of interest. References
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