Compressive sensing based routing and data reconstruction scheme for IoT based WSNs

Abstract

Data acquisition problem on large distributed wireless sensor networks (WSNs) is considered as a challenge in the growth of Internet of Things (IoT). Recently, the combination of compressive sensing (CS) and routing techniques has attracted much attention of researchers. An open question of this combination is how to integrate these techniques effectively for specific tasks. On the other hand, CS data reconstruction process is considered as one of the CS challenges because it requires to recover N data from only M measurement where M< <N. Through this paper, we propose a new scheme for data gathering in IoT based heterogeneous WSN that includes a new effective Deterministic Clustering using CS technique (DCCS) to handle the data acquisition problem. DCCS reduces the total overhead computational cost needed to self-organize WSN using a simple approach and then uses CS at each sensor node to decrease the overall energy consumption and increase the network lifetime. The proposed scheme includes also an effective CS reconstruction algorithm called Random Selection Matching Pursuit (RSMP) to improve the recovery process at the base station (BS). RSMP adds a random selection process during the forward step to give the opportunity for more columns to be selected as an estimated solution in each iteration. The simulation results show that the proposed scheme succeeds to minimize the overall network power consumption and prolong the network lifetime beside provide better performance in CS data reconstruction.

Keywords

Internet of things clustering based wireless sensor networks compressive sensing routing techniques data reconstruction network lifetime

1 Introduction

Internet of Things (IoT) is considered as a primary bridge connecting between physical and human world [45]. IoT becomes one of the significant and attractive fields of researches through which researchers hope to control all everyday usages via the Internet [1]. IoT elements include different objects from the technological environment, or even living organisms as well as devices that are already deeply embedded in technological environments such as smartphones or cars [6]. By integrating computational abilities in all kinds of things and living organisms, it will be possible providing a big leap in many sectors: Health, military, home, entertainment etc. [2, 3]. IoT consists of combinations between different technologies such as cloud computing, WSNs, big data and data information [5, 7]. Nowadays, WSNs widely used in various fields. Since IoT contains huge numbers of connected sensor nodes, WSNs are indeed able to integrate into IoT [42, 44]. The main task for IoT components (such as sensors, phones and RFID tags) is to sense, collect and store data then send them to the base station (BS) [41]. On the other side, data acquisition problem on large distributed WSNs is considered impediment in the further development of the IoT technology [8, 9].

It is highly required to find creative techniques that prolong the network lifetime [43]. Various techniques have been proposed such as routing protocols or data compression schemes [10–16 , 62–68]. The data compression methods can be used to minimize the overall wireless channels transmitted data. This technique can be used to reduce the energy consumed by nodes communication which is considered as one of the major power consumers in IoT.

In the perspective of the compression, CS has been given as a sufficient method for signal sampling and compression [34]. In CS, the signal can be successfully sampled less than the rate of Nyquist theory if the signal is sparse by natural or by transformer [34]. In CS, the signal is sampled with compress simultaneously, rather than sample then compress like the other traditional compression techniques [10]. It can be reconstructed without any significant loss in the information [11, 12]. The general CS framework equation can be expressed as the following: $y = φ x,$ (1)

Here, the compressed samples vector y ∈ R^M, with M << N, Φ is an M × N CS matrix, which is random matrices like Gaussian or Bernoulli distribution matrix in mostly CS methods, and signal vector x ∈ R^N. In this system, ∥x ∥ ₀ = S < M < N [13, 14]. Based on the CS method, if the sensors reading x is S-sparse, i.e., x has just S basis vectors where (N - S) are zeros and only S are nonzero. Then ∥L ∥ ₁ norm minimization solution as shown in Equation (2) can be used to reconstruct x using only M-measurements [37]. $x = argmin {∥ x ∥}_{1} subject to y = Φ x .$ (2)

In the context of routing algorithms, routing is considered as the most important communication paradigms that can optimize energy consumption in WSNs [26]. Designing suitable routing protocols for WSNs is considered as an important issue [21]. The hierarchical cluster-based routing protocol is considered as the most efficient protocol in terms of scalability and energy efficiency for WSNs [38]. In the Hierarchical protocols, sensor nodes are organized in groups called clusters [4]. In each cluster, one node acts as an aggregation point which called cluster head (CH) and cluster members. Each CH aggregates the data received from its cluster members. Finally, the BS receives these aggregated data from the CHs. In this case, the total data amount which is transmitted to the BS can be significantly reduced [27].

The integration between routing protocols and the CS method can help to solve the data acquisition problem [16]. However, finding an efficient way to integrate routing protocols and compressive data aggregation is an NP-complete problem [15]. Through this paper, we propose an effective Deterministic Clustering using CS technique (DCCS) for heterogeneous WSNs to handle the data acquisition problem. DCCS reduces the total overhead computational cost needed to self-organize WSNs using a simple approach and then using CS at each sensor node to minimize the overall network energy consumption and increases the network lifetime. Secondly, we propose an efficient reconstruction algorithm called Random Selection Matching Pursuit (RSMP) to improve the recovery process at the BS side using CS. RSMP adds a random selection process during the forward step to give the opportunity for more columns to be selected as an estimated solution in each iteration. The proposed algorithms are validated by simulations with respect to power consumption and network lifetime.

Our contributions can be highlighted in the following points:

We propose a new DCCS algorithm that distributes the network into a fixed number of clusters in each round to overcome the stability problem and optimize energy consumption. Electing a CH depends on the residual energy of sensor nodes as in [39].

In order to decrease the total energy consumption, DCCS divides the communication process into an intra-cluster and inter-cluster communication process. During the intra-cluster process, DCCS organizes the nodes in each cluster into a chain using the proposed chain construction procedure. In the inter-cluster process, using the proposed chain construction procedure, DCCS organizes the CHs in a chain considering CHs as cluster members with the BS as CH.

To enhance the CS data gathering and reconstruction process, DCCS allows the BS to dynamically change the measurement matrix depending on the network status.

To improve the reconstruction process at the BS, the RSMP algorithm is proposed. RSMP adds a random selection process to the forward step in order to give the chance for all columns to be selected as an estimated solution in each round.

Finally, we provide a comprehensive simulation results using randomly generated data and real data. The results prove that the performance of the proposed scheme exceeds existing baseline algorithms in terms of network lifetime, energy consumed and reconstruction error.

The rest of the paper is structured as follows: in Section II, the related works are explained. Section III presents the new algorithms. Section IV presents the simulation validation. Section V provides the conclusion of our research paper.

2 Literature review

During the last few years, IoT applications such as surveillance and monitoring applications have attracted a number of researchers. Nodes energy constraints problem led to several routing protocols for WSNs [23]. For example, Deterministic Energy-efficient Clustering (DEC) algorithm is proposed for WSNs [39]. In DEC, WSNs nodes are divided into clusters with a specific CH. DEC has declared itself as a robust and more stable algorithm comparing with other protocols [4, 40] because it selects a fixed number of CHs in each round instead of using probabilistic-based models. Additionally, DEC uses only residual energy of the sensor nodes as the eligibility criterion to optimize energy consumption for WSNs.

The novel energy-efficient clustering protocol (NEECP) [38] aims to maximize the WSNs lifetime. The basic idea of NEECP is that the CH selection process depends upon the initial energies and residual of all nodes. The possible CH can be chosen on the root of the sensing range of the nodes. NEECP uses the chain approach for aggregating and collecting data in each cluster. In [46], Stability Improved LEACH (SILEACH) is proposed to improve the stability of LEACH by considering the residual energy, distances between the nodes and the CH and the distances between the nodes and the BS in CH selection process. In [47], the authors presented Stability Election Protocol (SEP) in which the CH selection process is based on weighted election probabilities using the remaining energy of each sensor node. A stable energy efficient clustering protocol for WSNs (SEECP) is proposed in [48], where the energy load balancing among the nodes is achieved by selecting the CHs in a deterministic fashion. Enhanced Threshold Sensitive Stable Election Protocol (ETSSEP) for heterogeneous WSN is proposed in [49]. ETSSEP is based on dynamically changing CH election probability and it elects CHs on the basis of the residual energy level of nodes and the minimum number of clusters per round.

The routing protocols above do not consider data compression so that they cannot satisfy the huge data traffic of WSNs [19]. It is effective to apply compression before transmitting data to reduce total power consumption by a sensor node [27]. For these reasons, the latest researches have explained that using CS scheme in WSNs can significantly decrease the total number of data gathered and improve WSNs performance [14 , 50–55].

Compressive Data Gathering (CDG) [32] is the first work that introduced CS to WSNs. CDG combines routing techniques with CS for reducing the overall network energy consumption. The main problem of CDG is that it only uses the CS idea without any analysis. The proposed Efficient CS based routing technique (ECST) in [27] prolongs the network lifetime using compressive methods to compress sensors reading before sending them to BS, however, ECST does not take into consideration the effect of compression matrix on sensors data. The work in [14] aimed to reduce energy consumption by combining routing algorithms and compression techniques.

In [28], the authors proposed a CS scheme for collecting data in large-scale WSNs. [30] utilized signals data correlation to reduce the sampling ratio. In [31], the authors proposed a scheme to reconstruct losing data by exploiting the correlation between different nodes data. In [18], the authors combined between CS and tree routing protocols. However, it only succeeds to minimize the total forwarding energy consumption, but on the other side, it increases the power consumed by leaves and intermediate nodes. To solve the tree routing problem, the authors of [13] used a CS scheme in a hybrid way in which only parent nodes do CS operation but this solution is suitable only for small networks, however, cluster-based schemes are more efficient for large networks [19].

In [20], the authors integrated between CS and clustering based schemes and suggested an ideal number of clusters that can led to minimize the power consumption. In [21], the authors proposed a CS hybrid method that is integrated with the clustering method and studied the relationship between the cluster size and the number of transmissions in the hybrid CS method. In [51], the authors proposed a new Cluster Size Load Balancing for CS algorithm (CSLB-CS) which could achieve optimal utilization of CS method in an IoT-based WSN. The protocol in [22] combines between random walk (RW) routing protocol and CS to prolong the network lifetime. In [23], the authors proposed a distributed multi-chain compressive sensing-based routing algorithm (DMC-CS) in which all nodes are organized in a number of chains with a leader. Each chain leader collects the CS compressed samples from its members and then sends them to the BS. Although this algorithm succeeds to increase the network lifetime, it is costly because BS needs to know the distances among all sensors.

Multi-path routing protocol (RMPGST-IoT) schema proposed in [49]. It employs the Gray System Theory (GST) where routes with highest rank are selected for concurrent transmission of data, using a specific routine based on GST. A performance evaluation method of WSNs based on GST is proposed in [50]. In [51], the authors proposed a trust model with incentive mechanism to evaluate the reliability of nodes. The proposed model combines fuzzy sets with GST to evaluate every node’s trust credibility based on direct trust and indirect trust relationship. Only those with higher trust values can be chosen to forward packets. Those untrustworthy nodes with lower trust values will be detected and excluded from the trust list. Also, Integration of GST and fuzzy is employed in [52] to find the most optimal Gray-Fuzzy routing strategy and reduce the time complexity effectively.

The concept of linear Diophantine fuzzy sets (LDFSs) is a new approach for modeling uncertainties in decision analysis. Due to the addition of reference or control parameters with membership and non-membership grades, LDFS is more flexible and reliable than existing concepts of intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PFSs), and q-rung orthopair fuzzy sets (q-ROFSs) [53, 54].

The concept of spherical linear Diophantine fuzzy sets (SLDFSs) introduced in [55] with the inclusion of reference or control parameters. A SLDFS with parameterizations process is very helpful for modeling uncertainties in the multi-criteria decision making (MCDM) process. SLDFSs can classify a physical system with the help of reference parameters. SLDFSs have various real-life applications towards digital image processing, network systems, vote casting, electrical engineering, medication, and selection of optimal choice.

Multi Criteria Decision Making Method was employed in WSN in various work, e.g., [56, 57]. Effective Data Acquisition Protocol for Multi-Hop Heterogeneous WSNs Using Compressive Sensing (EDACP-CS) algorithm was proposed in [24]. EDACP-CS combines a clustering-based algorithm and CS method in which the CH selection depends on distances from the BS and sensor residual energy. However, EDACP-CS suffers from the overhead cost of computation related to CH search. The work proposed in [9] was the first work studied the CS with IoT from the viewpoint of data-compressed sampling. The main problem of the protocol in [9] is that it applies CS without considering the organization of the sensors in order to send or receive the data from and to the BS. In the context of CS reconstruction problem, Orthogonal Matching Pursuit (OMP) [35] determines the greatest magnitude values in Φ^Tr index during each iteration, where, r represents the residual of y. Then, the least squares (LS) problem is solved. The works in [58, 59] proposed two algorithms based on OMP where the Stagewise OMP (StOMP) algorithm in [58] is an enhancement of OMP. StOMP selects more than one column to enhance the forward step of OMP; then utilizes these columns to solve the LS problem. While in [59], OMP is enhanced by grouping the inner-products having identical magnitudes into sets; then the set with the largest energy is determined. The algorithms [35 , 59] do not have a backward step as they fall under the category of irreversible greedy algorithms. The advantage of the backward step is to recover from wrong selection that might have occurred during the forward step. On the other hand, reversible greedy algorithms e.g., IHT [60], CoSaMP [17], SP [33] and FBP [29] employ backward step to eliminate wrong selection added during the forward step. However, as a result of measurement noises, the MF does not usually give the indices of all correct columns. Indeed, the correct indices may not be selected because they give small correlation according to Equation (4).

As discussed above, the related algorithms suffer from non-stability because they used probabilistic-based models. In addition to, there is no efficient mechanism to regularly check the suitability of the selected measurement matrix in each round to decide either to change it or not and this was the motivation behind our new work in this paper. This paper proposes an efficient CS scheme to improve the performance of IoT based WSNs, prolong the network lifetime and improve the reconstruction process. The proposed scheme consists of two algorithms: Deterministic Clustering using CS protocol (DCCS) and Random Selection Matching Pursuit (RSMP). The details of the proposed algorithms can be shown during the next sections.

The used notations through the paper are listed in Table 1.

Table 1
Notions Description

Notation Description

X Sensors readings

x′ Estimated data

Φ Measurement matrix

Y Measurement vector (compressed samples)

S Sparse level (number of non-zero values)

ɛ The global seed

R Number of rounds

d _i The sensor’s i reading

C Set of clusters head

N _CH Number of clusters head

B Minimum error threshold

ChainList _i The chain list for cluster number i

α _j The coefficient vector for node j

E The difference x and x’.

y _j The compressed vector for node j

r ^K The residue after the kth iteration

E The approximation solution set

T Estimated set

F Least-squares signal approximation set

K _max Maximum number of iterations

β Termination parameter

Notation	Description
X	Sensors readings
x′	Estimated data
Φ	Measurement matrix
Y	Measurement vector (compressed samples)
S	Sparse level (number of non-zero values)
ɛ	The global seed
R	Number of rounds
d _i	The sensor’s i reading
C	Set of clusters head
N _CH	Number of clusters head
B	Minimum error threshold
ChainList _i	The chain list for cluster number i
α _j	The coefficient vector for node j
E	The difference x and x’.
y _j	The compressed vector for node j
r ^K	The residue after the kth iteration
E	The approximation solution set
T	Estimated set
F	Least-squares signal approximation set
K _max	Maximum number of iterations
β	Termination parameter

3 Compressive sensing based routing and data reconstruction scheme for iot based wsns

Recently, IoT technologies have attracted many researchers in the area of wireless networks. However, sensors energy constraints, designing effective sensor data aggregation techniques and managing a large amount of information are considered the major challenges facing IoT technologies. In this section, we describe our new scheme that integrates CS with an efficient routing technique. The proposed scheme includes two algorithms: (1) Deterministic Clustering using CS (DCCS) that divides the WSN into a number of clusters. In each cluster, a CH is selected according to sensor residual energy. DCCS organizes each cluster into a chain to start CS data gathering. Moreover, it allows BS to dynamically change the measurement matrix if it is not still suitable for the network and (2) Random Selection Matching Pursuit (RSMP) for data reconstruction. RSMP adds random selection during the column selection to increase the chance of finding the correct columns in each round and improve the reconstruction performance. Below, we give the details of the two algorithms.

A. Deterministic Clustering using CS (DCCS)

In the DCCS, a heterogeneous IoT based WSN is considered where each sensor node is in one of the following classes: normal, advanced and superior with their names refer to energy level. The DCCS algorithm diagram ispresented in Fig. 1. DCCS comprises of two phases: Data compression and Setup.

Fig. 1

DCCS Algorithm.

Setup Phase

DCCS executes this phase only once in the first round. The main goal of this phase is to collect all sensor data X without using CS at the BS with minimum energy consumption. Setup phase consists of three steps: Cluster Head Selection, Clusters Construction, and Learning.

In CH selection, depending on the residual energy (RE) of nodes, the BS selects a fixed number of nodes to be CHs.

In clusters construction, CH organizes its cluster members in a chain.

Finally, in learning step, using the received data from CHs, BS generates the CS matrix and calculate the threshold value.

The setup phase procedure will be as follows:

CH Selection: in this step, as in [39], BS selects a fixed number of nodes (NCH) to be the CHs based on the RE of every node such that the priority is given to the nodes with higher RE. After the first round, each cluster is responsible dynamically for selecting a new CH. This scenario reduces the computation cost accompanying with CH search in the present protocols. The selected CHs transmit their own information to all other nodes to select the nearby CH and then start Clusters Construction step.

Clusters Construction: Once the selected CHs (set C nodes) advertise themselves as CHs, the non-CHs nodes start to construct clusters by sending a join-request message (JRM) to the closest CH_i, where i = 1, 2, …, N_CH. This JRM contains (1) node identification (Node - ID), the selected CH identification (CH - id), the node residual energy (Node - RE), and the node’ location (Node - Loc). The DCCS divides the network into N_CH clusters each cluster has CH and members. In order to decrease the whole network power consumption to transmit data per round in each cluster, the DCCS organizes the member nodes within each cluster into chain(s). Every CH_i,, i = 1, 2, …, N_CH applies the Initialization and Update steps to construct ChainList (s). The procedures for this step are shown in Algorithm 1.

Initialization Step: In each cluster, CH_i uses its members information Node - Loc to create the ChainList_i, where ChainList_i, = [ChainList_N, , …, ChainList_{N
_CH}, ], by adding the nearest member C₀ to it. It then updates the ChainList_i with the nearest unselected member C_i to node C₀.

Update Step: CH_i decides the place of nearest unselected neighbor node C_j to node C₁ in ChainList_i, by comparing the distance between C₁, C_j and any consecutive nodes in ChainList_i. If the distance between C₁ and C_j is less than D where D the distance between C_j and any consecutive, then C_i adds it to the end of ChainList_i. Otherwise C_j will be added between the consecutive nodes that have minimum distance to C_j, for example, if C_r and C_k are consecutive nodes in the ChainList_i and if dis (C_j, C_last)> dis (C_j, C_r) and dis (C_j, C_last) > dis (C_j, C_k), then node C_j will be added between C_j and C_k. Otherwise, node C_j will be added to the end of the ChainList_i after node C_last, where C_last the last

Node is added to ChainList_i and dis (C_j, C_k) is the distance between C_j and C_k. CH_i repeats the previous Update Step to include all its members in ChainList_i. If a member dies in a ChainList_i, then ChainList_i will be reconstructed bypass the dead node.

By applying the previous steps, each node will send and receive the minimum distance, i.e., DCCS can reduce the energy consumption for each node.

3. Learning process: Measurement matrix selection is considered as one of the most important process in the CS method because of its effect in sensor data where this matrix is used by sensor nodes to compress their data and is also used by the BS to reconstruct sensors data. Thus, incorrect selection leads to the loss of lots of data.

The BS generates this matrix using a random seed ɛ, and then broadcasts ɛ to the entire network. To develop the seed selection process, DCCS uses the following scenario: During the intra-cluster process, every CH collects a non-CS data X from its chain members and then fuses these data. CHs start inter-cluster communication process (Algorithm 1) by creating a chain among them, considering the BS as a CH. Using this chain, BS collects all sensors data, and thenit finds the best ɛ that gives the minimum error. The BS uses this minimum error as the threshold β. Finally, the BS sends ɛ to the entire network to use during the Data Compression phase.

Algorithm 1. Clusters Construction Algorithm
: Input: Set of Cluster heads CH_i
2: Output: clusters organized in chain approach
3: Fori = 1 : N_CHdo 4: Initialization Step:
5: The non-CHs nodes (member nodes) start to construct clusters by selecting the closest CH_i.
6: CH_i begins to create ChainList_i by adding the nearest member node C₀ to it.
7: CH_i.updates ChainList_i with the nearest unselected node (C₁) to node C₀.
8: Update Step:
9: forj = 2: \|ChainList_i\| do
10: ifdis (C_j, C_j - 1) < dis (C_j, D) then
11: CH_i adds C_j, to the end of ChainList_i
12: else
13: CH_i.adds C_j, between consecutive nodes that have a minimum distance to C_j,.
14: end if
15: end for
16:Go to Update Step till includes all its members in ChainList_i
17: end for

Data Compression Phase

Data Compression Phase will be executed starting from the second round. It consists of four steps: CS Data Gathering within intra-cluster and inter-cluster, Reconstruction, Dynamic Re-Generate the Random Seed and CH rotation. At the end of this phase, DCCS re-executes Algorithm 1 to create the new clusters with the new CHs. The details of these steps are illustrated below.

[1] CS data Gathering within intra-cluster and inter-cluster

As described in the previous phase, there are N_CH clusters, every cluster has CH_i and chain members are organized in ChainList_i such that each ChainList_i = [c₀, c₁ … , c_last-1, c_last]. CS gathering data in each intra-cluster will be as follows:

Last node c_last in the ChainList_i uses the global received seed ɛ from the BS to generate α_{C
_last}.

c_last Computes its compress vector (measurement) y_{C
_last} = α_{C
_last}d_{C
_last}, where d_{C
_last} is the reading of sensor c_last, and then transmits the measurement y_{C
_last} to its previous neighbor node c_last-1 in the ChainList_i.

Node c_last-1 uses the same global seed ɛ to generate α_{C
_last-1} and compute its measurement y_{C
_last-1} = α_{C
_last-1}d_{C
_last-1}, and then transmits the summation vector y_{C
_last} + y_{C
_last-1} to the previous node c_last-2.

Once c_last-2 receives y_{C
_last} + y_{C
_last-1}, it computes its value y_{C
_last-2}, adds it to y_{C
_last} + y_{C
_last-1} and then sends the summation value to the previous node in ChainList_i and so on till the CH_i.

Now each CH_i has received the compressed vectory_i = [y_{c
₀}, yc_1c₁, …, y_{c
_last}] from their corresponding cluster members. Through inter-cluster communication, DCCS applies the same scenario used in Algorithm 1 to organize the CHs in a chain and consider them as cluster members of a cluster with the BS as CH. The same approach isused by both CHs and cluster members in a new cluster for sending their data to the BS. The communication process both inter-cluster and intra-cluster are shown in Fig. 2.

Fig. 2

Inter and Intra cluster communication processes.

[2] Reconstruction Step

Using the received compress vectors y = [y₁, y₂, y₃, …, y_i], where i = [1, 2, …, N_CH], BS generates the CS matrix depending on the predefined random seed ɛ. After that, the BS reconstructs the original data x0 of every cluster. In order to improve this step, Random Selection Matching Pursuit (RSMP) is proposed. The main process of RSMP will be described in Section B.

[3] Dynamic Re-Generate Random Seed

During the setup phase, the BS generates M × N CS matrix using random seed ɛ and then broadcasts ɛ to the entire network. In each round, every sensor node transmits and receives a vector M × 1 whatever the number of alive nodes in each round as displayed in CS Gathering data within intra-cluster and inter-cluster Step. This leads to the increment of the average power consumption and also has a negative reflection in the reconstruction process.

To overcome this problem, DCCS dynamically changes the CS matrix whenever the network status changes, i.e.

DCCS gives the ability to dynamically change the CS matrix depending on the network status and the number of alive nodes in each round.

In this case, the CS matrix size decreases as the number of alive nodes decreases, i.e., DCCS can successfully decrease the overall power consumption. The BS can obtain the number of dead nodes in every cluster from each CH. Each CH can simply use a HELLO message to know the number of dead nodes in its cluster in each round. The process of this step can be summarized as follows:

The BS compares the latest reconstructed data X′ with X and judges whether to re-generate depending on the error value of ɛ = X -- X′. If it goes beyond a predefined threshold β, it means that there is a change in network status, the BS regenerates new ɛ.

Otherwise, no need to change last seed.

[4] Cluster head rotation

Every CH_i checks the piggy-backed CM-REs information to decide whether it remains as CH or gives up their roles to any node in their clusters with the highest RE and assign these nodes as the new CHs. This step prevents WSNs from dying earlier by distributing energy consumption loads.

B. RMSP Algorithm

In this section, a new reconstruction technique called Random Selection Matching Pursuit (RSMP) is proposed. RSMP can be used by the BS to reconstruct the sensors readings again. It is a reversible greedy algorithm in the sense that it has reversible construction, the support set can be pruned (backward step) to remove the unreliable elements that chosen in the past (forward step). Before describing RSMP algorithm, some operations that used in the algorithm are defined as following: $resid (y, x) ≜ y - Φ x$ (3) $supp (x; k) ≜ {the set of indices corresponding to$ (4) $the k largest amplitude components of x},$ $rand (x; k) ≜ {the set of indices corresponding to$ (5) $the k random choose components of x}$

During the forward step, most CS reconstruction greedy algorithms used Matched Filter Detection (MF) operation Φ′y to calculate the correlation between matrix Φ columns and the Sampled Measurement Vector y. Then, Equation (4) is used to select the set of indices corresponding to the n largest amplitude components of Φ′y. The size of n is different in each algorithm, for example: n = 1, . . S, and 2S in Orthogonal Measurement Sampling (OMP) [35], Subspace Pursuit (SP) [33] and COSAMP [17] algorithms respectively. However, as a result of measurement noises, the MF does not usually give the indices of all correct columns. Indeed, the correct indices may not be selected because they give small correlation according to Equation (4). To solve this drawback, RSMP proposes a random technique to the selection process in the forward step to increase the probability to find the correct columns indices in each iteration. The process of RSMP algorithm is given in Algorithm 2. RSMP includes four steps: Initialization, Forward, Backward and Update. The description of the four main steps are as follows:

[1] Initialization: RSMP initializes the parameters: residual r⁰ = y, initial approximation E⁰ = 0 and estimated set T = φ.

[2] Forward: Most of MP algorithms use the n largest in-amplitude components from the MF, |n| depends on the algorithm, as a first estimation of the estimated set T. However, they depend only on the columns which have high correlation in MF equation without taking into consideration the others that have negative effect on the reconstruction performance especially when the sparse level increases. Due to the measurements noise, the correct columns do not usually give high correlation during MF process.

RSMP uses a simple way to improve this step. Instead of selecting the indices of largest amplitude components in the set F only, in each iteration, RSMP selects S + q columns where q is the random selection size. RSMP firstly selects the largest S components in F (H = supp (F, S)) to create set H and then uses Equation (5) to select q random components from setF (R = Rand (F, q)), and creates set R to overcome the interested case in which the correct columns do not give high correlation. Indeed, the probability to find the correct columns in both cases is increased. RSMP set q = M/2 -- S depends on the fact that the CS reconstruction problem can be resolved if the sparsity level S ⩽ M/2 [33]. Finally, RSMP uses the union set U = HR between set H and set R to expand the estimated set T and start the next step.

Algorithm 2. RSMP Algorithm
1: INPUT: Φ : M × N CS matrix, y: Compressed Vector and S: Signal Sparsity Level
2: OUTPUT: Reconstructed Signal EK
Initialization Step:
3: r0 = y ; E0 = 0 ; T = φ ; F = φ ; K = 0 ;
4: while true do
5: K = K + 1 Forward Step:
6: F = Φ^†rk - 1
7: H = supp (F, S)
8: R = Rand (F, q)
9: U = HR
10: T = Usupp (EK - 1)
Backward Step:
11: $W \| T = Φ_{T}^{†} y$
12: W\|T^c = 0
13: EK = WS
Update step:
14: r^K = resid (y, E^K)
15: if\|\|r^K\|\|₂ < γorK = K_max then
16: break
17: end if
18: end while

Backward: We can call this step as correction step because through this step the proposed algorithm removes incorrect column indices which were wrongly selected in the last step, i.e., the algorithm updates the approximation set E = W_S by removing S columns indices which have the smallest values in set W.

[4] Update: The samples are updated using Equation (3) as r^K = resid (y, E^K). There are two situations that terminate our algorithm: (1) if the residue set ${rr}_{2}^{K}$ is smaller than the β termination parameter. The termination parameter β selection process depends on the level of noise; (2) if the number of iterations exceeds K_max where K_max the maximum iterations is. At the end of the algorithm, E^K contains the corresponding nonzero values.

4 Experiments

This section provides the results of the simulation for evaluating the performance of our work. We divide this section into three parts: (1) in the first part, DCCS algorithm is evaluated in terms of a network lifetime (the first node die) and average power consumption, (2) in the second part, we evaluate RSMP reconstruction algorithm in terms of reconstruction error (Average Normalized Mean Squared) and compare its performance results with Orthogonal Matching Pursuit (OMP), COSAMP, Forward-Backward Pursuit (FBP) [29], Subspace Pursuit (SP) [33] and E-OMP algorithms [25], (3) Finally, the dynamic re-generate random seed step is evaluated in terms of average power consumption and reconstruction error.

A. Evaluate DCC Algorithm

In this section, MATLAB environment is used to perform the simulation. In this part, the network region size is 100m × 100m, and the total number of sensor nodes ranges from 50 to 200 nodes with increment of 50 nodes and the BS is located in the middle of the network. The DCCS algorithms is evaluated in case of homogenous and heterogeneous networks.

Performance Metrics: the proposed DCCS algorithm is evaluated according to the following performance metrics:

•Average Energy Consumption E: E is the total energy consumed by all the nodes dividing by the total number of nodes during their operations such as forwarding, sending and receiving. The average energy consumption for each round can be estimated as: $E = \frac{\sum_{i = 1}^{N} E_{i} (r)}{r},$ (6) , where N the number is considered WSNs sensor nodes and r is referred to a rounds number.

•Network lifetime: the network lifetime till the first node dies.

Homogenous Network Case:

In this case, DCCS performance is evaluated and compared with DMC-CS [23] and EDACP-CS [24]. In addition to, we use the same energy parameters used in [4] to send an l-bit message for a distance d. The radio power consumption is: $E_{Tx} (l, d) = {\begin{matrix} {lE}_{elec} + l ɛ_{fs} d^{2} d < d_{0} \\ {lE}_{elec} + l ɛ_{mp} d^{4} d ⩾ d_{0} \end{matrix} .$ (7)

In order to obtain this message, the radio expend is: $E_{Rx} (l) = {lE}_{elec} .$ (8)

The parameters which are used during this simulated model can be expressed as following: E_elec = 50nJ/bit, ɛ_fs = 10pJ/bit/m2, $ɛ_{mp} = \frac{13}{10000}$ pJ/bit/m4, $d 0 = \sqrt{ɛ_{fs} / ɛ_{mp}}$ . The Energy factor associated to super nodes is 2 J, Initial energy level associated to advanced nodes is 1.25 J and for normal nodes is 0.5 J.

Figure 4 shows the network lifetime of DCCS, EDACP-CS and DMC-CS. In EDACP-CS and DMC-CS, the death of the first node is earlier than DCCS, and also Fig. 4 illustrates the effectiveness of the DCCS algorithm in prolonging network lifetime than EDACP-CS and DMC-CS algorithms. This is because DCCS uses a fixed number of CHs (NCH) in each round, not the case by the others, which leads to achieving the stability of energy consumption among the nodes. Additionally, in DCCS the BS takes the role to select the CHs only in the first round and then dynamically change the CHs, which considerably decreases the overhead cost of computation associated with CH search comparing with others. DCCS reduces the transmitted CS measurement samples in each cluster which dynamically depends on the network status rather than using a fixed number of CS measurement samples in each round as in the other algorithms.

Fig. 3

Flow chart of DCCS Data Compression Phase.

Fig. 4

Network lifetime in DCCS, DMC-CS and EDACP-CS.

Figure 5 shows the network lifetime and the number of alive nodes per round in DCCS, EDACP-CS and DMC-CS. It is clear that the first and last nodes in DCCS live more than those of EDACP-CS and DMC-CS, which means that DCCS reduces the energy consumption overall sensors. This is because DCCS reduces the power consumption for each node by organizing cluster members in a chain such that each node sends and receives only from the nearest node, which is not the considered by EDACP-CS algorithm. During the chain construction, DCCS rearranges all nodes in the chain when it adds a new node to the chain list to take in consideration the distances between this node and the others in the chain, rather than adding only the nearest node to the last node in the chain like DMC-CS. In Fig. 6, it is clear that DCCS succeeds to decrease the average energy consumption compared to EDACP-CS and DMC-CS algorithms because DCCS dynamically re-generates CS matrix which is not considered by the others.

Fig. 5

Number of alive nodes as a function of number of rounds.

Fig. 6

Average energy consumption in DCCS, EDACP-CS and DMC-CS.

Heterogeneous Network Case:

In this section, we aim to evaluate the proposed algorithm in the case of a heterogeneous network. In this case, we assume that the total energy of the network is 102 J and the sensor nodes are divided into advanced, intermediate and normal according to their residual energy. DCCS performance is evaluated and compared with ETSSEP [49], SEECP [48] and SILEACH [46] based on CS method. It is clear from Fig. 7 that DCCS still provides good performance in terms of network lifetime extension compared to ETSSEP, SEECP and SILEACH algorithms because the dynamic CS matrix regeneration process in DCCS utilizes the CS matrix in an effective way to reduce the total number of transmitted data which leads to reduce the transmission energy consumption. On the other hand, the ETSSEP-CS, SEECP-CS, and SILEACH-CS algorithms use a fixed CS matrix in each iteration which may become not suitable for the network after a number of iterations. The same effect can be noticed in Fig. 8 where DCCS outperforms the other algorithms in terms of network lifetime in case of the death of half-nodes.

Fig. 7

Network lifetime (First node dies) in DCCS, ETSSEP-CS, SEECP-CS and SILEACH-CS.

Fig. 8

Network lifetime (half of node die) in DCCS, ETSSEP-CS, SEECP-CS and SILEACH-CS.

From Fig. 9, we can conclude that DCCS succeeds to reduce the total energy consumption compared with the ETSSEP-CS, SEECP-CS and SILEACH-CS algorithms because DCCS divides the network into a number of clusters and inside each cluster, it uses the proposed chain construction algorithm to organize the cluster members into a chain. Moreover, DCCS uses the same proposed chain construction algorithm to organize the CHs in chain using BS as a CH for transmission to the BS.

Fig. 9

Residual Energy in DCCS, ETSSEP-CS, SEECP-CS and SILEACH-CS.

B. Evaluate RMSP Algorithm

In this section, we evaluate the performance of RSMP reconstruction algorithm and compare its results with OMP, COSAMP, SP, FBP and E-OMP algorithms. First, we use RSMP algorithm to reconstruct the signals collected by the Intel Berkeley Research lab (real datasets) [36]. The whole process repeated over 500 times on randomly generated sparse samples S. Second, RSMP is applied to reconstruct computer-generated signals in which its nonzero coefficients are drawn from the uniform and Gaussian distributions. Finally, RSMP performance is measured over signal noise observations. The reconstruction is investigated by Gaussian matrix Φ with size M×N, where N = 256 and M = 128.

Performance Metrics

RSMP algorithm reconstruction’s performance is compared with different others reconstruction algorithms in term of Average Normalized Mean Squared Error (ANMSE), which is defined as the average ratio $\frac{∥ x - x^{\sim} ∥_{2}}{∥ x ∥_{2}}$ , where x is the original reading and x^∼ is the reconstructed one.

Experiments over real datasets:

In this section, we use RSMP algorithm to reconstruct the signals collected by Intel Berkeley Research lab [36].

Figure 10 shows the effectiveness of RSMP algorithm in terms of reconstructing the temperature signals. RSMP achieves similar performance in reconstructing the humidity signals as shown in Fig. 11. In Fig. 12, we illustrate the distribution of relative recovery error for different sensor nodes. It is clear that RSMP algorithm surpasses the performance of the other greedy algorithms, i.e., the COSAMP, OMP, EOMP, FBP and SP, respectively.

Fig. 10

Reconstruction results over Intel temperature signals.

Fig. 11

Reconstruction results over Intel humidity trace.

Different coefficient distributions:

In this part of simulation, uniform and Gaussian distributions are used to draw the non- zero values of the sparse signal and the sparse level S ranges from 5 to 60. In Fig. 13 where the sparse signal’s non-zeros values are drawn from uniform distribution, RSMP algorithm clearly provides lower ANMSE comparing to COSAMP, OMP, E-OMP, FBP and SP. In addition, ANMSE for RSMP algorithm is started to increase only when S > 56 while it increases when S > 42, S≥30, S≥44, S≥38 and S≥35 for COSAMP, OMP, E-OMP, FBP and SP algorithms respectively as shown in Fig. 13. Figure 14 shows ANMSE results when the sparse signal’s non-zero values are drawn from Gaussian distribution. In Fig. 14, RSMP algorithm still provides lowest ANMSE result comparing to COSAMP, OMP, EOMP, FBP and SP, as S > 59, S≥46, S > 34, S > 49, S > 47 and S > 45, respectively.

Fig. 12

Performance of six different reconstruction algorithms for temperature signals.

Fig. 13

Reconstruction results over sparsity for uniform sparse signals.

Fig. 14

Reconstruction results over sparsity for Gaussian sparse vector.

Reconstruction performance over different measurement vector lengths:

This part of simulation aims to test RSMP reconstruction performance when different measurement vector lengths- M are used with two different CS matrices: Gaussian and Bernoulli distribution matrices as shown in Figs. 15 and 16 respectively. To achieve this aim, sparse signals drawn from uniform distribution with length N = 120 is used and M values ranges from 10 to 60 with step size 1. From those figures, we observe that RSMP algorithm still provides the lowest ANMSE values comparing to the others.

Fig. 15

Reconstruction results over Gaussian matrix by different lengths of M.

Fig. 16

Reconstruction results over Bernoulli matrix by different lengths of M.

Reconstruction over noisy signal :

In this part, we add some noise equal to 10^- 4 to the original uniform as well as in Gaussian distributions signal where N = 256 and M = 128. The CS matrix Φ is drawn from the Gaussian distribution. The sparsityS levels are from 10 to 60 with step size 1.

Figures 17 and 18 depict the reconstruction errors for the noisy Gaussian and uniform sparse signals. We observe that RSMP algorithm produces less error than COSAMP, OMP, E-OMP, FBP and SP. In summary, RSMP algorithm improves the reconstruction process with higher performance than COSAMP, OMP, E-OMP, FBP and SP algorithms. This is because in each iteration RSMP gives the chance to the columns which do not give the largest values in MF process to be chosen.

Fig. 17

Reconstruction results for noisy uniform sparse signals.

Fig. 18

Reconstruction results for noisy Gaussian sparse signals.

C. Evaluate the Dynamic Regenerate Random Seed Step

In this test, a network with 100 m×100 m region size and the number of sensor nodes ranges from 50 to 200 nodes with increments of 50 and the BS is located at (x = 50, y = 50).

Performance Metrics: In this test, we call DCCS algorithm as DCCS-dynamic if it uses the proposed dynamic re-generate random seed step and DCCS-static otherwise. This section compares the performance of DCCs-dynamic and DCCS-static, in terms of the following: Average Energy Consumption and Average Normalized Mean Squared Reconstruction Error (ANMSE). During the reconstruction process, COSAMP [17] algorithm is used to recover the data in each round.

Figure 19 shows the effect of network status changing on the reconstruction process. It is clear that the reconstruction errors of both DCCS dynamic and DCCS-static are the same when the network is stable, i.e., the number of dead nodes is equal to zero. However, the reconstruction error increases when the number of dead nodes is zero in the case of DCCS-static because DCCS-static uses a fixed CS matrix whatever the number of alive nodes in each round. On the other hand, DCCS-dynamic uses the threshold β as the best reconstruction error and then in each round, compares the reconstruction error with β.. If the error is larger than β, the old matrix is not suitable and the DCCS-dynamic regenerates another one. In this case, DCCS-dynamic keeps the reconstruction error stable whatever the number of dead nodes as shown in Fig. 19.

Fig. 19

ANMSE as a function of number of died nodes in each round.

Figure 20 shows the ability of the DCCS-dynamic algorithm in the dynamic mode to increase the number of alive nodes in each round compared to DCCS in static mode. According to the DCCS-dynamic scenario, the number of measurement samples transmitted in intra-cluster or inter-cluster communication is decreased while the number of dead nodes is increased.

Fig. 20

Average energy consumption in DCCS-dynamic and DCCS-static.

5 Conclusion

The main goal of IoT components is to obtain information about any event correctly. However, there are some problems which impede the way to achieve this goal such as sensor batteries constraints and managing large amount of data acquisition. To solve these problems, this work has proposed a new CS scheme for IoT based WSN and explained how this scheme can be used to compress and reduce the total data traffic through the network. The proposed work consists of two algorithms, first, one is called DCCS algorithm in which the BS selects a fixed number of cluster heads according to RE of each node. Then, DCCS organizes each cluster members into a chain before starting the CS data gathering. In each round, the BS checks the suitability of the measurement matrix to the network to decide either to change or not. The second algorithm is called RSMP which can successfully reconstruct the original data at the BS. The proposed work achieved our goals to prolong the network lifetime and improve the reconstruction performance. Simulation results proved that our proposed scheme is an effective data collection tool for decreasing energy consumption in network, prolonging network lifetime and reducing reconstruction error. As apart of Future work, we are planning to apply DCCS for improving Wireless Body Area Network performance. In addition, we plan to combine between RSMP algorithm and one of swarm algorithms for more improving to the reconstruction process.

References

, Enterprise systems: State-of-the-art and future trends, IEEE Trans Ind Inf 7(4) (2011), 630640,

Zheng

, Simplot-Ryl

, Bisdikian

and Mouftah

H.T.

, The internet of things, IEEE Commun Mag 49(11) (2011), 3031.

Palopoli

, Passerone

and Rizano

, Scalable of- fline optimization of industrial wireless sensor networks, IEEE Trans Ind Inf 7(2) (2011), 328329.

Osamy

, Salim

and Khedr

A.M.

, An Information Entropy Based-Clustering Algorithm in Heterogeneous Wireless Sensor Networks, accepted in wireless networks, Springier, doi.org/10.1007/s11276-018-1877-y(0123456789, (2019).

Khedr

A.M.

and Omar

D.M.

, SEP-CS: Effective Routing Protocol for Heterogeneous Wireless Sensor Networks, Ad Hoc & Sensor Wireless Networks 26 (2015), 211–232.

Ejaz

, Yaqoob

, Gani

, Imran

, Guizani

, Rabbat

and Nowak

, Internet-of-things-based smart environments: state of the art, taxonomy, and open research challenges, IEEE Wireless Communications 23 (2016), 10–16.

Omar

D.M.

and Khedr

A.M.

, ERPLBC: Energy Efficient Routing Protocol for Load Balanced Clustering in Wireless Sensor Networks, Ad Hoc & Sensor Wireless Networks 42 (2018), 145–169.

Palopoli

, Passerone

and Rizano

, Scalable offline optimization of industrial wireless sensor networks, IEEE Trans Ind Inf 7(2) (2011), 328329.

, Xu

and Wang

, Compressed sensing signal and data acquisition in wireless sensor networks and Internet of things, IEEE Transactions on Industrial Informatics 9(4) (2013), 2177–2186.

10.

Candes

and Wakin

, An Introduction to Compressive Sampling, IEEE Signal Processing Magazine 25(2) (2008), 21–30.

11.

Baraniuk

, Compressive Sensing [Lecture Notes], IEEE Signal Processing Magazine 24(4) (2007), 118–121.

12.

Haupt

, Bajwa

, Rabbat

and Nowak

, Compressed Sensing for Networked Data, IEEE Signal Processing Magazine 25(2) (2008), 92–101.

13.

Luo

, Xiang

and Rosenberg

, Does Compressed Sensing Improve the Throughput ofWireless Sensor Networks? Proc. IEEE Intl Conf. Comm (ICC) (2010), 1–6.

14.

Xiang

, Luo

and Vasilakos

, Compressed Data Aggregation for Energy EfficientWireless SensorNetworks, Proc. IEEE Sensor, Mesh, and Ad Hoc Comm. and Networks (SECON 11) (2011), 46–54.

15.

Omar

D.M.

, Khedr

A.M.

and Agrawal

D.P.

, Optimized Clustering Protocol for Balancing Energy in Wireless Sensor Networks, International Journal of Communication Networks and Information Security (IJCNIS) 9(3) (2017), 367–375.

16.

Zhang

, Zhang

, Li

, Yang

and Liu

, Dynamic clustering and compressive data gathering algorithm for energy-efficient wireless sensor networks, International Journal of Distributed Sensor Networks 13(10) (2017).

17.

Needell

and Tropp

J.a.

, COSAMP: iterative signal re- covery from incomplete and inaccurate samples, Applied and Computational Harmonic Analysis 26(3) (2009), 301–321.

18.

Luo

, Wu

, Sun

, et al., Efficient measurement generation and pervasive sparsity for compressive data gathering, IEEE T Wirel Commun 9(12) (2010), 37283738.

19.

Luo

, Wu

, Sun

, et al., An efficient compressive data gathering routing scheme for large-scale wireless sensor networks, Comput Electr Eng 39(6) (2013), 19351946.

20.

Nguyen

M.T.

, Teague

K.A.

and Rahnavard

, CCS: energy-efficient data collection in clustered wireless sensor networks utilizing block-wise compressive sensing, ComputNetw 106 (2016), 171185.

21.

Xie

and Jia

, Transmission-efficient clustering method for wireless sensor networks using compressive sensing, IEEE T Parall Distr 25(3) (2014), 806815.

22.

Nguyen

M.T.

, Minimizing energy consumption in random walk routing for Wireless Sensor Networks utilizing compressed sensing, In: Proceedings of the 2013 8th international conference on system of systems engineering, Maui, HI, 26 297301. New York: IEEE, June (2013).

23.

Salim

and Osamy

, Distributed multi chain compressive sensing based routing algorithm for wire- less sensor networks, Wireless Netw 21 (2015), 13791390.

24.

Khedr

A.M.

, Effective Data Acquisition Protocol for Multi-Hop Heterogeneous Wireless Sensor Networks UsingCompressive Sensing, Algorithms 8(4) (2015), 910–928.

25.

Osamy

, Salim

and Aziz

, Sparse signals reconstruction via adaptive iterative greedy algorithm, International Journal of Computer Applications 90 (2014).

26.

Osamy

, Khedr

A.M.

, Aziza

and El-Sawya

, Cluster-Tree Routing Scheme for Data Gathering in Periodic Monitoring Applications, IEEE Access 6, 77372–77387.

27.

Aziz

, Singh

, Osamy

and Khedr

A.M.

, Effective Algorithm for Optimizing Compressive Sensing in IoT and Periodic Monitoring Applications, Journal of Network and Computer Applications 126 (2019), 12–28.

28.

Haupt

, Bajwa

and Rabbat

, Compressed Sensing for Networked Data, IEEE Signal Processing Magazine 25(2) (2008), 92–101.

29.

Burak

and Erdogan

, Compressed sensing signal recovery via forward-backward pursuit, Digital Signal Processing 23 (2013), 1539–1548.

30.

Duarte

, Sarvotham

, Wakin

, Baron

and Baraniuk

, Joint Sparsity Models for Distributed Compressed Sensing, Online Proceedings of the Workshop on Signal Processing with Adaptative Sparse Structured Representations (SPARS) (2005).

31.

Jin

, Shao Jie

, Baocai

and Yang

, Data gathering in wireless sensor networks through intelligent compressive sensing, Digital Signal Processing 23 (2013), 1539–1548.

32.

Chong

, Feng

, Jun

and Chang

, Compressive data gathering for large-scale wireless sensor networks, In Proceedings of the 15th Annual International Conference on Mobile Computing and Networking, MobiCom ’09, 145–156, New York, NY, USA, (2009). ACM.

33.

Wei

and Olgica

, Subspace Pursuit for Compressive Sensing Signal Reconstruction, IEEE Trans Inf Theor 55(5) (2009), 2230–2249.

34.

Donoho

, Compressed sensing, IEEE Trans. In- form. Theory 52(4) (2006), 1289–1306.

35.

Tropp

and Gilber

, Signal recovery from random measurements via orthogonal matching pursuit, IEEE Trans Inform Theory 53(14) (2007), 4655–4666.

36.

Intel Berkeley Research Lab Data Set, [Online]. Available: http://db.csail.mit.edu/labdata/labdata.html, Access date: 9 OCT, time: 9:20 pm, (2017).

37.

Venkataramani

and Bresler

, Sub-nyquist sampling of multiband signals: perfect reconstruction and bounds on aliasing error, IEEE International Conference on Acoustics, Speech and Signal Processing(ICASSP) (1998), 12–15.

38.

Singh

, Chand

, Kumar

, Malik

and Kumar

, NEECP: Novel energy-efficient clustering protocol for prolonging lifetime of WSNs, IET Wireless Sensor Systems 6(5) (2016), 151–157.

39.

Aderohunmu

F.A.

, Deng

J.D.

and Purvis

M.K.

, A Deterministic Energy-efficient Clustering Protocol for Wireless Sensor Networks, Proceedings of Seventh IEEE International Conference on Intelligent Sensors, Sensor Networks and Information Processing (2011), 341–346.

40.

Salim

, Osamy

and Khedr

A.M.

, IBLEACH: Effective LEACH Protocol for Wireless Sensor Networks, Wireless Networks 20 (2014), 1515–1525.

41.

Dhumane

A.V.

and Prasad

R.S.

, Multi-objective fractional gravitational search algorithm for energy efficient routing in IoT, Wireless Networks 25(1) (2019), 399–413.

42.

Al-Kashoash

H.A.

, Kharrufa

, Al-Nidawi

and Kemp

A.H.

, Congestion control in wireless sensor and 6LoWPAN networks: toward the Internet of Things, Wireless Networks (2018), 1–30.

43.

Kavitha

and Geetha

B.G.

, An efficient city energy management system with secure routing communication using WSN, Cluster Computing (2017), 1–12.

44.

Rahmani

A.M.

, Gia

T.N.

, Negash

, Anzanpour

, Azimi

, Jiang

and Liljeberg

, Exploiting smart e-Health gateways at the edge of healthcare Internet-of-Things: A fog computing approach, Future Generation Computer Systems 78 (2018), 641–658.

45.

Oberländer

A.M.

, Röglinger

, Rosemann

and Kees

, Conceptualizing business-to-thing interactions–A sociomaterial perspective on the Internet of Things, European Journal of Information Systems (2017), 1–17.

46.

Al-Zubaidi

, Ariffin

and Al-Qadhi

, Enhancing the Stability of the Improved-LEACH Routing Protocol for WSNs, J ICT Res Appl 12(1) (2018), 1–13.

47.

Smaragdakis

, Matta

and Bestavros

, SEP: A Stable Election Protocol for clustered heterogeneous wireless sensor networks, In Proceeding of the International Workshop on SANPA, (2004).

48.

Mittal

, Singh

and Singh Sohi

, A stable energy efficient clustering protocol for wireless sensor networks, Wireless Netw 23 (2017), 809–1821.

49.

Wang

, Li

, Zhang

and Cao

, MCDM-ECP: Multi criteria decision making method for emergency communication protocol in disaster area wireless network, Applied Sciences 8(7) (2018), 1165.

50.

Ahmad

, Hu

, Ahmad Zaid-ul-Huda

and Khurshid

, Optimal Cluster Leader Selection Using MCDM Methods inMWSN: A Comparative Study, 2019 IEEE 14th InternationalConference on Intelligent Systems and Knowledge Engineering (ISKE), Dalian, China, (2019), 240–247, doi: 10.1109/ISKE47853.2019.9170426

51.

Khaleghnasab

, Bagherifard

, Nejatian

and Ravaei

, Energy Efficient Multi-Path Routing Algorithm Using Gray System Theory for Improvement of Routing and Network Stability in Internet of Things. (2020).

52.

Jing

J.-l.

and Yang

, Evaluation of performance for wireless sensor networks based on Gray theory, (2012).

53.

, Du

, Hu

, et al., A dynamic trust model exploiting the time slice in WSNs, Soft Comput 18 (2014), 1829–1840. https://doi.org/10.1007/s00500-014-1377-7.

54.

Xin-hua

, Fang-bing

and Zong-bo

, Multi-Objective Optimization QoS Routing Based on Grey Fuzzy Theory, In 2009 International Symposium on Computer Network and Multimedia Technology.

55.

Riaz

, Hashmi

M.R.

, Kalsoom

, Pamucar

and Chu

Y.-M.

, Linear Diophantine Fuzzy Soft Rough Sets for the Selection of Sustainable Material Handling Equipment, Symmetry 12(8) (2020), 1215. https://doi.org/10.3390/sym12081215.

56.

Riaz

and Hashmi

M.R.

, Linear Diophantine fuzzy set and its applications towards multi-attribute decision-making problems, Journal of Intelligent & Fuzzy Systems 37(4) (2019), 5417–5439.

57.

Riaz

, Hashmi

M.R.

, Pamucar

and Chu

, Spherical Linear Diophantine Fuzzy Sets with Modeling Uncertainties in MCDM, Computer Modeling in Engineering & Sciences 10.32604/cmes.2021.013699.

58.

Deanna

and Roman

, Uniform Uncertainty Principle and Signal Recovery via Regularized Orthogonal Matching Pursuit, Found Comput Math 9(3) (2009), 317–334.

59.

Donoho

D.L.

, Tsaig

, Drori

and Starck

J.L.

, Sparse solution of underdetermined systems of linear equations by stagewise orthogonal matching pursuit, IEEE Trans Inf Theor 58(2) (2012), 1094–1121.

60.

Cevher

and Jafarpour

, Fast hard thresholding with nesters gradient method, in: Neuronal Information Processing Systems, Workshop on Practical Applications of Sparse Modeling, Whistler, Canada, (2010).

61.

Balraj

, Leelasankar

, Ayyanar

, Yesudhas

H.R.

, Kumar

and Long

H.V.

, An Effective Traceback Network Attack Procedure for Source Address Verification, Wireless Personal Communications, https://doi.org/10.1007/s11277-021-08110-1.

62.

Jeyasudha

, Geethalakshmi

, Saravanan

, Kumar

and Long

H.V.

, A novel Z-source boost derived hybrid converter for PV applications, Analog Integrated Circuits and Signal Processing https://doi.org/10.1007/s10470-021-01800-7.

63.

Bhoi

S.K.

, Jena

K.K.

, Panda

S.K.

, Hoang

V.L.

, Raghvendra

, Subbulakshmi

and Jebreen

H.B.

, An Internet ofThings assisted Unmanned Aerial Vehicle based artificial intelligence model for rice pest detection, AnInternet of Things assisted Unmanned Aerial Vehicle based artificial intelligence model for rice pest detection 80 (2021), 103607.

64.

Jha

, Prashar

, Long

H.V.

and Taniar

, Recurrent Neural Network for Detecting Malware, Computers & Security 99 (2020), 102037.

65.

Tuan

L.M.

, Son

L.H.

, Long

H.V.

, Priya

L.R.

, Soundar

K.R.

, Robinson

Y.H.

and Kumar

, ITFDS: Channel-aware Integrated Time and Frequency-based Downlink LTE Scheduling in MANET, Sensors 20(12) (2020), 3394. https://doi.org/10.3390/s20123394.

66.

Krishnamoorthy

, Vaiyapuri

, Ayyanar

, Robinson

Y.H.

, Kumar

, Long

H.V.

and Son

L.H.

, An Effective Congestion Control Scheme for MANET with Relative Traffic Link Matrix Routing, Arabian Journal for Science and Engineering 45 (2020), 6171–6181.

67.

Krishnan

R.S.

, Julie

E.G.

, Robinson

Y.H.

, Kumar

, Son

L.H.

and Tuan...

T.A.

, Modified Zone Based IntrusionDetection System for Security Enhancement in Mobile Ad-hoc Networks, Wireless Networks 26(2), 1275–1289.

68.

Sahu

, Singh

, Manju

, Taniar

, Tuan

L.M.

, Son

L.H.

, Abdel-Basset

Mohamed

and Viet Long

Hoang

, Heuristic Search Based Localization in Mobile Computational Grid, IEEE Access 7 (2019), 78652–78664, doi: 10.1109/ACCESS.2019.2922400.