Enhanced meta-heuristic optimization of resource efficiency in multi-relay underground wireless sensor networks

UG2UG-UG2AG channel model

In UWSNs, the source node is buried deeper than relay nodes according to the ground surface. As shown in Fig. 1, a three-dimensional (3D) space is considered. The location of each node X ∈ {S∪N_R} is identified by its Cartesian coordinates X^x, X^y and X^z measured from the origin O. The base station is positioned at the origin of x-axis, while, the ground surface, called G, represents the origin of y-axis and the horizontal distance between nodes is measured according to the z-axis. According to Vuran & Akyildiz (2010), the UG2UG path loss ℓuu_SRv of the link between S and R_v, v ∈ [1, N_R] is defined as follows (1)${\displaystyle \ell {uu}_{S{R}_v}=6.4+20lo{g}_{10}\left(d_{S{R}_v}\right)+20lo{g}_{10}\left(\beta \right)+8.69\alpha d_{S{R}_v}-lo{g}_{10}\left(V\right)}$ where d_SRv is the distance in metres between S and R_v given by (2)${\displaystyle d_{S{R}_v}=\sqrt{{\left(S^x-R_v^x\right)}^2+{\left(S^y-R_v^y\right)}^2+{\left(S^z-R_v^z\right)}^2}.}$ The constants α and β measure the attenuation and the phase shifting, respectively. The factor V represents the attenuation of the reflection path obtained when the wave is reflected by the ground surface. Hence, the UG2UG communication results from propagation of the signal in the reflection path and in the direct path between sensors (Vuran & Akyildiz, 2010). Dobson et al. (1985) utilized an electromagnetic propagation model to provide the detailed expressions of the constants α and β. The soil medium dielectric characteristics along with the system operating frequency q, volumetric water content, percentages of sand and clay in soil, and bulk density constitute the main parameters on which these constants depend (Patitz, Brock & Powell, 1995). The soil and air constitute the two media throughout pass the communication between R_v, v ∈ [1, N_R] and B. However, there is no refraction loss from the under-to-aboveground transition due to the perpendicular propagation of the signal from higher to lower medium density (Dong & Vuran, 2013). Then, according to Dong & Vuran (2013), the path loss ℓua_RvB, of the channel between R_v, v ∈ [1, N_R] and B, is obtained by adding the path losses ℓuu_RvG and ℓaa_GB for both underground and aboveground portions respectively, as follows (3)${\displaystyle \ell {ua}_{R_{v}B}=\ell {uu}_{R_{v}G}+\ell {aa}_{GB}}$ with ℓuu_RvG is given by (4)${\displaystyle \ell {uu}_{R_{v}G}=6.4+20lo{g}_{10}\left(d_{R_{v}G}\right)+20lo{g}_{10}\left(\beta \right)+8.69\alpha d_{R_{v}G}}$ and ℓaa_GB is given by (5)${\displaystyle \ell {aa}_{GB}=-147.6+10\mu lo{g}_{10}\left(d_{GB}\right)+20lo{g}_{10}\left(q\right)}$ where d_RvG is equal to the burial depth of the relay node R_v, $d_{GB}=\sqrt{d_{O{R}_v}^2+d_{OB}^2}$, with d_ORv represents the distance between the origin O and R_v, d_OB is the height of the aboveground base station B, and μ is the attenuation coefficient via air.

Multi-relay UWSN communication

Here, the uplink communication procedure among nodes is presented. A time-division based transmission, and so, absence of co-channel interference are assumed. Each node X ∈ {S∪N_R} is, then, assigned to one time slot in each packet transmission. Also, each node is characterized by a limited battery capacity C_X and, at each packet transmission, t ∈ [1, τ], it consumes a power $P_X^t$. To transmit a data packet d^t, the process requires two phases. In the first phase, the source node S transmits the packet which reaches the set of relay nodes R_v ∈ [1, N_R] located within the source communication range. The resulting received signal $y_{R_v}^t$ at each R_v is given by: (6)${\displaystyle y_{R_v}^t=\sqrt{P_S^t}{h}_{S{R}_v}^t{d}^t+n_{R_v}^t}$ such that $h_{S{R}_v}^t$ represents the gain of the UG2UG channel between S and R_v, which obeys the Rayleigh distribution (Vuran & Akyildiz, 2010) with the underground path loss ℓuu_SRv calculated in Eq. (1), and $n_{R_v}^t$ defines the zero-mean complex Additive White Gaussian Noise (AWGN) vector with variance N₀. Then, in the second phase, $N_R^S$ selected cooperative relay nodes amplify and forward, each in a time slot, the signal $y_{R_v}^t$ to B. The proposed relay selection scheme will be presented in the next section. The received signal $y_B^t$ at B is calculated as follows: (7)${\displaystyle y_B^t=A_v^t\sqrt{P_{R_v}^t}{h}_{R_{v}B}^t{y}_{R_v}^t+n_B^t}$ where $h_{R_{v}B}^t$ is the UG2AG distributed Rayleigh channel between R_v and B (Vuran & Akyildiz, 2010) with the underground path loss ℓua_RvB calculated in Eq. (3), $n_B^t$ is the zero-mean complex AWGN vector, and $A_v^t=\frac{1}{\sqrt{P_S^t|h_{S{R}_v}^t{|}^2+N_0}}$ is the amplification factor. Since the received signals from the $N_R^S$ time slots are affected by different channel transfer function, the base station B combines them using the Maximum Ratio Combining (MRC) to compute the decision variable. As a result, the SNR at the output of the MRC, received at B, is expressed as the sum of the individual instantaneous SNRs of the two-hop links $\left(S,R_v,B\right),R_v\in \left[1,N_R^S\right]$ and is given by (8)${\displaystyle {{\Gamma }_{MRC}}^t=\sum _{v=1}^{N_R^S}{{\Gamma }_{S,R_v,B}}^t=\sum _{v=1}^{N_R^S}\frac{{A_v^t}^2{P}_{R_v}^t{P}_S^t\left|h_{R_{v}B}^t{|}^2\right|h_{S{R}_v}^t{|}^2}{b{N}_0\left({A_v^t}^2{P}_{R_v}^t|h_{R_{v}B}^t{|}^2+1\right)}}$ where b denotes the channel bandwidth in Hz, which is, here, equal to the operating frequency q. Then, the maximum data rate of the cooperative network, denoted by R^t, is given by (9)${\displaystyle R^t=b{log}_2\left(1+{{\Gamma }_{MRC}}^t\right).}$ Hence, the energy efficiency EE^t, defined as the total bits generated per unit energy consumed by sensor and relay nodes, equals (10)${\displaystyle E{E}^t=\frac{R^t}{P_S^t+\sum _{v=1}^{N_R^S}{P}_{R_v}^t}.}$ Moreover, the spectral efficiency SE^t, which represents the total delivered bits per unit bandwidth, equals (11)${\displaystyle S{E}^t=\frac{R^t}{b}.}$

Hybrid chaotic salp swarm with crossover algorithm

The meta-heuristic HCSSC algorithm, proposed in Ayedi, ElAshmawi & Eldesouky (2022), is based on the the Salp Swarm Algorithm (SSA) which is one of the recent swarm algorithms proposed in Mirjalili et al. (2017) and is widely used in solving many optimization problems (Abualigah et al., 2020). The SSA emulates the motion of Salpidae that possess a limpid barrel-shaped body and live in deep oceans (Madin, 1990). Salps are organized in the form of a swarm called a salp chain. Each salp xⁱ, i ∈ [1, N] in the algorithm population corresponds to a possible solution for the optimization problem where N is the total number of salps and M is the dimension of the salp which equals to the number of variables to optimize. The salp chain is divided mathematically into two groups: a leader, x¹, which is the first salp of the chain, and followers, xⁱ, i ∈ [2, N], which are the remaining salps that follow the leader. Since the global optimal solution of any optimization problem is unknown, the best solution can be obtained by moving the swarm leader, followed by the followers, towards the food source. As a result, the whole salp chain moves towards the global optimum.

For our considered problem, the resource efficiency optimization in the considered multi-relay UWSN is modelled as a multi-dimensional optimization problem with the maximized objective function is given in Eq. (12). Each salp $x^i=\left(x_1^i,\dots ,x_M^i\right)$ has M = N_R + 1 variables $x_j^i,j\in \left[1,M\right]$ which are the transmission powers of source and relay nodes used at each transmission t. Thus, $x^i=\left(x_1^i,\dots ,x_M^i\right)=\left(P_S^t,P_{R_1}^t,\dots ,P_{R_{N_R}}^t\right)$. The value of each variable $x_j^i=P_X^t$ is searched within the lower and upper bounds lb_j = P_Xmin and ub_j = P_Xmax.

Crossover technique

Each follower xⁱ, i ∈ [2, N] in the population updates its position based on how far the current position is from the best salp’s position. Since the uniform crossover proves its efficiency compared to other crossover operators (Syswerda et al., 1989; Hussain, Muhammad & Sajid, 2018; Umbarkar & Sheth, 2015), authors in Ayedi, ElAshmawi & Eldesouky (2022) propose to integrate it in the salps positions updates for one-relay network. In the following, we detail the application of the crossover technique in case of multi-relay UWSN.

Each current individual $a=\left(a_1^i,\dots ,a_M^i\right)$ along with the actual best individual $b=\left(b_1^i,\dots ,b_M^i\right)$, where M = N_R + 1, are nominated as parents. The individuala a and b are mate using a binary mask, having the same length M as well. The mask consists of binary digits and is generated randomly. The digits of two offsprings, $\tilde{a}$ and $\tilde{b}$, are duplicated from parents as per the bits of the mask. For the first offspring $\tilde{a}$, if the digit in a mask is 1, then the digit is taken from a, otherwise, it is taken from b. For the second offspring $\tilde{b}$, the complement of the mask is used. The two obtained offsprings $\tilde{a}$ and $\tilde{b}$, are considered as two new salps in the population. Then, the objective function, which is the resource efficiency, RE^t given in Eq. (12), of each offspring, is evaluated. The offspring having the highest resource efficiency is chosen to be x_ucross. Consequently, each follower in the salp chain updates its position as follows (16)${\displaystyle x_j^i=\frac{1}{2}\left(x_{ucross}+x_j^{i-1}\right)\forall i\ge 2}$ Figure 2 illustrates an illustrative example of the uniform crossover for N_R = 3. The leader and followers update their positions iteratively until reaching the maximum number of iterations IT_max. Hence, the optimal values of the source and relay nodes powers are obtained.

Relay selection approach

Having obtained the optimal powers for N_R relay nodes, the base station B decides which relay nodes should actually participate in the data transmission by comparing $P_{R_v}^{t^{opt}},R_v\in N_R$ to a given threshold γ and feeds back the CSI to those nodes. If $P_{R_v}^{t^{opt}}\ge \gamma$, the relay is selected to cooperate. Otherwise, the relay node is not selected and his power is set to 0. This criteria ensures that only the most beneficial relay nodes to the communication performance are selected and simultaneously, the total consumed power is minimized as the number of cooperating relays is limited. Generally, the determination of the value of this threshold is based on the designer objective related to the available resources in terms of bandwidth and power. The impact of this threshold adjustment is studied in Section 5.

The overall algorithm for optimizing the resource efficiency based on the HCSSC-RC algorithm is described in Fig. 3.