Deterministic clustering based compressive sensing scheme for fog-supported heterogeneous wireless sensor networks

Setup phase

DCCS executes this phase only once in the first round. The basic aim of this phase is to collect all sensor data X with non-CS compression in the FN with possible minimum energy consumption of sensors. To achieve that, this phase consists of four steps: CH Selection, Clusters Construction, FN Selection and Learning. We describe these steps in detail as follows:

(A) Step 1: CH Selection: This step adopts the same idea as proposed in Aderohunmu, Deng & Purvis (2011) where, the CH selection process depends only on the RE of the nodes (residual energy). In the DCCS algorithm, the Fog leader node selects a fixed number of nodes ( $n_{ch}$) to be CHs depending on RE of every node such that the priority is for nodes with highest RE (fog leader node selection process will be described later in “Setup Phase” A). The $n_{ch}$ value is predetermined by the cloud and can be estimated by the algorithm in Raghuvanshi et al. (2010).

After the first round, each cluster is responsible for selecting a new CH dynamically. This scenario reduces the cost for searching and selecting new CH. The selected CHs transmit their own information to all other (non-CH) nodes. The non-CH nodes will select the nearby CH to start with the Clusters Construction step.

(B) Step 2: Clusters Construction: once the selected CHs advertise themselves as CHs, the non-CH nodes start to construct clusters by selecting a closest CH Ci, where i = 1, 2, …, $n_{ch}$, and send join-request message (JRM) to it. 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 converts the WSN into NCH clusters where each cluster has a CH and a set of member (CM) nodes. In order to decrease the whole network power utilization for transmitting data per round in each cluster, the DCCS algorithm starts to organize the member nodes within each cluster into chain. For all clusters, each CH Ci, i = 1, 2, …, $n_{ch}$ applies the following Initialization and Update Step to construct ChainList (s) for nodes. The procedure for this step is shown in Fig. 2, where $n_{C{M}_i}$ represents the total number of members of cluster Ci, $\mathrm{d}\mathrm{i}\mathrm{s}{}_{\mathrm{m}\mathrm{i}\mathrm{n}{}_j}=\mathrm{m}\mathrm{i}\mathrm{s}{}_{j<k\le n_{C{M}_i}}\mathrm{d}\mathrm{i}\mathrm{s}$ (cj, ck) denotes the smallest distance between cj and other consecutive nodes ck.

Initialization Step: in each cluster, Ci uses its member nodes information to create the ChainListi, where ChainListi = [c0, c1, …, clast-1, clast] by adding the nearest member node c0 to it. It then updates the ChainListi with the nearest unselected member node (c1) to node c0.

Update Step: after that, Ci holds the nearest unselected neighbor node cj to node c1 in waiting to decide wherever it will be placed in ChainListi or not, by comparing the distance between c1, cj and any consecutive nodes in ChainListi. If the distance between c1 and cj is less than D, where D the distance between cj and any consecutive node, then Ci adds it to the end of ChainListi. Otherwise cj will be added between the consecutive nodes that have least distance to cj, e.g., if cr and ck are consecutive nodes in the ChainListi and if dis(cj, clast) > dis(cj, cr) and dis(cj, clast) > dis(cj, ck), then node cj will be inserted between cr and ck. Otherwise, node cj will be inserted to the end of the ChainListi after node clast, where clast is the last node of the ChainListi and dis(cj, ck) is the distance among node cj and node ck. Ci repeats the previous Update Step to include all its members in ChainListi. If a member node dies in a ChainListi, then Ci will reconstruct the chain to bypass the dead node.

By applying the previous steps, each node will send and receive with the possible minimum distance. Thus, DCCS can save power of each node.

(C) Step 3: FN Selection: each CH selects the nearest FN for transmitting its data. FN receive the data transmitted by the CHs, perform aggregation operation and deliver the data to the cloud using a routing technique.

(D) Step 4: learning process: measurement matrix selection is considered as one of the most important processes in the CS method due to its impact on nodes data where this matrix is used by sensor nodes to compress their data and is used by the cloud to reconstruct the sensor data. Incorrect selection may lead to large data loss; hence, selection of proper measurement matrix is crucial.

Each FN generates this matrix using a random seed ξ, and then broadcasts ξ to the whole WSN. For seed selection process, DCCS applies the following scenario: DCCS starts seed estimation process by learning step. During the intra-cluster process, the CH starts to collect data X by a non-CS from its chain members and then fuse these data. Then, using inter-cluster communication process, data is combined by FN towards Fog leader node and send to cloud by Fog leader node. Then, the cloud starts to find the best ξ that gives minimum error. The cloud uses this minimum error as threshold β. Finally, the cloud sends ξ to the entire network to use during Data compression phase.

Data compression phase

Deterministic Clustering based CS scheme repeats this phase starting from the second round. This phase consists of four steps: CS based data gathering within intra-cluster (cluster member to CH) and inter-cluster (FN to cloud), Reconstruction, Dynamic Re-Generation of Random Seed and CH rotation. At the end of this phase, DCCS reuses Algorithm 1 to create the cluster with the new inputs (new CHs will be the output from this phase). The details of these steps are illustrated below:

(A) CS based data gathering

As described in the previous steps, there are NCH clusters with CH Ci and chain member nodes organized in ChainListi such that each ChainListi = [c0, c1, …, clast-1, clast].

Intra-cluster (from cluster member to CH): DCCS starts CS gathering in each intra-cluster as follows: the last node clast in the ChainListi uses the global seed ξ received from the BS to generate αclast. The clast node computes its compress vector (measurement) ylast = αc_last dc_last, where dc_last is the reading of sensor clast, and then transmits the measurement yc_last to its previous neighbor node clast-1 in the ChainListi. After that, node clast-1 uses the same global seed ξ to generate αc_(last-1) and compute its measurement yc_(last-1) = αc_(last-1) dc_(last-1) and then delivers the summation vector yc_last + yc_(last-1) to the previous node clast-2. Once clast-2 receives yc_last + yc_(last-1), it computes its value yclast-2, adds it to yc_last + yc_(last-1) and then transmits the summation value to previous node in ChainListi and so on till the CH Ci. Now each CH Ci has already received the compressed vector yi = [yc_0, yc_1, …, yc_last] from their corresponding CMs. Then, each CH sends the compressed samples to the nearest FN.

Inter-cluster (from FN to cloud): Through inter-cluster communication, DCCS applies the same scenario used in Algorithm 1 to organize the FN in chain and consider them as CMs of a cluster with the cloud as CH.

The communication among FN is restricted to adjacent FNs in each round, and the fog leader node will be selected to deliver the gathered data to the cloud. As the scenario is same as in Algorithm 1, FNs are organized into a chain to deliver the information among FNs and to deliver the aggregated data to the cloud. The formed chain allows the nodes to interact and exchange information with their chain neighbors. CHs deliver their collected data to FNs, and the data will be fused at the FNs.

Finally, fog leader node will deliver the fused data to the cloud. The selection of fog leader node depends on their energy and the distance to the cloud. Formation of a chain among FNs and choosing one among them as fog leader to send the data to the cloud could save more energy in the network than sending the data independently by each FN to the cloud. The communication process for both inter-cluster and intra-cluster are shown in Fig. 3.

(B) Reconstruction Step When the cloud gets the compress vector y = [y1, y2, y3, …,yi], where i = [1, 2, …, $n_{ch}$] transmitted by the FN leader, cloud generates the CS matrix depending on the predefined random seed ξ. After that, the cloud reconstructs the original data x0 of every cluster. In order to improve this step, in this paper, RSMP is proposed. The working of RSMP will be described in “RSMP Algorithm”.

(C) Dynamic re-generation of random seed

The main idea of this step is that DCCS gives the ability to dynamically change the CS matrix depending on the network status, and the number of nodes that are still alive, instead of using the same CS matrix generated during the Setup phase in all rounds.

The problem of using the fixed CS matrix is that: in each round, every sensor node transmits and receives fixed size vector whatever the count of alive nodes in each round (which should be varied according to the count of alive nodes); this leads to an increment in the average power consumption and also has negative reflection in the reconstruction process.

To overcome this problem, DCCS dynamically changes the CS matrix whenever the network status changes, i.e., the CS matrix size reduces in accordance with the number of alive nodes. In this situation, DCCS can successfully decrease the overall power consumption. The cloud can obtain the dead nodes count in every cluster from FN through the CHs. Where, each CH can simply use a HELLO message to identify the dead nodes count in its cluster in each round.

The working procedure of this step can be summarized as follows: the cloud compares the latest reconstructed data x′ with X and decides whether to re-generate depending on the error value, $\epsilon =||x-x^{\prime }||$, where ||·|| is $L_n-norm$. If it goes beyond a predefined threshold β which means that there is a change in network status, the cloud regenerates new ξ, otherwise no need to change last seed.

(D) CH rotation

CHs check the piggybacked CM–REs information to make decision on whether to continue as CHs or give up their CH roles to any other node in their respective clusters based on RE and assign these nodes as the new CHs. This step prevents WSNs from dying earlier by balancing the energy consumption. The whole process of the data compression phase can be seen in Fig. 4.

Case 1: homogeneous network

In this case, DCCS algorithm performance is evaluated in comparison with DMC-CS (Salim & Osamy, 2015) and EDACP-CS (Khedr, 2015). We use the same energy parameters as used in Salim, Osamy & Khedr (2014). To send a message of size l-bits to a distance d, the power consumed by the radio, we use Eqs. (3) and (4) in “Network Assumptions”.

Figure 6 shows the lifetime for DCCS, EDACP-CS and DMC-CS. In EDACP-CS and DMC-CS, the death of the first node is earlier than in DCCS, and also Fig. 6 shows the potency of the DCCS algorithm in enhancing the lifetime of the network than compared to EDACP-CS and DMC-CS algorithms. The reason is that the DCCS uses a fixed count of CHs (NCH) per round, which leads to achieve better stability in energy utilization among the nodes, when compared to other algorithms. Additionally, in DCCS, the BS takes the role to select the CHs only in the first round and then the CHs change dynamically, which considerably decreases the overhead cost of computation associated with CH search when compared 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 other algorithms.

Figure 7 depicts the lifetime and the count of alive nodes in the network per round for DCCS, EDACP-CS and DMC-CS. It clearly shows that the first and last node death in DCCS happen several rounds later than those of EDACP-CS and DMC-CS, which means that DCCS minimizes the energy utilization among all sensors. This is because DCCS reduces the power consumption of each node by organizing the nodes of each cluster in a chain such that each node sends and receives only from the nearest node, which is not 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 into consideration the distances between that node and the others in the chain, rather than simply adding the closest node as the last node of the chain like DMC-CS. From Fig. 8, it is evident that DCCS succeeds to decrease the average energy consumption when compared to EDACP-CS and DMC-CS algorithms. The main reason for this is due to the dynamic re-generation of CS matrix in DCCS, which is not considered in the other algorithms.

Case 2: heterogeneous network

Here, we focus to evaluate the proposed algorithm performance in a heterogeneous network scenario. In this case, we make an assumption that the total network energy is 102 J, where the nodes are divided into advanced, intermediate and normal nodes according to their residual energy. DCCS performance is evaluated in comparison with ETSSEP (Kumar, Kant & Kumar, 2015), SEECP (Mittal, Singh & Singh Sohi, 2017) and SILEACH (Al-Zubaidi, Ariffin & Al-Qadhi, 2018) based on CS method. It’s clear that DCCS still provides good performance with reference to network lifetime in terms of first node dies enhancement in comparison with ETSSEP, SEECP and SILEACH algorithms as shown in Fig. 9. That is because the dynamic CS matrix regeneration process in DCCS gives it the ability to utilize CS matrix in an effective way to minimize the total transmitted data which leads to reduce the transmission energy expenditure. Whereas, the other algorithms use the same CS matrix in each iteration which may become inappropriate for the network after a number of iterations. The same effect can be noticed in Fig.10 where DCCS performs better than the other algorithms with reference to network lifetime in half-node death case.

From Fig. 11, we can conclude that DCCS succeeds to minimize the total energy expenditure in comparison with the others. That is because DCCS divides the network into various clusters and inside every cluster, it uses the proposed chain construction algorithm to arrange the CMs into a chain. In addition, DCCS uses the same proposed chain construction algorithm to organize the FN transmission to the Cloud.

Performance metrics

Random Selection Matching Pursuit algorithm performance in signal reconstruction is compared with other reconstruction algorithms with reference to Average Normalized Mean Squared Error (ANMSE), which is the average ratio ${\displaystyle \frac{||x-{x^{\text{∼}}||}_2}{||x_2||}}$, where $x$ and $x^{\text{∼}}$represent the original and reconstructed readings respectively.

Experiments over real datasets

In this section, we use RSMP algorithm for reconstructing the signals obtained from Intel Berkeley Research lab.

Figures 12A and 12B: 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 Figs. 12C and 12D. In Fig. 13, we illustrate the distribution of relative reconstruction error for different reconstruction algorithms. It is evident that RSMP algorithm exceeds the performance of other greedy algorithms, i.e., the COSAMP, OMP, EOMP, FBP and SP respectively.

Different coefficient distributions: In this part of simulation, Uniform and Gaussian distributions are utilized to draw the non-zero values of the sparse signal and the sparse level S ranges from 5 to 60. In Fig. 14 where the sparse signal’s non-zeros values are taken from uniform distribution, RSMP algorithm has lower ANMSE comparing to COSAMP, FBP, OMP, E-OMP and SP. Moreover, ANMSE for RSMP algorithm appear to rise only when s > 49 while it increases when s > 42, s ≥ 34, s ≥ 44, s ≥ 38 and s ≥ 41 for COSAMP, OMP, E-OMP, FBP and SP algorithms respectively as shown in Fig. 14. Figure 15 shows the results of ANMSE when the non-zero entries of sparse signal are taken from Gaussian distribution. From Fig. 15, it is evident that RSMP algorithm still gives least ANMSE result when compared to COSAMP, OMP, EOMP, FBP and SP, as s > 59, s ≥ 46, s > 34, s > 49, s > 47 and s > 45, respectively.

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. 16 and 17 respectively. To achieve this aim, sparse signals taken from Uniform distribution having length n = 120 is utilized and m values from 10 to 60 with step size of 1. From those figures, we can understand that RSMP algorithm still provides the least ANMSE values when compared to other algorithms.

Reconstruction over noisy signal: In this part, we add some noise equal to 10⁻⁴ to the original Uniform as well as in Gaussian distribution signal where n = 256 and m = 128. The CS matrix Φ is drawn from the Gaussian distribution. The sparsity S levels are from 10 to 60 with step size 1.

Figures 18 and 19 depict the reconstruction errors for the noisy Uniform and Gaussian sparse signals. We can see that RSMP algorithm produces less error than COSAMP, OMP, E-OMP, FBP and SP. In summary, RSMP algorithm improves the reconstruction process and gives better 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.

Performance metrics

We call DCCS algorithm as DCCS-dynamic if it uses the proposed dynamic re-generation of random seed and DCCS-static otherwise. This section compares the performance of DCCS-dynamic and DCCS-static, with reference to the following: Average Energy Consumption and Average Normalized Mean Squared Reconstruction Error (ANMSE). During the reconstruction process, COSAMP (Needell & Tropp, 2009) algorithm is used to recover the data in each round.

Figure 20 shows the performance of DCCS algorithm in both dynamic (DCCS-dynamic) and static (DCCS-static) mode in terms of number of alive nodes per round. According to DCCS-dynamic scenario, the number of measurement samples transmitted in intra or inter-cluster communication decreases while the count of dead nodes are increased. Moreover, DCCS-static uses a fixed CS matrix whatever the count of alive nodes per round. On the other hand, DCCS-dynamic uses the threshold β value with reference to the best reconstruction error and then compares the reconstruction error in each round with β. If the error is larger than β, the old matrix is considered as not suitable and therefore regenerates another one.