# Energy-Spectral Efficiency Optimization in Wireless Underground Sensor Networks Using Salp Swarm Algorithm

Authors: Mariem Ayedi; Esraa Eldesouky; Jabeen Nazeer
Journal: Journal of Sensors
 (2021)

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## Abstract

Achieving high data rate transmission is critically constrained by green communication metrics in Wireless Sensor Networks (WSNs). A unified metric ensuring a successful compromise between the energy efficiency (EE) and the spectral efficiency (SE) is, then, an interesting design criterion in such systems. In this paper, we focus on EE-SE tradeoff optimization in Wireless Underground Sensor Networks (WUSNs) where signals penetrate through a challenging lossy soil medium and nodes’ power supply is critical. Underground sensor nodes gather and send sensory information to underground relay nodes which amplify-and-retransmit received signals to an aboveground sink node. We propose to optimize source and relay powers used for each packet transmission using an efficient recent metaheuristic optimization algorithm called Salp Swarm Algorithm (SSA). Thus, the optimal source and relay transmission powers, which maximize the EE-SE tradeoff under the maximum allowed transmission powers and the initial battery capacity constraints, are obtained. Further, we study the case where the underground medium properties are dynamic and change from a transmission to another. For this situation, we propose to allocate different maximum node powers according to the soil medium conditions. Simulation results prove that our proposed optimization achieves a significant EE-SE tradeoff and prolongs the network’s lifetime compared to the fixed allocation node power scheme. Additional gain is obtained in case of dynamic medium conditions.


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## Body

## 1. Introduction

Wireless Underground Sensor Networks (WUSNs) are a promising territory of real-time monitoring and exploration in many underground applications involving intelligent agriculture, pipeline fault diagnosis, subway tunnels, coal mines, earth geology, and earthquake disaster prediction. In this network type, wireless sensor nodes are buried under the ground and exchange sensory information through soil medium [1, 2]. A primary privilege of using WUSNs is that buried nodes are generally not affecting the functional operations on the ground [3]. In compared with terrestrial WSNs, designing structure in WUSNs is challenging due to the harsh underground environment, the restrictive communication node range, and the difficulty of the sensor energy supplement. Signal propagation among nodes using electromagnetic (EM) wave has been studied in [4–6]. The effect of various factors, such as soil properties in terms of moisture, clay, and sand percentages and system parameters like operating frequency and depth of buried sensor nodes, on the path loss, is also discussed. In [7], authors detail the characteristics of three channels in WUSNs: (1) underground-to-underground channel (UG2UG), (2) underground-to-aboveground channel (UG2AG), and (3) aboveground-to-underground channel (AG2UG).Usually, direct communications between sensor nodes and aboveground sinks cannot be guaranteed since sensor nodes are possibly buried at deep positions and have limited communication ranges. Consequently, the employment of relay nodes in WUSNs is an encouraging way to achieve high capacity and to extend network coverage. Several works have been proposed regarding the relay employment in WUSNs [8–11]. The usage of relay nodes to track water pipes through multilayered underground channel modelling was studied in [8]. This work is aimed at controlling the energy consumed by the buried nodes depending on the optimal positioning of aboveground relay nodes. In [9], the optimal relay node placement that is aimed at prolonging the network’s lifetime under limited relay number, load balancing, and network topology constraints is discussed. However, authors in [10] locate virtually changeable relay nodes in two-tier wireless networks in tunnels. Similarly, a hierarchical relay node deployment framework for underground coal mine is suggested in [11]. The sensed data are forwarded through the partitioned regions of the relay nodes which provide efficient coverage for the WUSNs. Although most WSNs research study individually the spectral efficiency (SE), which measures the system data rate in a limited frequency spectrum, and the energy efficiency (EE), which considers the consumed power cost, recent works [12–16] propose to jointly optimize the tradeoff EE-SE between both metrics. However, to the best of our knowledge, this tradeoff optimization has not been yet studied in WUSNs where relay nodes are used. In fact, the throughput optimization in WUSNs, where transmission is based on magnetic induction (MI), is addressed in [17]. Moreover, authors in [18, 19] aim to optimize the throughput in WUSNs where underground sensors harvest RF energy from an aboveground access point. These researches motivate us to study the tradeoff EE-SE optimization in WUSNs in order to enhance the resource allocation and to prolong the lifetime of these networks.Nowadays, metaheuristic optimization algorithms have been used to solve many complex problems in WSNs by searching for the best solution, among several values, of an optimized objective function known as fitness function. Swarm optimizations and genetic algorithms are the two main categories of metaheuristic algorithms. In the literature, the genetic algorithm (GA) had been used in WUSN optimization to achieve better network lifetime [20, 21]. In [20], the wireless sensor nodes of underground mine network are clustered based on GA to obtain a green communication environment. Likewise, the relay node placement in underground room and pillar mines is optimized using GA in [21]. In [22], a single-hop-based routing algorithm for multiple mobile sinks in WSNs is exhibited. The method is composed of two parts: the park position selection based on the Particle Swarm Optimization (PSO) and multipath scheduling for mobile sinks based on the GA. The studies [20–22] target reaching minimized energy and extended network lifetime in WSNs. In [23, 24], the Gravitational Search Algorithm (GSA) is used to enhance the energy efficiency of WSNs. In [23], authors calculate the optimal number of clusters and determine the best cluster heads maximizing the efficient energy consumption by applying the novel version of GSA. In [24], authors propose a trust-based energy-aware routing algorithm to select the optimal route from a source to a destination based on energy-aware GSA approach. Another metaheuristic algorithm called Artificial Bee Colony (ABC) has been used for of energy efficient clustering and routing problems in WSNs [25, 26]. The work [27] suggests the use of Ant Colony Optimization (ACO) to save distance and residual energy of neighbour nodes. Besides, it selects the node with lower energy as next hop, resulting in energy efficient load balancing of the network. A recent metaheuristic algorithm named Salp Swarm Algorithm (SSA) is proposed by [28]. Authors in [28] prove the outperforming of SSA over PSO, GSA, and differential evolution (DE) through experiments on 19 different benchmark functions. Thus, SSA has been used in many fields including engineering issues [29–31], image processing [32], and machine learning [33]. The study [33] integrates SSA with machine learning to achieve automatic image classification. The proposed approach was implemented on three learning algorithms which are Decision Tree, K-nearest Neighbours, and Naïve Bayes. In WSNs, SSA is used to optimize the node localization [34, 35]. Moreover, authors in [36] focused on a security aware and energy efficient multihop routing protocol in WSNs using a modified algorithm named Taylor-based Cat Salp Swarm Algorithm (Taylor C-SSA). In [37], a novel strategy is applied for optimal sensor deployment in WSNs. In this work, an improved version of SSA called weighted SSA (WSSA) based on adding weighted distance position update strategy is proposed. Interestingly, this work proves that even the original SSA algorithm provides energy consumption, coverage, and lifetime optimization compared to many other algorithms like PSO, Whale Optimization Algorithm (WOA), Grey Wolf Optimization (GWO), and Multiverse Optimization (MVO). Therefore, we propose to use the SSA to optimize the resource efficiency in WUSNs employing relay nodes. To the best of our knowledge, our work is the first assessment which studies this topic.In this paper, we consider a WUSN where underground source nodes transmit sensory information to underground amplify-and-forward (AF) relay nodes through UG2UG communication links. Buried relay nodes retransmit received packets to an aboveground sink node through UG2AG links. To avoid high-power interference signals as discussed in [17], the Time Division Multiple Access (TDMA) scheme is employed. Therefore, nodes use the whole frequency band in their transmissions. We propose to study the EE-SE tradeoff, named resource efficiency (RE), considering the UG2UG and UG2AG link characteristics. The primary objective is to find the optimal source and relay powers required to transmit a new data packet maximizing the total RE of all transmissions that can be performed and considering the initial node battery capacities. Because of the complexity of the considered problem, we use the SSA to optimally estimate the node powers ranging between minimum and maximum allowed values. The complexity of the proposed scheme is studied. The impact of soil composition and system parameters on RE is also well-studied and formulated. Since in some real cases, the composition of underground environment is dynamic and can variate with time [38], we propose to study the case where the soil properties in terms of moisture vary among two successive node transmissions. In addition, an adaptive power allocation, by considering different power constraints among transmissions, is addressed to further improve the RE of the dynamic underground system. The major contributions of our work are listed as follows:
(1)
A power allocation scheme maximizing the RE in a WUSN where underground source nodes transmit sensory information to an aboveground sink node through underground relay nodes using UG2UG and UG2AG communication links is proposed(2)
The SSA is used to optimally find the source and relay powers required to transmit a new data packet maximizing the RE and considering minimum and maximum allowed values and the initial node battery capacities(3)
The complexity of the proposed scheme is studied(4)
A significance in RE performance and network’s lifetime compared to the conventional WUSN scheme is proved(5)
The proposed scheme is extended to the dynamic underground system where the soil properties in terms of moisture vary among two successive node transmissionsThis paper is organized as follows: in Section2, we present the considered WUSN system model. In Section 3, we detail the channel model for the UG2UG and UG2AG communications. In Section 4, we present the proposed SSA-based power allocation algorithm. In Section 5, we present the simulation results, and in Section 6, we give conclusions.


## 2. WUSN System Model

We consider a WUSN consisting of sensor nodes which collect and transmit sensory information to an aboveground sink node with the help of half-duplex relay nodes. The link between a sensor node and a relay node is an UG2UG link while the communication link connecting a relay node and the aboveground sink node is an UG2AG link as shown in Figure1. To avoid receiving interference signals, we assume a TDMA scheme. We detail, here, the uplink communication process between a sensor node S, a selected AF relay node R, and the aboveground sink node A. Each node X∈S,R has a battery with finite power capacity PX, X∈S,R. Each node X∈S,R uses some quantity of power PXt when transmitting a new packet t with t∈1,T, and T is the total number of transmissions that can be performed over the link S–R–A under the nodes’ initial power capacity constraints PS and PR. A list of important symbols and notations used in this paper are given in Table 1.Figure 1
WUSN topology.Table 1
Symbols and notations.
SymbolDefinitionPXBattery power capacity of nodeX∈S,RTTotal number of transmissions that can be performed over the linkS−R−APXtPower used to transmit a packett∈1,ThSRtUG2UG Rayleigh distributed channel betweenS and RhRAtUG2AG Rayleigh distributed channel betweenR and AnXYtZero-mean complex Additive White Gaussian Noise (AWGN) vector with power spectral densityN0WSystem bandwidthGtAmplification factorLSRUG2UG path lossLRAUG2AG path loss composed by the path losses at the underground and the aboveground portionsLRAug and LRAagPXminMinimum power allowed for each transmissionPXmaxMaximum power allowed for each transmissionPXt∗Optimal power of nodeX∈S,RPXtRemaining battery capacity of nodeX∈S,R at t∈1,TSNRSRAtTotal SNR of the linkS−R−ARSRAtMaximum achievable total transmission data rate of the linkS−R−AλEEtEnergy efficiency of the linkS−R−AλSEtSpectral efficiency of the linkS−R−AλREtResource efficiency of the linkS−R−AThe communication process requires two steps. In the first step,S transmits a data packet, denoted by xSt to R. Hence, the received signal at the relay node R is
(1)ySRt=PSthSRtxSt+nSRt,where hSRt is an UG2UG Rayleigh distributed channel between S and R (as explained in [4]) and nSRt is the zero-mean complex Additive White Gaussian Noise (AWGN) vector with power spectral density N0. In underground transmission, electromagnetic propagation dependents on soil properties and the path loss model are different from the path loss model of the transmission in the air.The instantaneous signal to noise ratio (SNR) of the transmission betweenS and R denoted by SNRSRt, is expressed as
(2)SNRSRt=PSthSRt2WN0,where W denotes the channel bandwidth in hertz.The maximum achievable transmission data rate in bits per second for the transmission betweenS and R, denoted by RSRt, is expressed as
(3)RSRt=Wlog21+SNRSRt.In the second step,R amplifies and retransmits the received signal to A. Then, the received signal at A is given by
(4)yRAt=GtPRthRAtySRt+nRAt,where hRAt is an UG2AG Rayleigh distributed channel between R and A (as explained in [4]), Gt is the amplification factor given by 1/PSthSRt2+N0 and nRA is the zero-mean complex AWGN vector. For soil to air communication, the propagation model is affected by the soil-air interface and the propagation through air.The instantaneous SNR of the transmission betweenR and A, denoted by SNRRAt, is as follows:
(5)SNRRAt=Gt2PRtPSthRAt2hSRt2WN0Gt2PRthRAt2+1.The maximum achievable transmission data rate in bits per second for the transmission betweenR and A, denoted by RSRt, is calculated as
(6)RRAt=Wlog21+SNRRAt.Hence, the total SNR of the linkS–R–A, denoted by SNRSRAt, depends on the SNRs of the two hops SNRSRt and SNRRAt that is given by
(7)SNRSRAt=SNRSRtSNRRAt1+SNRSRt+SNRRAt.The maximum achievable total transmission data rate of the linkS–R–A, denoted by RSRAt, is expressed as
(8)RSRAt=Wlog21+SNRSRAt=Wlog21+SNRSRtSNRRAt1+SNRSRt+SNRRAt.Therefore, the energy efficiencyλEEt of the link S–R–A, where energy consumption includes the sensor and the relay node energies, is defined as the total delivered bits per unit energy and is computed as
(9)λEEt=RSRAtPSt+PRt=Wlog21+SNRSRAtPSt+PRt.On the other hand, the spectral efficiencyλSEt of the link S–R–A is defined as the total delivered bits per unit bandwidth and is given by
(10)λSEt=RSRAtW=log21+SNRSRAt.Finally, the total energy efficiencyλEE and the total spectral efficiency λSE of the link S–R–A over T transmissions are, respectively, given by
(11)λEE=∑t=1TλEEt,λSE=∑t=1TλSEt.The mathematical derivations of the UG2UG and UG2AG path lossesLSR and LRA, of the signal propagation between S and R and between R and A, respectively, are detailed in the next section.


## 3. Channel Model for the UG2UG and UG2AG Communications

In WUSN, sensor and relay nodes are both buried into the soil: the relay node is buried close to the ground surface, and the sensor node is deeper as shown in Figure1. In this scenario, a second path resulting from the wave reflection by ground surface should be considered in addition to the direct path between the two nodes [4]. According to [4], the underground path loss LSR of the channel between the sensor node S and the relay node R is given by
(12)LSR=6.4+20log10dSR+20log10β+8.69αdSR−10log10V,where dSR is the distance in meter between the sensor node S and the relay node R. To simplify the computation, we consider the two-dimensional (2D) plane WUSN deployment which represents the nodes’ distances in the plane using Cartesian coordinates defined on x- and y-axes. As illustrated in Figure 2, the sink location is the origin of x-axis whereas the ground surface is the origin of y-axis. The xX is the x-axis and yX is the y-axis coordinates, which equals the node burial depth dXG, of node X∈S,R. Then, dSR is computed as follows
(13)dSR=xS−xR2+yS−yR2.Figure 2
Coordinates ofS and R.According to [4], the factor V is the attenuation factor of the second path given by
(14)V=1+Γexp−αΔr2−2Γexp−αΔrcosπ−∅−2πλΔr,where Γ and ∅ are the amplitude and phase angle of the reflection coefficient at the reflection point P, Δr=r−dSR is the difference between the two paths as shown in Figure 1, and λ is the wavelength in soil.The constantsα, which is the attenuation constant and β, which is the phase shifting constant, depend on the dielectric properties of soil medium. To calculate these parameters, a model, which describes the electromagnetic propagation considering the soil properties and conditions, is required [39]. The constants α and β are, respectively, given by
(15)α=2πfμ0μrϵ0ϵ121+ϵ2ϵ12−1,β=2πfμ0μrϵ0ϵ121+ϵ2ϵ12+1,where f is the operating frequency, μ0 is the free space permeability, μr is the soil relative permeability [40], ϵ0 is the permittivity of free space, and ϵ1 and ϵ2 are the real and imaginary parts of the complex soil’s dielectric constant given by Peplinski’s model [41] as follows:
(16)ϵ1=1.151+ρbρsϵsα1+mvβ1ϵfw1α1−mv1/α1−0.68,(17)ϵ2=mvβ2ϵfw2α11/α1,where ρb is the soil bulk density, ρs is the specific density of the solid soil, mv is the water volume fraction of the mixture, also called the volumetric water content (VWC), and α1=0.65 is an empirically determined constant. The dielectric constant of soil’s solid ϵs is
(18)ϵs=1.01+0.44ρs2−0.062.The parametersβ1 and β2 in equations (16) and (17) are empirically determined from the sand percentage S and the clay percentage C of the soil and are given by
(19)β1=1.2748−0.519S−0.152C,β2=1.3379−0.603S−0.166C.Moreover, the real and imaginary parametersϵfw1and ϵfw2of the relative dielectric constant of free water, mentioned, respectively, in equations (16) and (17), are expressed as
(20)ϵfw1=ϵw∞+ϵw0−ϵw∞1+2πfτw2,ϵfw2=2πfτwϵw0−ϵw∞1+2πfτw2+σeff2πϵ0fρs−ρbρsmv,with τw is the relaxation time for water, ϵw0 is the static dielectric constant for water, and ϵw∞=4.9 is the high frequency limit of ϵfw1 [42]. Values of τw and ϵw0 depend on the temperature room. At 20°C, 2πfτw=0.58∗10−10and ϵw0=80.1. The effective conductivity of σeff for the 0.3−1.3 GHz band is given by
(21)σeff=0.0467+0.224ρb−0.4111S+0.6614C.From these equations, it is clear that the path loss model in soil is dependent on the operating frequencyf, the composition of soil in terms of sand S and clay C percentages, the bulk density ρb, the internode distance dSR, and the volumetric water content mv.The communication between the relay nodeR and the aboveground sink node A consists of two parts, the underground part (soil medium) and the aboveground part (air medium). The refraction loss from underground to the aboveground is absent since the signal propagates perpendicularly from a higher density medium to a lower density medium [7]. Then, based on [7], the path loss LRA of the channel between the relay node R and the aboveground sink node A is given by
(22)LRA=LRAug+LRAag,where LRAug and LRAag are the path losses at the underground and the aboveground portions, respectively, and are computed as
(23)LRAug=6.4+20log10dRG+20log10β+8.69αdRG,LRAag=−147.6+10ηlog10dGA+20log10f,with η is the attenuation coefficient in air with value in the range of 2.8−3.3 according to [43] and dGA is the distance between the relay and the aboveground sink node’s antenna given by
(24)dGA=hRA2+hA2,where hRA is the horizontal distance between the relay node R and the aboveground sink node A and hA is the height of the aboveground sink node A.When TDMA is used in WUSNs, nodes transmit packets using the whole frequency band in different time slots. Then, the operating frequencyf is set to the system bandwidth.


## 4. Optimization Problem and Proposed Power Allocation Algorithm

In this section, we review first the algorithm SSA employed in the EE-SE tradeoff optimization. Then, the considered problem is formulated assuming a static underground environment. At the end of this section, we propose to adapt the proposed algorithm to the case where the soil property in terms of VWC varies among two successive node transmissions.


### 4.1. Salp Swarm Algorithm (SSA)

One of the latest metaheuristic swarm algorithms, that successfully have been employed to optimize different problems in several research areas, is the SSA [44]. This algorithm was firstly introduced by Seyedali Mirjalili in 2017 which mimics the floating of salps that navigate in aquarium environments such as oceans and seas [28]. In deep oceans, salps compose a swarm which is called salp chain. The algorithm divides the populations of salps (i.e., search agents) into two groups: the leader and the followers. The leader salp is at the beginning of the chain and guides the salp population while the rest are followers since they follow the leader.SSA is simple and like other swarm-based intelligent algorithms. The position ofN salps is randomly initialized in an n dimensional search space where n is the number of variables of the considered problem. Additionally, the positions of salps are stored in a two-dimensional matrix called x. A food source called fd in the search space is defined as the swarm’s target. Then, the fitness of each salp is determined to select the leader with the best fitness. The position of the leader is updated using the following equation.
(25)xj1=fdj+c1ubj−lbjc2+lbjc3≥0,fdj−c1ubj−lbjc2+lbjc3<0,where the xj1 is the position of the leader in the jth dimension, fdj is the food source in the jth dimension, lbj and ubj are the lower bound and the upper bound of the jth dimension, respectively, c2 and c3 are random numbers between [0, 1], and c1 is defined as follows:
(26)c1=2e−4l/L2,with l is the current iteration and L is the maximum number of iterations. The position of the ith follower is updated using the equation given by
(27)xji=12xji+xji−1i≥2,where xji is the position of the ith follower in the jth dimension.Using equations (25) and (27), the positions of the salp chain population are updated until the suitable solution is obtained or a stopping criterion is met.


### 4.2. Optimization Problem and Proposed Algorithm

As the conventional design usingλEEt or λSEtis limited in respect of the inefficient use of resources, we are interested to determine the power allocation vector P=PSt,PRt at each t transmission performed over the link S−R−A that jointly maximizes the energy efficiency λEEt and the spectral efficiency λSEt for all transmissions t∈1,T. Since nodes are equipped with batteries with finite capacities, the optimization of the power PXt of each node X∈S,R, used at the tth transmission, should consider the initial battery capacity PX, the spent powers in previous transmissions PX1,⋯,PXt−1, and the power limitation range PXmin,PXmax allowed for each transmission. The proposed multiobjective optimization problem is as follows:
(28)PSt∗,PRt∗=max∑t=1TλEEtPSt,PRt,λSEtPSt,PRtSubjectto∑t=1TPXt≤PX.where PXt∈PXmin,PXmaxforX∈S,R.Since optimizing simultaneously two functions which are competing is challenging, we propose to optimize the unique weighted objective function, called the resource efficiencyλREt, exploiting the tradeoff between λEEt and λSEtas discussed in the work [12]. The resource efficiency λEEt of the link S−R−A at the tth transmission, for t∈1,T, is given by
(29)λREt=λEEt+ωλSEt,where the factor ω is computed as
(30)ω=ω¯WPtot,with ω¯ is a constant, W is the available bandwidth, and Ptot is the total power budget allocated to the link S−R−A at each transmission. Then, Ptot=PSmax+PRmax. The weighted factor ω is introduced to ensure the balancing between λEEt and λSEt because λSEt is practically smaller than λEEt. Moreover, ω corrects the inconsistence of adding two metrics with different units since the unit of λEEt is bits/joule while the unit of λSEt is bits/s/Hz. Then, the unit of λREt is similar to λEEt which is still bits/joule. Besides, optimizing λREt tends to optimize λEEt if ω¯=0 and to optimize λSEt if ω¯=∞. Generally, the choice of the value of this constant is based on the designer objective and the available resources in terms of bandwidth and power [12]. We propose to evaluate this constant for the considered WUSN in Section 5.Consequently, the constrained multiobjective optimization problem in equation (28) is transformed into a single-objective problem as follows: where
(31)PSt∗,PRt∗=max∑t=1TλREtPSt,PRtSubjectto∑t=1TPXt≤PX,PXt∈PXmin,PXmaxforX∈S,R.The considered problem in equation (31) is NP-hard since the number of variables to optimize equals two (PStand PRt) and the presence of variable products in equations (5) and (7) caused by the AF relay transmission. Therefore, the metaheuristic algorithm SSA is used to compute the optimal solution of the problem. The followed procedure is presented below.Step 1.
Each nodeX∈S,R has a finite battery capacity PX. We define PXt as the remaining battery capacity of nodeX∈S,R at the tth transmission. Before transmitting, PX0=PX.Step 2.
The number of variables isn is set to 2: PSt and PRt. The upper bounds ub1 (of the variable PSt) and ub2 (of the variable PRt) are set, respectively, to PSmax and PRmax. The lower bounds lb1 (of the variable PSt) and lb2 (of the variable PRt) are set, respectively, to PSmin and PRmin. The number of search agent (salps) N is fixed.Step 3.
The objective (fitness) function is formulated as(32)FPSt,PRt=maxλREtPSt,PRt.Step 4.
Optimal node powersPSt∗ and PRt∗ are determined.Step 5.
The remaining battery capacity is decremented as follows:(33)PXt+1=PXt−PXt∗,X∈S,R.Step 6.
Repeat the steps 3−6 untilPSt≤PSmin or PRt≤PRmin.The SSA can be implemented at the sink nodeA which is assumed to have perfect channel knowledge. After that, computed optimal powers are sent to sensor and relay nodes prior to their transmissions.


### 4.3. Computational Complexity Analysis

We propose, in this section, to evaluate the complexity of the proposed power allocation scheme. First, it requires a constant running time to initialize the system parameters which can be expressed asO1 time. At each t∈1,T transmission, the SSA algorithm is computed. The computational complexity of SSA is generally written in [28] as follows OLnN+CofN, where L is the total iterations, n is the number of variables, Cof is the cost of the objective function, and N is the salp population. In our case, the number of variables n is set to 2; then, the running time of the SSA algorithm is OL2N+CofN. The total complexity of SSA computation over T transmissions is OTL2N+CofN. The computation of the remaining battery capacity is done at each transmission for both relay and source nodes in equation (33). Then, the required time for this operation is O2T. Hence, the total running time of the proposed algorithm is O1+OTL2N+CofN+O2T.


### 4.4. Case of Dynamic Underground Environment

In the previous section, we assumed that the underground environment is unchanged with time. However, in some real cases, the water content in the soil can variate due to the soil irrigation or to the weather change during different seasons [38]. We propose, here, to study the case where the soil composition in terms of VWC varies among two successive node transmissions. In addition, an adaptive power allocation based on assigning different power constraints to different node transmissions is suggested. Therefore, the optimization problem is as follows:
(34)PSt∗,PRt∗=max∑t=1TλREtPSt,PRtSubjectto∑t=1TPXt≤PX.wherePXt∈PXmin,PXmaxt for X∈S,R,and(35)PXmaxt=δtPXforX∈S,R,where δt is the power fraction assigned to the tth transmission for t∈1,T and ∑t=1Tδt=1. Here, the same procedure, described in Section 4.2, is followed considering a given maximum power PXmaxt for each t transmission.


## 4.1. Salp Swarm Algorithm (SSA)

One of the latest metaheuristic swarm algorithms, that successfully have been employed to optimize different problems in several research areas, is the SSA [44]. This algorithm was firstly introduced by Seyedali Mirjalili in 2017 which mimics the floating of salps that navigate in aquarium environments such as oceans and seas [28]. In deep oceans, salps compose a swarm which is called salp chain. The algorithm divides the populations of salps (i.e., search agents) into two groups: the leader and the followers. The leader salp is at the beginning of the chain and guides the salp population while the rest are followers since they follow the leader.SSA is simple and like other swarm-based intelligent algorithms. The position ofN salps is randomly initialized in an n dimensional search space where n is the number of variables of the considered problem. Additionally, the positions of salps are stored in a two-dimensional matrix called x. A food source called fd in the search space is defined as the swarm’s target. Then, the fitness of each salp is determined to select the leader with the best fitness. The position of the leader is updated using the following equation.
(25)xj1=fdj+c1ubj−lbjc2+lbjc3≥0,fdj−c1ubj−lbjc2+lbjc3<0,where the xj1 is the position of the leader in the jth dimension, fdj is the food source in the jth dimension, lbj and ubj are the lower bound and the upper bound of the jth dimension, respectively, c2 and c3 are random numbers between [0, 1], and c1 is defined as follows:
(26)c1=2e−4l/L2,with l is the current iteration and L is the maximum number of iterations. The position of the ith follower is updated using the equation given by
(27)xji=12xji+xji−1i≥2,where xji is the position of the ith follower in the jth dimension.Using equations (25) and (27), the positions of the salp chain population are updated until the suitable solution is obtained or a stopping criterion is met.


## 4.2. Optimization Problem and Proposed Algorithm

As the conventional design usingλEEt or λSEtis limited in respect of the inefficient use of resources, we are interested to determine the power allocation vector P=PSt,PRt at each t transmission performed over the link S−R−A that jointly maximizes the energy efficiency λEEt and the spectral efficiency λSEt for all transmissions t∈1,T. Since nodes are equipped with batteries with finite capacities, the optimization of the power PXt of each node X∈S,R, used at the tth transmission, should consider the initial battery capacity PX, the spent powers in previous transmissions PX1,⋯,PXt−1, and the power limitation range PXmin,PXmax allowed for each transmission. The proposed multiobjective optimization problem is as follows:
(28)PSt∗,PRt∗=max∑t=1TλEEtPSt,PRt,λSEtPSt,PRtSubjectto∑t=1TPXt≤PX.where PXt∈PXmin,PXmaxforX∈S,R.Since optimizing simultaneously two functions which are competing is challenging, we propose to optimize the unique weighted objective function, called the resource efficiencyλREt, exploiting the tradeoff between λEEt and λSEtas discussed in the work [12]. The resource efficiency λEEt of the link S−R−A at the tth transmission, for t∈1,T, is given by
(29)λREt=λEEt+ωλSEt,where the factor ω is computed as
(30)ω=ω¯WPtot,with ω¯ is a constant, W is the available bandwidth, and Ptot is the total power budget allocated to the link S−R−A at each transmission. Then, Ptot=PSmax+PRmax. The weighted factor ω is introduced to ensure the balancing between λEEt and λSEt because λSEt is practically smaller than λEEt. Moreover, ω corrects the inconsistence of adding two metrics with different units since the unit of λEEt is bits/joule while the unit of λSEt is bits/s/Hz. Then, the unit of λREt is similar to λEEt which is still bits/joule. Besides, optimizing λREt tends to optimize λEEt if ω¯=0 and to optimize λSEt if ω¯=∞. Generally, the choice of the value of this constant is based on the designer objective and the available resources in terms of bandwidth and power [12]. We propose to evaluate this constant for the considered WUSN in Section 5.Consequently, the constrained multiobjective optimization problem in equation (28) is transformed into a single-objective problem as follows: where
(31)PSt∗,PRt∗=max∑t=1TλREtPSt,PRtSubjectto∑t=1TPXt≤PX,PXt∈PXmin,PXmaxforX∈S,R.The considered problem in equation (31) is NP-hard since the number of variables to optimize equals two (PStand PRt) and the presence of variable products in equations (5) and (7) caused by the AF relay transmission. Therefore, the metaheuristic algorithm SSA is used to compute the optimal solution of the problem. The followed procedure is presented below.Step 1.
Each nodeX∈S,R has a finite battery capacity PX. We define PXt as the remaining battery capacity of nodeX∈S,R at the tth transmission. Before transmitting, PX0=PX.Step 2.
The number of variables isn is set to 2: PSt and PRt. The upper bounds ub1 (of the variable PSt) and ub2 (of the variable PRt) are set, respectively, to PSmax and PRmax. The lower bounds lb1 (of the variable PSt) and lb2 (of the variable PRt) are set, respectively, to PSmin and PRmin. The number of search agent (salps) N is fixed.Step 3.
The objective (fitness) function is formulated as(32)FPSt,PRt=maxλREtPSt,PRt.Step 4.
Optimal node powersPSt∗ and PRt∗ are determined.Step 5.
The remaining battery capacity is decremented as follows:(33)PXt+1=PXt−PXt∗,X∈S,R.Step 6.
Repeat the steps 3−6 untilPSt≤PSmin or PRt≤PRmin.The SSA can be implemented at the sink nodeA which is assumed to have perfect channel knowledge. After that, computed optimal powers are sent to sensor and relay nodes prior to their transmissions.


## 4.3. Computational Complexity Analysis

We propose, in this section, to evaluate the complexity of the proposed power allocation scheme. First, it requires a constant running time to initialize the system parameters which can be expressed asO1 time. At each t∈1,T transmission, the SSA algorithm is computed. The computational complexity of SSA is generally written in [28] as follows OLnN+CofN, where L is the total iterations, n is the number of variables, Cof is the cost of the objective function, and N is the salp population. In our case, the number of variables n is set to 2; then, the running time of the SSA algorithm is OL2N+CofN. The total complexity of SSA computation over T transmissions is OTL2N+CofN. The computation of the remaining battery capacity is done at each transmission for both relay and source nodes in equation (33). Then, the required time for this operation is O2T. Hence, the total running time of the proposed algorithm is O1+OTL2N+CofN+O2T.


## 4.4. Case of Dynamic Underground Environment

In the previous section, we assumed that the underground environment is unchanged with time. However, in some real cases, the water content in the soil can variate due to the soil irrigation or to the weather change during different seasons [38]. We propose, here, to study the case where the soil composition in terms of VWC varies among two successive node transmissions. In addition, an adaptive power allocation based on assigning different power constraints to different node transmissions is suggested. Therefore, the optimization problem is as follows:
(34)PSt∗,PRt∗=max∑t=1TλREtPSt,PRtSubjectto∑t=1TPXt≤PX.wherePXt∈PXmin,PXmaxt for X∈S,R,and(35)PXmaxt=δtPXforX∈S,R,where δt is the power fraction assigned to the tth transmission for t∈1,T and ∑t=1Tδt=1. Here, the same procedure, described in Section 4.2, is followed considering a given maximum power PXmaxt for each t transmission.


## 5. Numerical Results and Discussions

In this section, we present the simulation results illustrating the performance of the proposed power allocation algorithm. Simulations are performed using MATLAB-R2015a simulator on a Windows 7 OS with 2 GB RAM memory. Table2 summarizes the list of parameters used in the path loss computation and their values. All simulation results are calculated by averaging over 1000 channel realizations. The x-axis coordinates xX of node X∈S,R is set to 0.2 m. The depth of node X∈S,R equals its y-axis coordinate: dXG=yX. The height hA of A is set to 0.7 m. We assume that the batteries of source and relay nodes have equal power capacitiesPS=PR=P. For Figures 3–9 and Table 3, we assume that underground medium conditions are unchanged with time. We also consider that the physical limitations of each transmission power are PSmin=PRmin=Pmin=5mw and PSmax=PRmax=Pmax.Table 2
Values of path loss parameters.
ParametersValuesS5%C15%μ04π10−7 N/A2μr1ϵ08.85∗10−12F/mρb1.5 g/cm3ρs2.66 g/cm3mv5%–25%τw1/2πf0.58∗10−10sϵw080.1ϵw∞4.9η3W0.3–1.3 GHzN0-130 dBm/HzΓ5∅60°Figure 3
Convergence behavior ofλRE versus the number of iterations for different numbers of search agents N with dSG=0.6 m, dRG=0.1 m, P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%.Figure 4
Impact of weighted factorω¯ on λRE with dSG=0.6 m, dRG=0.1 m, P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%.Figure 5
Resource efficiency of the proposed power allocation scheme compared to conventional WUSN scheme with fixed powers versus the maximum allowed powerPmax for different battery capacities P∈2,3,4 with dSG=0.6 m, dRG=0.1 m, W=300 MHz, and mv=5%.Figure 6
Resource efficiency of the proposed power allocation scheme compared to conventional WUSN scheme with fixed powers versus the system bandwidthW for different battery capacities P∈2,3,4 with dSG=0.6 m, dRG=0.1 m, W=300 MHz, and mv=5%.Figure 7
Increase in number of transmissionsT of the proposed power allocation scheme compared to the conventional WUSN scheme with fixed powers for different node burial depths dSG and dRG configurations with P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%.Figure 8
Resource efficiency of the proposed power allocation scheme, the UG2UG path lossLSR and the UG2AG path loss LRA versus the relay depth dRG with dSG=1 m, P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%.Figure 9
Resource efficiency of the proposed power allocation scheme compared to conventional WUSN scheme with fixed powers versus the volumetric water content (VWC)mv with dSG=0.6 m, dRG=0.1 m, P=3 V, Pmax=50 mw, and W=300 MHz.Table 3
Statistical results.
SchemeMaxMinStdMean±confidenceλRE using SSA-based optimization (Mbits/joule)778.68424.689587.1813114.9157±5.4100λRE using fixed powers (Mbits/joule)302.61092.044240.221557.5342±2.4959Figure3 illustrates the convergence of the resource efficiency λRE as a function of the number of iterations for different numbers of search agents (salps) N used by the SSA algorithm in the optimal node power computation. We consider that S and R are buried at depths dSG=0.6 m and dRG=0.1 m, respectively. The node battery capacity P is set to 3 V, and the maximum allowed power for each transmission Pmax is set to 50 mw. The VWC mv is set to 5%. The system bandwidth W is set to 300 MHz. As it is clearly shown, increasing the number of search agents enhances the computation accuracy of the maximum of λRE. Also, the convergence of the SSA algorithm is fast as less than five iterations are required to reach the optimal values of λRE for all values of N. Therefore, the algorithm requires small memory storage, and it can be easily implemented with low cost of computational complexity. We consider that N=20 in the rest of simulation results.Table3 shows the resource efficiency λRE statistical results, using a set of performance measures, of the proposed SSA-based optimization scheme compared to the conventional WUSN scheme with fixed node powers. We consider P=3 V, Pmax=50 mw, W=300 MHz, dSG=0.6 m, dRG=0.1 m, and mv=5%. For the conventional WUSN scheme with fixed powers, we adopt equal node power allocation set to the maximum allowed powers, PXt=Pmax for X∈S,R and t∈1,T. The performance measures are the maximum (max), the minimum (min), the standard deviation (Std), and the average (mean) with confidence value. The confidence value is computed using the confidence level 95%. Compared to the conventional WUSN scheme, the proposed SSA-based optimization scheme achieves better performance for all evaluated performance measures.Figure4 shows the variation of the resource efficiency λRE, the energy efficiency λEE, and the weighted spectral efficiency ω¯W/PtotλSE=ωλSE versus the weighted factor ω¯. We consider dSG=0.6 m, dRG=0.1 m, P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%. The λEEis constant since it does not depend onω¯. The weighted spectral efficiency ωλSE increases with the increasing of ω¯. As expected, when ω¯ is small, optimizing λRE leads to simply optimizing λEE and when ω¯ is larger, more weight is added to λSE and balancing between λEE and λSE is more insured. Clearly, when ω¯=2.1, λRE results from the best balancing between λEE and λSE. We notice that the weighted factor ω¯ is here greater than the weighted factor in [12]. Indeed, the nature of the underground medium in WUSNs causes lower λSE than that in WSNs considered in the work [12]. Hence, a higher weighted factor is needed in the case of WUSNs. As a result, we set ω¯ to 2.1 in the rest of simulation results.Figure5 exhibits the resource efficiency λRE performance of the proposed node power optimization scheme compared to the conventional WUSN scheme with fixed node powers versus the maximum power allowed for each transmission Pmax for different power capacities P∈2,3,4. We consider dSG=0.6 m, dRG=0.1 m, W=300 MHz, and mv=5%. Compared to the conventional WUSN scheme, the proposed scheme with optimal node powers provides a better resource efficiency for the same total power cost. Indeed, the proposed power allocation scheme improves efficiently the total number of delivered bits with considering the optimal node power distribution according to the power physical limitations. The resource efficiency λRE increases when the power capacity P of node batteries increases. Moreover, the resource efficiency λRE decreases when Pmax increases. In fact, increasing the maximum power Pmax harms the energy efficiency λEE and the weighted spectral efficiency ω¯W/PtotλSE as well. Consequently, for a given resource efficiency requirement, designer can adjust the maximum power allowed for each transmission depending on the available resource in terms of battery capacities.Figure6 shows the resource efficiency λRE performance of the proposed node power optimization scheme compared to the conventional WUSN scheme with fixed node powers versus the system bandwidth W for different battery capacities P∈2,3,4. We consider dSG=0.6 m, dRG=0.1 m, Pmax=50 mw, and mv=5%. Clearly, the proposed scheme enhances the λRE performance compared to the conventional WUSN scheme for the same used system bandwidth W. According to Shannon’s formula, traditional design focuses on expanding the bandwidth and reducing the transmit power to achieve a target data rate requirement. Hence, as the bandwidth increases, the λEEincreases whereas the λSE decreases. As shown in the figure, increasing the system bandwidth harms the EE-SE tradeoff performance of the considered WUSN. Indeed, the increase of the operating frequency increases the UG2UG and UG2AG path losses and mitigates the channels as demonstrated in [4]. Hence, the use of lower bandwidths is better for the considered WUSN where relay nodes are deployed.Figure7 illustrates the impact of the proposed power allocation scheme on the number of transmissions T that can be performed through the link S−R−A for different sensor depths dSG∈0.3m,0.6m and different relay depths dRG∈0.05m,0.1m,0.2m. We consider P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%. Clearly, the number of transmissions T is enhanced using the proposed node power optimization. It is more improved when S is closer to R and R is closer to the ground surface. Thus, the proposed power allocation scheme efficiently extends the node battery lifetime and additionally the network lifetime.Figure8 presents the resource efficiency λRE performance of the proposed node power optimization scheme and the variation of the UG2UG path loss LSR and the UG2AG path loss LRA for different relay depths dRG∈0.1m,0.9m. We assume that the sensor S is buried at fixed depth yS=dSG=1m. We consider P=3 V, Pmax=50 mw, W=300 MHz, and mv=5%. The increase of the burial relay depth dRG means that R is closer to S and further from the ground surface. Obviously, the UG2AG path loss LRA increases when dRG increases while the UG2UG path loss LSR decreases when dRG increases. We notice that λRE is high when R is buried close to the surface due to the good quality of the UG2AG link. When the relay is in middle location between S and the ground surface,λRE is low due to the increase of LRA, i.e, poor quality of UG2AG link. Moreover, λRE increases again when R is closer to S although the high value of the path loss LRA. Indeed, the enhancement of the UG2UG link predominates the deterioration of the UG2AG link and conducts the enhancement of λRE. This is very important in the topology design of WUSNs where relay nodes are deployed. Placing the relay close to the sensor else to the ground surface is beneficial to the λRE performance.Figure9 shows the resource efficiency λRE performance of the proposed node power optimization scheme compared to the conventional WUSN scheme with fixed node powers versus the VWC mv. We consider dSG=0.6 m, dRG=0.1 m, P=3 V, Pmax=50 mw, and W=300 MHz. As shown in the figure, the proposed scheme with optimal node powers ameliorates the λRE performance compared to the conventional WUSN scheme for the same soil condition in terms of water content. Moreover, the resource efficiency λRE significantly decreases with higher water content in soil due to the significant UG2UG path loss increase when mv increases, as proven in [4].In Figure10, we study the effect of water content mv variation among different transmissions on the resource efficiency λRE. We focus, here, to only two successive transmissions performed through the link S−R−A. Then, T=2. We assume that mv equals 5% at the first transmission and mv is changed to a value in the range (10%, 25%) at the second transmission. We consider dSG=0.4 m, dRG=0.2 m, P=3 V, Pmax=50 mw, and W=300 MHz. As mentioned in Section 4.4, we propose to allocate unequal maximum powers Pmax1=δ1P and Pmax2=δ2P=1−δ1P, where δt∈0,1, t∈1,2, allowed to the first and to the second transmission, respectively.Figure 10
Resource efficiency of the proposed power allocation scheme when the volumetric water content (VWC)mv variates among transmissions for T=2 with dSG=0.4 m, dRG=0.2 m, P=3 V, Pmax=50 mw, and W=300 MHz.Figure10 illustrates the resource efficiency λRE performance of the proposed node power optimization scheme for the following 4 cases:
(i)
δ1=3/4, i.e., Pmax1=3P/4 and Pmax2=P/4(blue curve)(ii)
δ1=1/2, i.e., Pmax1=Pmax2=P/2(pink curve)(iii)
δ1=1/4, i.e., Pmax1=P/4 and Pmax2=3P/4(red curve)(iv)
Conventional WUSN scheme with fixed node powers (green curve)We remark that the proposed node power optimization scheme whenPmax1=Pmax2=P/2 outperforms the conventional WUSN scheme with fixed node powers when mv is changed between transmissions. Furthermore, the redistribution of the maximum powers offers the best λRE performance when Pmax1=3P/4 and Pmax2=P/4. This motivates us to allocate more power to the first transmission where mv is relatively low and to not spend a lot of power in the second transmission where mv is high. The novel proposed maximum power allocation successfully divides the available battery capacity P on different transmissions according to the soil condition in each transmission and additionally ameliorates the total λRE. It should be noted that the adjustment of the distribution of the power budget among transmissions should be emphasized in future works.The deployment of sensor nodes in WUSNs may be restricted in some situations since it depends highly on the application and the environmental conditions. For agricultural application, authors in [4] investigate that the increase of VWC more than 25% results the interruption of the UG2UG communication for some particular soil type where the capacity to hold the bound water is low. Consequently, in case of a rainfall, the UG2UG communication can remain interrupted for several days depending on the type of the soil. For underground mine application, UG2UG communications may break down in case of an incident, i.e., rock fall or explosion. We notice that the extended periods of communication interruption in such cases should be taken into account in the proposed power allocation algorithm and, generally, in the design of any new protocols.


## 6. Conclusions

In this paper, we studied the problem of sensor and relay power allocation in WUSNs. This is aimed at maximizing the RE, which represents the EE-SE tradeoff, of all allowed transmissions under node battery capacity constraint. The metaheuristic algorithm SSA is used to find optimal node powers from an interval between a minimum and a maximum allowed value. Both invariable and dynamic soil properties among node transmissions are considered. Simulations showed that the proposed scheme provided a better RE for the same resource, in terms of power cost and system bandwidth, compared to the conventional WUSN scheme where fixed maximum powers are used. Also, the proposed scheme efficiently increased the number of transmissions that can be performed through a link and additionally extended the network lifetime. The optimal relay node placement according to the RE maximization is also discussed. For dynamic underground system, we found, through simulations, that allocating more power to the transmission where the water content is low, compared to the second transmission where the water content is high, is the best power distribution maximizing the RE performance.



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*Source: 6683988-2021-01-15.xml*