3D E-CRUSE: Energy-based throughput analysis of three dimensional underwater network using RF communication

Pavan Ganesh PSS , Hrishikesh Venkataraman

Next Generation Communication Group, Indian Institute of Information Technology Sri City (IIITS), AP, 517 646, India

ABSTRACT Monitoring the ocean shore continuously in real-time is essential for important applications like port security, coastal surveillance, assistance in navigation etc.This needs a high data rate for the transmis- sion of data from underwater nodes to the surface.Acoustic communication is the traditional approach for underwater networks and offers long-range communication.However, the achievable data rate using acoustic communication is in the order of kbps only.Radio frequency (RF) based communication per- forms better than acoustic communication and provides a data rate of up to 100 Mbps in an underwater environment.Nonetheless, due to high propagation loss, the communication range using RF is limited to a few meters.More importantly, the underwater nodes are battery-operated and recharging the bat- tery is difficult.Therefore, it is imperative that underwater RF networks are analyzed using an accurate energy model for its deployment and management.This requires that the underwater network is prop- erly modeled.In this work, a cluster-based three-dimensional (3D) architecture for underwater networks using RF communication is proposed.Importantly, the energy-based throughput of the 3D architecture using multi-hop communication, 3D E-CRUSE , is obtained using a mathematical model.The throughput is then observed for various water environments, various parameters and the results are compared to the existing two-dimensional architecture.It is observed that the throughput of the proposed 3D architecture is up to 3 times more than the 2D architecture.

Keywords: Cluster Energy model Multi-hop Throughput Radio frequency Underwater

1.Introduction

Underwater networks have applications in many areas like disaster prevention, navigation and control, port security, coast surveillance and oil-rig protection, etc [1] .The conventional ap- proach used for underwater sensing is to set up underwater nodes to record the data and then retrieving the equipment after some time [2] .As there is no real-time data transfer, this method is not suitable for applications such as security and surveillance.Hence, an underwater network that is capable of transmitting the data in real-time and supports large data rates is necessary.A wired net- work can support large data rates.However, there are few opera- tional difficulties and potential hazards in wired networks [3] .In addition, cables are the dominant obstacles to moving objects such as ships and divers in shallow water regions [4] .Wireless commu- nication, on the other hand, has gained prominence due to its ease of operation and benefits.

Wireless communication networks in water use various com- munication techniques like acoustic signal, optical signal, magnetic induction (MI) and radio frequency (RF) [3] .Acoustic communi- cation is the proven technology for modern underwater wireless communications and it provides communication up to 20 km dis- tance [5] .However, it has several limitations like:Multi-pathprop-agationattheboundaries,lowbandwidth,reflectionsatboundaries,diffractionandambientnoise[6] .These factors degrade the signal and also the networks performance.On the other hand, in deep water, a data rate of up to 1 Gbps can be achieved using optical communication.Nevertheless, the quality of the optical signal de- pends upon the water quality [7,8] .Magnetic Induction also sup- ports the data rate in the order of Mbps, yet the generation of high currents for MI signal with limited on-board energy is highly diffi- cult [9] .

Nomenclature 2D Two dimensional 3D Three dimensional CH Cluster head D Depth of the water T Temperature of the water S Salinity of the water M Cluster side size N Number of nodes in a cluster α Attenuation constant of the medium σ Conductivity ∈ Electric permittivity μ Magnetic permeability f Operating frequency E resN Residual energy in a node E resCH Residual energy in a CH E NtoCH Threshold energy necessary to transmit a data packet from a node to the CH E CHtoCH Energy necessary to transmit the data from one CH to another CH E CHtoB Energy necessary to transmit the data from a CH to the buoy E txelec Energy consumption at transmitter electronics E init Initial energy in a node E initCH Initial energy in a cluster head E Rx Energy consumed per bit at the receiver E da Energy consumed at the receiver for data aggrega- tion e amp Energy consumption at the amplifier stage of the transmitter d N Distance from a node to the CH d CH Distance between a CH and another CH d B Distance between a CH and the buoy P sTx Probability of successful transmission k Length of the data packet c 1 , c 2 Parameters from the energy model

RF-based Communication is the most widely used technique for terrestrial wireless communications.The major advantage of an RF signal in water is that it is suitable for communication in shallow water and supports a data rate of up to 100 Mbps in a small-sized network [10] .These large data rates can be used for surveillance of the shore by live video transmission.Moreover, RF signal gen- eration is comparatively easier than MI and the RF signal is less affected by the water turbidity and quality of water, as well as im- mune to ambient acoustic noise [11] .Nonetheless, due to high at- tenuation and propagation loss, the communication range using RF signals underwater is limited to a few meters.

Usually in underwater networks, the nodes have limited energy as the source of energy is only an on-board battery [12] .The bat- tery energy at the nodes is used for different applications such as data sensing, data processing, implementing MAC and routing pro- tocols, etc.Notably, it is difficult to recharge or replace the battery in a harsh underwater environment [13] .Only a few services are offered by taking into account node issues such as energy.There- fore, multiple nodes are deployed in a network for various appli- cations, which leads to repeated deployment.Moreover, redundant deployment is also adopted to ensure data reliability.The deploy- ment of multiple nodes may lead to severe signal interference [14] .Underwater nodes are usually developed for a specific task using dedicated sensors.Repeated and redundant deployment increases the implementation cost of the network.On the other hand, an intelligent system that changes the node parameters such as trans- mitting power and operating frequency may solve the deployment- related problems and reduces the cost [15] .However, there should be no trade-offcan be formed between the repeated deployment for multiple services and redundant deployment for reliable ser- vice.

In this regard, the analysis of an underwater network using the energy model for RF communication is important for its deploy- ment and operation.To the best knowledge of the authors, there is less literature is available on the study of the performance of un- derwater networks using an energy model and RF communication.In the work presented in [16] , an energy model suitable for under- water,RSU-Energy, was proposed and an energy-based throughput for a two-dimensional (2D) network (2DE-CRUSE) was obtained.The network considered in [16] comprised two independent clus- ters with a dedicated cluster head (CH) for each cluster.It was assumed that the two clusters are placed at the same depth in the underwater (2D architecture) and use a two-hop communi- cation.However, for real-world deployment, it is essential to es- tablish a three-dimensional (3D) network with multiple layers of nodes for applications like intruder detection and surveillance [17] .Moreover, the analysis of the 3D network is important to observe the performance of the network.Hence, in this work, a 3D multi- layered network architecture with a clustering technique is pro- posed.In the proposed architecture, the communication from a node to the buoy is a multi-hop communication, in which the clus- ter heads act as relays.More importantly, a mathematical model is developed to obtain the energy-based throughput,3DE-CRUSE, in terms of the probability of successful transmission of a data packet from a node to the buoy.

The remaining sections of the paper are organized as fol- lows.Section 2 details the physical and electrical characteristics of the underwater channel and a multi-hop based multi-layered three-dimensional network model in an underwater environment.In Section 3 , the energy-based throughput of 3D architecture, i.e.,3DE-CRUSE, in terms of probability of successful transmission of a packet from a node to the buoy is obtained.The analysis of 3D E-CRUSE for various parameters is presented in Section 4 .Fi- nally, Section 5 concludes the paper.

2.Underwater channel characteristics and network model

From a wireless communication perspective, water behaves dif- ferently than free space.Based on the physical and electrical prop- erties of the water, the water medium is categorized as either conducting or dielectric medium whereas free space is a non- conducting medium.The physical and electrical characteristics of the water that affects the RF propagation are briefly given in the following subsection.

2.1. Properties of water

The important physical characteristics of the water are temper- ature (T), salinity (S), pressure and density [18] .The physical char- acteristics often change with many parameters.The temperature of the water varies with the depth of the water.Mostly, the tem- perature is low at more depths and warm towards the surface.Moreover, the temperature changes with the atmospheric condi- tions.Similarly, salinity varies with depth and the variation is more in shallow water than deep water due to various factors like the flow of fresh water, water evaporation, rains, etc.The salinity vari- ation relies also on the existence of salts in a water body.These variations in the temperature and salinity greatly affect the elec- trical properties of the water medium and also the propagation of RF signals in water.Globally, the average density of the water is 1.03g/cm3[18] .However, the density is not uniform and varies in the vertical.Moreover, in oceans, the pressure increases by 1 at- mosphere for every 10m increase in depth.Regardless, the effect of pressure and density on the propagation of RF signals in any medium is negligible.

The electrical parameters that describe the RF propagation in any medium are - conductivity (σ), electric permittivity (∈) and magnetic permeability (μ) [19,20] .The relative electric permittiv- ity of water is a function ofT,Sand operating frequency (f) [21] .Hence, the permittivity of the underwater channel varies with its physical properties.The typical value of relative permittivity of wa- ter is about 71 at VHF.The conductivity of water is also a function ofTandS.The water body having more salinity processes more conductivity.Generally, the conductivity of freshwater is about 0.01 S/m and the conductivity of seawater is about 4 S/m.As water is a non-magnetic medium, the magnetic permeability of water is about the same as that of free space.Variation of the electri- cal properties of the channel significantly affects the attenuation and path loss of the RF signal.Hence, it is important to observe the physical properties of the water medium before analyzing the performance of a network underwater.A detailed analysis of the variation of the electrical properties with the physical properties of water of various water bodies is given in [22] .As the physical properties of the water significantly affect the electrical parame- ters and channel characteristics, RF propagation underwater is dif- ferent from free space.Notably, the water is categorized as a lossy- dielectric medium and the propagation principles of RF signal in a lossy-dielectric medium are to be considered [22] .

2.2. 3D Underwater wireless networks

Underwater Wireless Networks (UWNs) is formed by a collec- tion of surface floating devices called buoys and underwater nodes to perform underwater sensing and coverage operations [23] .Usu- ally, in a 2D underwater network, the nodes are placed on a sea bed and the nodes experience less mobility.In a 3D network, the sensor nodes can be drowning at different depths to form a 3D network architecture.Although the 3D network is more advanta- geous than 2D architecture in terms of coverage; due to the com- plex architecture, the existing 2D network solutions are not suit- able for 3D wireless networks.While implementing a 3D network, the important issues that need to be considered are the topology, localization, routing and communication protocols [24] .

For better coverage and network connectivity, topology man- agement is very important in UWNs.Moreover, topology affects the performance of a network by affecting the routing and MAC protocols [25] .Ducrocq et al.[26] observed the performance of var- ious topologies for wireless sensor networks and concluded that various topologies result in up to 25% difference in packet deliv- ery ratio and the average path distance; the difference in energy cost is more than 100%.Hence, topology is a primary criterion to build a UWN.Especially in a 3D underwater network, maintain- ing the topology is a challenging task.There is more chance for a change of position of the nodes due to heavy water currents under- water.This makes the performance of a network poor and some- times it leads to network failure [27] .Usually, a grid topology is better suited for surveillance and security applications [28] .Hence, a multi-layered square-shaped grid topology is considered in this work.Moreover, it is also assumed that the sensor nodes are static and not affected by the water currents and maintains a uniform topology.Localization is also significant in underwater applications like surveillance and monitoring.High attenuation of RF waves re- stricts the use of a global positioning system (GPS) for underwater localization.Hence, in the proposed network, it is taken that the sensor nodes are aware of their own 3D position and the positions of other nodes and the buoy.

While deciding a proper path between a node and a base sta- tion, the routing protocol plays a significant role.For terrestrial wireless networks, many routing protocols were developed; but these protocols are not directly applicable to UWNs due to the harsh underwater channel environment [29] .Two major factors to be considered for designing the routing protocols for UWNs are en- ergy and node mobility [30] .In UWNs, the available power at the node is limited and no source of natural energy is available.This shows the need for energy-efficient routing algorithms in UWNs.Furthermore, the sensor nodes deployed in water are considered mobile due to tide current.Therefore, the topology of the network changes dynamically even with small node displacements.Because the acoustic signal speed is much lower, communication signals experience extreme Doppler distortions due to transceiver move- ment or changing conditions such as surface waves and internal turbulence [31] .The routing protocols used for the acoustic net- works are therefore not suitable for RF-based UWNs.As underwa- ter RF channels suffer from high attenuation, the routing protocols must be designed carefully.

The role of a MAC protocol is to share the channel in a fair way and prevent the collision of data in the network.The development of a suitable MAC protocol is very critical in order to achieve high energy efficiency in any network [32] .The characteristics of the underwater acoustic channel, particularly restricted energy, large delays in propagation and limited bandwidth, present significant challenges for MAC.Many MAC protocols for acoustic-based UWNs are proposed by considering the above challenges.There are few MAC protocols developed for RF-based underwater networks in deep water.Generally, the MAC protocols depend on various multi- ple access schemes like carrier sense multiple access (CSMA), code division multiple access (CDMA), frequency division multiple ac- cess (FDMA) and time division multiple access (TDMA).These tech- niques are generally employed in wireless networks based on vari- ous parameters and constraints of the channel.FDMA, CSMA and CDMA-based protocols have more limitations in the underwater channels.Therefore, a TDMA based protocol is considered as MAC protocol.A major requirement for TDMA is strict time synchro- nization.As the velocity of RF signal in water (i.e.3 ×106m/s) is several hundred times more than the velocity of acoustic sig- nal (1500 m/s), the propagation delay of the signal is negligible for short distances and the problems like time-synchronization and Doppler shift can be neglected.Moreover, there will be no packet collisions in the network.But one of the nodes, preferably a relay node is responsible for time-slot management and time synchro- nization, which leads to more energy consumption in that node.To the authors’ understanding, a TDMA based MAC protocol is most appropriate for RF-based UWNs.

2.3. Proposed network model

The cluster-based architecture of a 3D underwater network is shown in Fig.1 .Clustering is a basis for an efficient routing mech- anism that uses a multi-hop technique in a complex network ar- chitecture for multimedia delivery [33,34] .In clustering, a set of nodes is considered to be in a cluster and a node among these is denoted as a controller or cluster head (CH).The controller is now responsible for collecting the data from other nodes and re- transmitting the data to the buoy.The data transmission from a node in a cluster to buoy is in multi-hop mode.The first hop is from node to controller and the others are from controller to con- troller or controller to buoy.A node belonging to a cluster trans- mits data to the respective controller instead of the buoy, thus by reducing the effective communication distance, the energy con- sumption in the node decreases.

Fig.1.Three dimensional cluster-based underwater RF network.

In the proposed network, every cluster is considered as a square-shaped grid with a side size ofM.Nnumber of nodes are positioned uniformly in every cluster.The buoy is placed at a heighthfrom the bottom of the network.The nodes are arranged as a cubical grid of side sizeMand all the nodes at a depth or level in the cube are considered to be within a cluster.Each cluster is square-shaped and has a dedicated cluster head to re-transmit the aggregated data in the respective cluster.The communication from a node in one level to the buoy is through the CH of the same level and the CHs of upper levels.The lower level cluster head (say CH1) communicates to the cluster head above its level (i.e.CH2) instead of buoy directly.This uses a three-hop communi- cation for two-layered architecture and (L+ 1) hop communication for anL-layered architecture.In the proposed architecture, the dis- tance between a node and the buoy or a CH and the buoy reduces to a half or less, which depends on the number of levels.There- fore, the energy consumption in an individual node and a CH is less, which in turn gives better throughput than direct communi- cation or two-hop communication.

Generally, single CH/controller architecture is used in cluster- based networks.A single CH can manage the tasks in a small- scale underwater network.However, there will be more nodes in large-scale networks.When a single CH is used for management in large-scale networks, all data is forwarded to a single CH and the data increases when the number of nodes increased.There- fore, a single CH is a bottleneck of the system.Moreover, when the network is large, the underwater nodes far from the CH can- not get the feedback in time [35] .As an RF-based communication is used in the proposed model and the speed of the RF signal in water ( 3 ×106m/s) is several thousand times more than the ve- locity of the acoustic signal (1500 m/s), the delay is neglected for short-distance communication links.Hence, the feedback or data transfer can be expected in an allocated time slot.Moreover, in a multi-CH 3D architecture, the CH in each level or layer may have an unequal number of nodes.As the number of nodes handled by each CH is different, the load on each CH will be different.Hence, the load-balancing among control nodes is important [36] .How- ever, in the proposed system model, each level/layer is assumed to have an equal number of nodes so that the load on each CH is uniform.

In an underwater network, there exist multiple nodes that use the same channel for communication and makes the channel to be a scarce resource heavily shared by underwater nodes.More- over, with the increase of applications, the efficiency of systems will be reduced, and it will lead to the rapid exhaustion of en- ergy.The resource allocation and energy efficiency are dealt with in terrestrial communication using a relay-based or cluster-based network.However, two important issues that need to consider in this method are relay selection and an appropriate resource allo- cation strategy.Similar technology can be adopted in underwater networks also.To achieve relay selection and resource allocation, the transmitter requires some knowledge of the channel state con- veyed from the receiver side [37] .Due to the harsh underwater en- vironments, the channel state at the transmitter will be imperfect, which leads to improper channel allocation or collision and hence the poor performance in the conventional underwater acoustic sys- tems.To overcome this problem, there are some mechanisms that use limited feedback for acoustic channels.Those systems might be used to relay selection and efficient resource allocation to improve the system capacity.However, the authors have not found any such mechanisms in RF-based underwater networks and are not using any feedback mechanism to allocate the channel or power in the proposed model.In the proposed system model, the channel al- location is based on a TDMA based protocol.The TDMA based time-frame for a two-layered three-hop communication is shown in Fig.2 .

Fig.2.TDMA based scheduling for packet transmission in 3D underwater network using RF communication.

3.Network throughput

The throughput is a measure of successful data transfer from a transmitter to a receiver at any given time.It is a significant in- dicator of a network’s performance.Therefore, the throughput is analyzed using an energy model suitable for underwater RF com- munication.Network throughput is obtained in terms of the prob- ability of successful transmission (PsTx) of a packet from a node to a buoy.PsTxis defined as the probability that a packet transmitted from a node does not suffer any collision at both the cluster head and buoy.

The intra-cluster communication, inter-cluster communication and cluster to buoy communication are organized using a TDMA scheduling as shown in Fig.2 .In each time frame (TN), all the nodes in a cluster communicate to the CH within their sub-time framest1toti.The cumulative data at the CH (say CH1) will be transferred to the CH of its upper level (say CH2) duringTN+1.To avoid the collision at CH2 , there is no data collection from the nodes of level 2 duringTN+1.In the time slotTN+2, the data ag- gregated at the CH2will be transmitted to the buoy.In the pro- posed architecture, as only one CH is communicating to the buoy, there will be no collision at the buoy.The data packet gener- ated at a node (say n1in cluster-1) withkbits length successfully reaches the buoy with the events given below.In the acronym of the events defined, sTx represents successful transmission, n rep- resents a node, CH represents cluster head and, B represents the buoy.

1.sTx_n1toCH1 : Successful packet transmission from the node n 1 incluster-1totheCH1duringitssub-timeframeinthemain time frameTN.As every cluster is at a specified depth, it is a hor- izontal communication in a two-dimensional square shaped grid architecture.

2.sTx_CH1toCH2 : Packet successfully transmitted from CH1to CH2duringTN+1.Thecommunicationisfromalowerlevelcluster to the upper level cluster.Therefore, it is a vertical communication and all the CHs may not be on the same vertical plane.

3.sTx_CH2toB : Packet successfully transmitted from CH2to buoy duringTN+2.It is also a vertical communication; CH2and the BS may not be on the same vertical plane.

The probability of successful transmission (PsTx) of a packet gen- erated at the node n1to the buoy is the combination of all the events and can be written as

Since the transmission from every node in the network is inde- pendent of other nodes, the events mentioned in Eq.(1) are inde- pendent.Therefore, Eq.(1) is rewritten as

To transmit a packet of lengthkbits from a node to a CH, the residual energy in the node must be greater than the energy nec- essary to transmitkbits.Similarly, to transmit a packet from one CH to another CH, the residual energy in the transmitting CH must be greater than the energy necessary for the packet transmission.With the increase in time, the energy in a node reduces.There- fore, it is imperative to consider the residual energy in a node af- ter some transmission duration and obtain the performance.There- fore, the individual probabilities are written in terms of the re- maining energy in the node and the remaining energy in the CH.Eq.(2) now has been written in terms of the energy available in the node and the energy available in the CH as

Where,EresN,ENtoCH,EresCH,ECHtoCHandECHtoBare the residual energy in a node, threshold energy necessary to transmit a data packet from a node to the CH, residual energy in a CH, the energy necessary to transmit the data from one CH to another CH, and the energy necessary to transmit the data from a CH to the buoy re- spectively.To obtain the probabilitiesP(EresN＞ENtoCH),P(EresCH1＞ECHtoCH)andP(EresCH2＞ECHtoB),RSUEnergy, the energymodelfor underwater, proposed by Ganesh and Venkataraman [16] is used.From RSU-Energy, the energy consumed at a node to transmitkbits to a distance ofdis given as

Where,Etxelecis the energy consumption at transmitter electron- ics;eampis the energy consumption at the amplifier stage of the transmitter;σwis conductivity of the water andαis the attenua- tion constant in the medium.Now, in a network havingNnodes, the residual energy in an individual node, residual energy in an in- termediate CH and the residual energy in an uppermost CH after some transmission duration or some number of rounds(r) is ob- tained and the equations are given in Eqs.(5) , (6) and (7) respec- tively

WhereEinitandEinitCH are the initial energies in the node and clus- ter head respectively,ERxandEdaare the energy consumed per bit while receiving and energy consumed at receiver for data aggrega- tion respectively.It can be observed that the remaining energy in a transmitting node or in a CH is a function of the electronic circuit parameters, packet size, transmission duration, medium character- istics and more importantly the distance from a node to the CH (dN), the distance between a CH and another CH (dCH), and the dis- tance between a CH and the buoy (dB).When the nodes are sym- metrically arranged in the cubical grid, it can be assumed that the distancesdCHanddBare equal.Now, using Eqs.(4) and (5) , the energy relationEresN＞ENtoCHin Eq.(3) can be written as

After substituting the residual energy in a node given in Eqs.(5) , (8) becomes

Similarly, the energy relationsEresCH1＞ECHtoCHandEresCH2＞ECHtoBcouldbeexpressedas

After substituting the residual energy in a CH given in Eqs.(6) , (10) becomes

The distancedNin Eq.(9) is the distance to be considered between two arbitrary points in a square shaped grid.Similarly, the distancedCHin Eq.(11) is the distance between two arbi- trary points in a cube.These distances are random variables and the probability density function of these random variables is taken from Philip [38] .However, obtaining the probability density func- tion for the terme2αdd2withdas a random variable is found ex- tremely difficult.Hence, in Eqs.(9) and (11) , an approximation is made to the terme2αdd2for the attenuation constant (α) in fresh- water, seawater andd＜100 m.The closest approximation is an exponential form, is given in Eq.(12) .

Whereaandbare constants.

After substituting the approximation for the terme2αdd2, Eqs.(9) and (11) could be written respectively as

Where,

The probability of successful transmission defined in Eq.(3) is now written as

In Eq.(17) , the termP(dN＜c1)represents the distribution function for the random variabledN in a 2-dimensional square grid.The termsP(dCH＜c2)andP(dB＜c2)represents the distri- bution functions ofdCHanddBrespectively in a cubical grid.Since the distancesdCHanddBare in a cube, the distribution functions are equal.After substituting the distribution functions for the dis- tance between two arbitrary points in a square and the distance between two arbitrary points in a cube, thePsTxis obtained as

WhereMis the size of a side for the cubical grid.In the grid, all the nodes at a level are considered as a cluster.Therefore, the size of a cluster will beM×M.The nature of the Eq.(18) can be exam- ined by observing the nature of individual parameters of the equa- tion as given in [39–43] .It is to be noted that thePsTxin a 3D static underwater network is a function of the size of the data packet (k), medium conductivity (σw), size of the cluster (M), the number of nodes in each cluster (N) and the residual energy in the RF node.As the equation forPsTxis a probability of successful transmission of a packet from a node to a base station, the range of the equa- tion can be expected between 0 and 1.Notably, the throughput of the 3D underwater network is expressed as the percentage of probability of successful transmission.Hence, the throughput lies between 0 and 100.Moreover, the network throughput depends upon cluster dimension and is inversely proportional to the cluster side size.Hence, a non-linear decrease in throughput can be ob- served with the increase in cluster size.Moreover, the variablesc1andc2are the functions of the conductivity of the water, data rate and transmission duration.As the variablesc1andc2are logarith- mic in nature; the throughput may increase or decrease exponen- tially with the change in data rate, network duration and conduc- tivity.Notably, the throughput may decrease with the increase in network transmission duration and conductivity.With the increase in transmission duration, the residual energy in the node decreases and the probability of successful transmission also decreases.Sim- ilarly, an increase in conductivity increases the path loss and also increases the energy consumption in a node, which further de- creases the throughput.For a fixed number of nodes (N= 25) in the network, the throughput is simulated for variable conductivity, variable cluster size, and varying transmission duration.

4.Simulation and results

The throughput of the proposed three-dimensional architecture is simulated for different depths in three different scenarios: freshwater, waters of the Northern Arabian Sea and Northern Bay-of-Bengal.The data for the physical parameters of the oceans considered is taken from Sagar [18] .Moreover, the throughput is observed for the various sizes of the cubical grid and the trans- mission time up to 50,0 0 0 sec.Generally, the data rate required to transmit a good quality video is from 800 kbps to 1200 kbps.Hence, a fixed data rate of 1 Mbps is considered for the simula- tions.The simulations are carried out using MATLAB 2020a on a Linux platform and the simulation parameters are given in Table 1 .

Table 1 Underwater network parameters.

4.1. Throughput vs. Cconductivity

The throughput of the 3D architecture is observed in freshwa- ter and at various conductivities of the seawater.The conductiv- ity of the seawater typically varies with the depth (D).Therefore, the throughput is observed at the depths of 10 m and 20 m in the Northern Arabian Sea and Northern Bay-of-Bengal, the results are shown in Fig.3 .It is observed from Fig.3 that the throughput of 3D architecture in freshwater is approximately 20% more than the throughput in conducting water.Moreover, in sea waters, the throughput at 10 m depth is nearly 2% more than the throughput at 20 m depth.In the shallow waters of the oceans, as the depth increases, conductivity also increases.The increase in conductivity increases the signal attenuation and the node needs more energy for transmitting a packet successfully to the buoy.This drains the battery quickly and the corresponding throughput decreases.It is also observed that the throughput using 3D E-CRUSE is nearly 1.4 times more in freshwater and 2.6 times more in seawater than in 2D E-CRUSE.In the three-dimensional architecture, communication from a node to the buoy is using more than two hops.Therefore, the transmission distance between a node and the buoy is less than the transmission distance in the two-dimensional network.The reduction in the distance between nodes reduces the energy consumption and increases thePsTxof a packet and the through- put of the network.

Fig.3.Throughput for various water sources.a : Fresh water; b : Northern Bay-of- Bengal, D = 10 m; c : Northern Bay-of-Bengal, D = 20 m; d : Northern Arabian Sea, D = 10 m ; e : Northern Arabian Sea, D = 20 m.

4.2. Throughput vs. Ttransmission duration

The throughput of the 3D architecture is observed for vary- ing transmission duration in Northern Bay-of-Bengal at a depth of 10 m, is shown in Fig.4 .The communication process is considered as rounds and each round is 1 sec.By taking a 1 Mbps data rate, the throughput is simulated for 50,0 0 0 seconds, i.e.13.8 h.Since the underwater nodes are battery-operated, after every round, the nodes and the CH lose some of their energy.Therefore, the in- crease in transmission time reduces the stored energy at a node or CH.Hence, the energy-based throughput also reduces with the in- crease in time.However, at any instance of time, since the energy consumption is less in 3D architecture compared to 2D architec- ture, the throughput of the 3D model is higher than the 2D model.Notably, this increase is up to 3 times that of the 2D model.

Fig.4.Network throughput with transmission duration ( r ).

4.3. Throughput for different grid sizes

The throughput of the 3D network in Northern Bay-of-Bengal at a depth of 10 m for different grid side lengths (M) is observed and is shown in Fig.5 .Firstly, it is observed that the throughput using 3D E-CRUSE is up to 2.9 times more than 2D E-CRUSE for the grid side length up to 20 m.The transmission distance from a node to the CH or a CH to the buoy is less in 3D E-CRUSE compared to the 2D E-CRUSE.Hence, the energy consumed in the node as well as in the CH is less compared to the direct or two-hop commu- nication.Therefore, the probability of successful transmission of a packet increases, and the corresponding throughput also increases.It is also observed that the throughput decreases with an increase in the grid size.An increase in the grid size increases the distance from a node to the CH; the distance from a CH to another CH; and the distance from a CH to the BS.Hence, energy consumption will be increased and the corresponding throughput decreases.When the grid size is beyond 25 m, the throughput of the 3D model is nearly zero.This shows the limitation of RF signal for long-range communication.

Fig.5.Network throughput for different cluster sizes.

5.Conclusion

A cluster-based 3D architecture for underwater networks us- ing RF communication has been proposed and the performance is investigated in this work.Importantly, the probability of success- ful transmission of a packet from a node to the buoy in terms of the residual energy in the node, physical characteristics of the medium and the network physical parameters is derived using a mathematical model.The energy-based throughput of the 3D un- derwater network using multi-hop communication, 3D E-CRUSE, is then obtained.The network throughput is observed with respect to the important parameters like conductivity of the medium, cluster side size and the transmission duration.Firstly, in 3D E-CRUSE, it is observed that the throughput in freshwater is nearly 1.4 times more; in seawater 2.6 times more than in 2D E-CRUSE.It is also observed that the network throughput is less for the water hav- ing more conductivity.An increase in conductivity increases the energy consumption in a node and in a CH which in turn de- creases the throughput.Moreover, the throughput decreases with the increase in transmission duration and with the increase in the cluster size.The residual energy in a node and CH decreases with the increase in time.This reduces the chance of successful trans- mission of a packet and decreases the throughput.Moreover, an increase in cluster size increases the distance between the trans- mitting node and CH, CH and buoy.This leads to more energy consumption and less throughput.However, even with increasing time duration, the throughput in sea waters with the proposed 3D architecture is up to 3 times more than the 2D architecture.Al- though the results are presented for different water environments in the Indian peninsula, the analysis is applicable to any water body.Importantly, the proposed 3D architecture and its analysis would have a significant impact on the analysis and maintenance of next-generation RF-based networks for high data rate underwa- ter applications.

Declaration of Competing Interest

The authors declare that there is no conflict of interests regard- ing the publication of this paper.

The authors declare that they have no known competing finan- cial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors would like to thank the Naval Research Board (NRB), India for their technical support and advise.