Oceans cover approximately %71 of the Earth’s surface and provide significant benefits to humanity, such as climate regulation, transportation, food supply, recreation, medicine, and a variety of natural resources . In order to protect oceans and reap their full profits at the same time, it is crucial to transport, store, organize and process the surging amount of data acquired from underwater sensors and fixed/mobile maritime terminals. To this aim, the internet of underwater things (IoUT) is a technological revolution towards integrating physical and digital worlds by interconnecting smart underwater objects . Thus, IoUT could mark a new era for scientific, industrial, and military underwater applications, e.g., disaster prevention, offshore exploration, environmental monitoring, tactical surveillance, and assisted navigation.
Emerging IoUT applications demand an ambitious quality of service, which necessitates high-speed, ultra-reliable, and low latency underwater networking solutions. However, such goals pose daunting challenges for most electromagnetic frequencies due to the hostile channel impediments of the aquatic medium. Although acoustic communication is a proven technology that is widely adopted by existing underwater applications, its limited bandwidth and low achievable rates are not sufficient for emerging IoUT applications. In spite of its desirable omnidirectional transmission and long communication range, the low propagation speed of acoustic waves (1500 m/s) yields a high latency that disrupts the proper functioning of long-range applications, especially for real-time operation and synchronization tasks .
Recently, underwater optical wireless communication (UOWC) has gained attention by its advantages of higher bandwidth, lower latency, and enhanced security. Nonetheless, UOWC systems are mainly restrained by its directivity and short communication range. The following phenomena primarily drive these restrictions : The transmitted light intensity reduces along the propagation path, this energy dissipation is referred to as absorption and caused by the transformation of photon energy into the internal energy of the absorber (e.g., heat, chemical, etc.). Unlike the ballistic photons, some other photons deflect from the default propagation path; this is also known as scattering and caused either by water particles of size comparable to the carrier wavelength (i.e., diffraction) or by constituents with different refraction index (i.e., refraction). Therefore, the relation between absorption and scattering primarily characterizes the fundamental tradeoff between range and beam divergence angle.
Therefore, multihop UOWC is of the utmost importance to extend communication ranges and realize underwater optical wireless networks (UOWNs) in real-life. In particular, the design and provision of advanced routing protocols top the list of open networking problems as it couples medium access control issues with unique physical layer characteristics of UOWCs. First and foremost, existing routing protocols developed for omnidirectional terrestrial wireless sensor networks and underwater acoustic networks cannot be used for UOWNs in a plug-and-play fashion. Due to the directed nature of the light propagation, the coverage region of a light source is in a sector shape whose central angle (i.e., the divergence angle of the light beam) and radius (i.e., communication range) are inversely proportional. Hence, a wide divergence angle (e.g., light-emitting diodes) allows reaching nearby neighbors, whereas employing a narrow divergence angle (e.g., lasers) renders communicating with a distant node . While the latter requires less number of hops to reach the destination at the cost of equipping the transceivers with accurate pointing-acquisitioning-tracking (PAT) mechanisms, the former may operate without PAT at the expense of a higher number of hops and power consumption .
Apart from the traditional unicast routing (TUR) protocols that transmit packets to a unique next-hop forwarder, opportunistic routing (OR) broadcasts packets to a set of candidate nodes. TUR protocols retransmit unicast lost packets to the forwarder, which are eventually discarded after a specific number of re-transmission. On the contrary, by leveraging the broadcast nature of UOWC, OR involves other candidates in forwarding the packets if the chosen forwarder fails to receive the packet. For instance, Fig. 1 demonstrates two different routes: The former is the route when the highest priority node (green) successfully receives the packet while the latter is over the second-highest priority node (red) when the highest priority fails to receive packet correctly. Hence, OR improves the packet delivery ratio as the likelihood of having at least one successful packet reception is much higher than that in TUR.
In this way, OR provides more energy, throupput, and delay efficient communications by reducing the expected number of re-transmissions. Furthermore, OR is especially suitable to UOWNs because of the connection interruptions caused either by underwater channel impediments (e.g., pointing errors, misalignment, turbulence, etc.) or sea creatures passing through the transceivers’ line-of-sight. Nonetheless, OR requires effective cooperation and coordination mechanisms among the candidate nodes to avoid duplicate transmissions and collisions. To this end, this paper proposes a distributed Sector-based Opportunistic Routing (SectOR) protocol. Being inspired by the sector-shaped coverage region of the light sources, the SectOR discovers routing path towards the destination by exploiting local or global OR metrics based on topology information available at IoUT nodes.
I-a Related Works
The IoUT concept is surveyed in  and  where IouT and its potential applications are presented in a similar fashion to underwater acoustic sensors networks. A more comprehensive approach is provided in  where authors consider software-defined IoUT nodes that can employ acoustic, optic, and magnetic induction signals to overcome the peculiarities of the underwater environment. A software-defined opto-acoustic network architecture design is also proposed in  where authors explain inextricably interwoven relations among functionalities of different layers and introduce network function virtualization (NFV) to realize application specific cross-layer protocol suites through an NFV management and orchestration system.
Although physical layer issues of UOWC is relatively mature, its networking aspects still stays unexplored. Recent efforts on UOWNs can be exemplified as follows: Assuming a Poisson point process based spatial distribution, Saeed et. al. analyzed the -connectivity of UOWNs . In , authors characterized the performance of relay-assisted underwater optical CDMA system where multihop communication is realized by chip detect-and-forward method. Similarly, Jamali et. al. consider the performance anaylsis of multihop UOWC using decode-and-forward (DF) relaying . In , we addressed modeling and end-to-end performance analysis of multihop UOWNs under both DF and amplify-and-forward methods. We extended this work in  to investigate the impacts of location uncertainty on key performance metrics such as achievable rate, bit error rate, and power consumption. Excluding [5, 4], these works do not deal with the effective UOWN routing protocols which is of utmost importance to extend the limited communication range of UOWCs. In [5, 4], proposed protocols follow a traditional unicast routing approach which adapts shortest path algorithms to find paths with minimum distance/error/power consumption or maximum rate. OR has been extensively studied for terrestrial wireless networks [8, and references therein]. OR is also applied to underwater acoustic networks [21, 11, 10, 9]. To the best of authors knowledge, this work is first to develop an OR protocol for UOWNs.
I-B Main Contributions
Our main contributions in this paper can be summarized as follows:
Based on unicast link performance analysis, the performance of broadcast links are characterized in terms of data rate, maximum range, packet delivery ratio, and expected number of retransmissions. Using these performance characterizations as building blocks, we then developed both local and global OR metrics such as distance progress, energy efficiency, and low latency.
Since pointing direction and rangebeamwidth tradeoff yield different candidate set diversities, a candidate filtering and selection technique is proposed to find a pointing and divergence angle. By manipulating the pointing angles and leveraging adaptive beamwidths, we find the candidate set that delivers the best OR metric of interest. Based on this technique, each node maintains its best pointing and divergence angle, and forward received packets along with the priority order of its candidates. Moreover, candidate coordination is facilitated by acoustic communications to mitigate the directivity and range limitations of UOWC.
I-C Notations and Paper Organization
Throughout the paper, sets and their cardinality are denoted with calligraphic and regular uppercase letters (e.g.,
), respectively. Vectors and matrices are represented in lowercase and uppercase boldfaces (e.g.,and ), respectively. Superscripts , , , and are used for indexing source, destination, current forwarder, and next forwarder nodes, respectively. The optimal/best values of variables are always marked with superscript , e.g., .
The remainder of the paper is organized as follows: Section II introduces the network and channel models. Section III analysis the performance of unicast and broadcast links. These performance characterizations are then used to develop local and global OR metrics in Section IV. Section V provide the details of the proposed SectOR protocol and summarizes the algorithmic implementation. Section VI presents the numerical results. Finally, Section VII concludes the paper with a few remarks.
Ii Underwater Opto-Acoustic Networks
In this section, we introduce the UOAN of interest, present the UOWC channel model, and explain the tradeoff between communication range and beamwidth.
Ii-a Network Model
We consider a UOAN that consists of a single sink/surface station and IoUT nodes, as demonstrated in Fig. 1. IoUT nodes are equipped with low-cost optical transceivers to enable UOWC in both forward and backward directions. Light sources are assumed to be capable of adapting their beamwidth and communication range by adjusting the divergence angle . Although optical transceivers are primarily employed to deliver a large volume of sensing data via high-speed UOWC links, the limited range and directivity of UOWC hinder its ability to serve as a reliable control medium for network management tasks. Thanks to its omnidirectional propagation characteristics, each node also has a single acoustic transceiver to provide the network with highly connected control links. The sink station is responsible for aggregating data from sensors and disseminating this information to mobile or onshore sinks. Since IoUT data is generally useful only if it is geographically tagged to an accurate sensing location, we assume that each node is aware of its own location () along with the neighbors within its acoustic communication range. Underwater location information can be obtained either by a fully optic [24, 26] or hybrid opto-acoustic  network localization methods.
Ii-B Channel Model
According to the Beer’s law, absorption and scattering effects of the aquatic medium can be characterized by an extinction coefficient where , , and denote the carrier wavelength, absorption coefficient, and scattering coefficient, respectively. Based on Beer-Lambert formula, the propagation loss factor between two generic IoUT nodes and is defined as follows
where is the perpendicular distance between the nodes and is the angle between the receiver plane and the transmitter-receiver trajectory, as shown in Fig. 2 where is located at point . In case of a perfect alignment, (1) reduces to if is located at point . On the other side, the geometrical loss is a result of spreading the light beam to an area larger than the receiver aperture size and can be given for a semi-collimated transmitter emitting a Gaussian beam by
where is the is full-width beam divergence angle of that is measured at the point where the light intensity drops to of its peak. In the case of perfect alignment, (2) reduces to the approximation given in . Accordingly, the channel gain between and is given by the product of (1) and (2) as
that is merely based on the received ballistic photons which propagate without being disturbed by the scattering effects. That is, (3) neglects all of the scattered photons received by by assuming their total loss. By modifying [14, Eq. (4)], scattered rays can be taken into account as follows
where is a correction coefficient which can be determined based on parameters such as , , , field-of-view (FoV) angle of the receiver, etc. By analyzing (3) and (4), one can gain valuable insight into the tradeoff between divergence angle and communication range. As illustrated in Fig. 2, a wide divergence angle results in a short communication range so that the source can reach the neighbor nodes within its proximity. On the other hand, a narrow divergence angle helps to reach a distant receiver, which naturally requires an agile and accurate PAT mechanism to sustain a reliable communication link.
Iii Performance Characterization
Single-Hop Unicast Links
In this section, we characterize the performance of unicast and broadcast links which are used as building blocks of the OR metrics developed in the next section.
Iii-a Unicast Links in TUR
The source node groups messages destined to the destination node into packets, each has a length of bits that consist of a header and a payload. While control messages (e.g., destination address, next forwarder, ACK signaling, etc.) are included in the header, data is encapsulated in the payload that is extracted and used by IoUT applications. TUR paths are formed by consecutive unicast links, i.e., data is forwarded to a unique node at each hop. Thus, we first characterize the performance of a unicast link in terms of distance, reliability, and achievable rates.
Let us consider an arbitrary multihop path between and , . Assuming that the number of photons follows a Poisson Process, photon arrival rate from to is given by 
where is the received power by , is the transmission power of , () is the transmitter (receiver) efficiency of (), is the detector counting efficiency of , is the data rate, is pulse duration, is Planck’s constant, and
is the underwater speed of light. As per the central limit theorem, the Poisson distribution can be approximated by a Gaussian distribution if the number of received photons is large enough. For intensity-modulation/direct-detection (IM/DD) with on-off keying (OOK) modulation, bit error rate (BER) of the link betweenand is given by 
where is the complementary error function, and are the numbers of photon arrivals when binary 1 and binary 0 are transmitted, respectively, is the additive noise due to dark counts, and is the background illumination noise. Accordingly, the packet error rate (PER) and packet delivery ratio (PDR) can be given by
where is the dark count noise power, is the background noise power, and . For a given data rate , the communication range between and is obtained from the perpendicular distance by using (3)-(6) as follows
where is the principal branch of product logarithm,
At this point, it is important to relate the previously discussed rangebeamwidth tradeoff with the ratereliability one. While the former is specific to OWC since link distance reduces as the divergence angle increases, the latter is common for any communication systems as data rate and PDR are inversely proportional to each other, which follows from (9). Following from (10), these two tradeoffs are also coupled as the range is a function of rate, PDR, and divergence angle.
Assuming that the packet is dropped after
retransmission attempts, probability of having a successful transmission toin delivery attempts is given by
Hence, expected number of transmissions (ExNT) can be obtained as
where is the probability of dropping the package. If the ExNT is normalized to the probability of having a successful transmission within retransmission, we obtain unicast ExNT as
which is independent of .
Iii-B Broadcast Links in OR
Unlike the TUR protocols, OR selects a candidate set (CS) that can overhear the broadcast packets and forward them to the next-hop in a prioritized and coordinated manner. Assuming that is one of the forwarder nodes from to [c.f. Fig. 3], is denoted as the candidate index set of the forwarder node 111 may also include the destination node if it is within the communication range.. For simplicity, we assume that is ordered in the descending order of forwarding priority. That is, the member of attempts to forward packet only if the member fails, . In this case, packet delivery fails if none of the CS members successfully receives the packet, i.e.,
Accordingly, successful packet forwarding ratio is obtained as
which is the probability that successfully receives the packet from given that higher priority candidates , , fail. Hence, ExNT in the OR scheme is given by
where the first term is the ExNT for successfully delivering a package to and the second term accounts for the package drop event. As in (13), the ExNT normalized to the success probability is given by
which is referred to as broadcast ExNT in the rest of the paper.
Iv Opportunistic Routing Metrics
OR metrics play a crucial role in the performance of the routing protocol since it has a direct impact on the candidate selection and prioritization outcomes. Based on the available network state information at each node, the OR metrics can be classified intolocal and global metrics, which require information from neighboring nodes and the entire network topology, respectively. We denote as the sector-shaped coverage region of with divergence angle centered at the pointing angle . Notice that one can alter the sector-shaped optical coverage area of by changing and . That is, the elements of vary with different pairs of and . For the sake of clarity, we omit these parameters from , and focus our attention on a single CS, , throughout this section. Next, we present local and global OR metrics that account for different routing objectives.
Iv-a Local Opportunistic Routing (LOR) Metrics
Local OR metrics are generally preferred to avoid the cost of updating and storing the entire topology state. We assume that each node has the location information of itself, one-hop neighborhood (i.e., acoustic coverage), and the destination (i.e., the sink). In what follows, we introduce local OR metrics for distance progress, energy consumption, and delay.
Iv-A1 Distance Progress
One of the most common local OR metrics is the distance progress (DP), which selects and orders the candidate according to their closeness toward the destination . The DP metric for is given as
Accordingly, the prioritized for DP metric is given by
Lastly, the DP fitness of is given by
Notice that measuring the OR metric in traveled distance implicitly sets the routing objective to minimize the number of hops. In terrestrial WSNs, the DP metric is limited to the scenario where a very far away candidate is selected merely based on its proximity without accounting for the link quality. Due to the short-range and directed propagation of light in the water, the negative consequences of this limitation can be mitigated by restricting the candidate set to the sector-shaped coverage region. A more advanced version of DP is the expected distance progress (EDP) that considers the average DP  by accounting for the link quality. The EDP metric of is given by
which accounts for connectivity, link quality, and distance advancement toward the sink at the same time. Accordingly, the j element of priority set can be iteratively determined as follows
where the first element is determined based on highest individual performance of nodes while the remaining nodes are iteratively determined based on the latest form of the priority set. Lastly, the EDP fitness of is given by
Iv-A2 Energy Efficiency
Since IoUT nodes operate on limited battery capacity, energy-efficient OR plays a crucial role in UOAN lifetime maximization. Indeed, the consumed energy increases with the number of transmission attempts, each of which costs an energy dissipation as a result of transmission, reception, and coordination. Hence, the energy cost of making transmission can be formulated as
where is the transmission duration, is the listening power consumed by decoding and signal processing circuitry, and is the coordination power consumed by candidates during the coordination duration 222We revisit the components of during the candidate coordination discussion in Section V-C.. Based on (24), the energy efficiency metric (EEM) for is given by
where can be obtained by (12). Accordingly, the prioritized for EEM metric is given by
Thus, EEM fitness of is given by
where is the unicast ExNT given in (13).
Iv-A3 Low Latency
Latency is a critical metric, especially for delay intolerant underwater applications. Similar to EEM, low latency metric (LLM) increases with the number of transmission attempts, each of which costs a delay due to the transmission and coordination among the candidate nodes. Hence, the delay caused by transmission attempts can be formulated as
which can be used to calculate the LLM of as follows
Similarly, the prioritized for LLM metric is given by
Lastly, the LLM fitness of is given by
where is the unicast ExNT given in (13).
Iv-B Global Opportunistic Routing (GOR) Metrics
The main objective of the global OR metric is to reduce the ExNT such that end-to-end (E2E) ExNT, energy consumption, and delay is minimized. Since global OR metrics capture the ExNT while taking all possible multipath, they are generally expressed in recursive formulas. Naturally, these require a massive control signaling overhead and computational power.
For a forwarder node , an E2E metric can be obtained by summation of two components: 1) The metric from to its CS and 2) The metric from its candidates to the destination node, . In this case, we can rewrite the global version of (24) in a recursive form as follows
is given in (16). Correspondingly, the probability that transmission is failed in previous attempts and is successfully received the packet at the attempt333To make this happen, nodes with a priority higher than must also fail in the attempt. is given by
Finally, the EEM fitness of is derived as
which is the expected total energy cost of reaching to the destination node through the forwarders in Following from (34), the candidates can be prioritized by their energy consumption towards the destination node as follows
which then can be used to calculate the LLM fitness of as
which is the expected total delay to reach the destination node through the forwarders in . Following from (37), the candidates can be prioritized by their energy consumption towards the destination node as follows
These E2E metrics can also be transformed into a global ExNT metric as explained at the end of previous section.
V SectOR: Sector-Based Opportunistic Routing
In this section, we focus on the design and provision of the proposed SectOR protocol that consists of three main components: 1) Candidate Filtering, 2) Candidate Selection, and 3) Candidate Coordination. Then, we provide algorithmic implementation of the SectOR.
V-a Candidate Filtering
The sector-shaped optical coverage region changes with two prominent parameters; pointing direction and divergence angle. Thus, candidate filtering determines the search space (SS) where we manipulate these angles to find CS with the best fitness. To provide a better insight into the candidate filtering, let us pictorially explain it with the help of Fig. 4 where the acoustic transmission range is set to the maximum optical communication range. For a given divergence angle range , the maximum and minimum distance and can be obtained by substituting and into (10), respectively. Since the CS is to be extracted from the SS, we should filter the SS out of the disk-shaped acoustic communication range. Thus, the SS of is given by
which is the set of locations falls within the coverage region with a positive DP [c.f. Fig. 4]. Notice that positive DP condition is crucial especially for local EEM and LLM metrics, where paths may be routed to wrong directions. Since GOR metrics have the global network view, the SS of GOR metrics are allowed to consider all nodes within the acoustic range, i.e., .
In our previous work , we adopted the conventional method of fixing pointing vector towards the sink station as in [28, 18]. Here, we allow each node to determine its pointing angle within the SS area. To this end, can rotate in the counter-clockwise direction and record the angle wherever a new node is entered into the SS. The list of these recorded pointing angles of is denoted by . Accordingly, evaluates the fitness of each pointing angle as described in the next section and select the best pointing angle as in (39). These two approaches are illustrated in Fig. 4 where setting the pointing vector towards the sink station is not desirable because it delivers a poor performance.
V-B Candidate Selection
As a result of ratereliability and rangebeam-width tradeoffs, the divergence angle has the main impact on feasible candidate sets (colored sectors in Fig. 4) and their performance in terms of the underlying OR metric. For a data and error rate pair, divergence angle determines the range and thus the CS size, which eventually affects DP, EDP, ExNT, energy consumption, delay, etc.
Therefore, SectOR manipulates the rangebeamwidth tradeoff to obtain a CS which delivers the best OR metric. Now let us consider the pointing angle and denote the set of feasible CSs by where . In , the first and the last CSs can be given by and which are shown in black colored dashed and dotted-dashed sectors in Fig. 4, respectively. The rest of CSs may be obtained by quantizing the interval which may be computationally complex for higher resolution. However, this complexity can be augmented by selecting only necessary quantization points based on the node locations within the SS. As shown by colored sectors in Fig. 4, we widen starting from and create a new CS whenever a new node is covered by the sector shaped coverage region. Accordingly, the best CS of is determined by (40).
V-C Candidate Coordination
For the candidate coordination, we consider an acknowledgment (ACK) based method where candidates return ACK messages in the priority order embedded in the received packet’s header. Slotted Acknowledgment (SA) is one of the first coordination methods  where each candidate sends its ACK with a delay of short interframe space (SIFS) duration, , which yields a coordination delay of where is the duration of ACK signal. Since SA is vulnerable to the collision of data and ACK packages, a compressed slotted acknowledgment (CSA) method is developed by means of channel sensing techniques  that has a coordination delay of . We must note that SectOR is not vulnerable to the collision between data and ACK packages since data and control signals are carried in light and acoustic spectrum, respectively. However, SectOR still needs to account for data transmission of multiple candidates. Hence, we adopt fast slotted acknowledgment (FSA) , where each candidate waits before deciding whether it should broadcast ACK. This waiting duration is given by where is the acoustic channel sensing duration, and is the priority order in the candidate set. Accordingly, FSA eliminates the possibility of data packet collision at the cost of coordination delay. Noting that is negligible in comparison with other terms, FSA requires only a single pair of and .
V-D Algorithmic Implementation of SectOR
Algorithmic implementation of SectOR protocol is summarized in Algorithm 1 which first initializes the path and current forwarder node to . Until is reached, while loop between lines 3 and 8 repeats the following procedure: The current forwarder node , execute the candidate filtering, selection, and prioritization procedure by calling Filter-Select-Prioritize (). In this procedure, lines 10 and 11 calculate the SS, , and set of pointing angles,, based on , respectively. Then, the nested for loops between lines 12 and 17 compute OR metrics, evaluates fitness functions, and select the best CS, . Line 18 sets the best pointing angle using (39), then corresponding CSs are calculated using (40) in line 19. Lines 20 ans 21 prioritize the elements of and return it, respectively. Notice that this procedure is not required to be repeated as long as there is no change in the location vector . Following the procedure, broadcast the packet with the header along with the necessary information such as destination node and priority set. After coordination duration, is selected to forward the data packet received from . Accordingly, line 6 set as the next forwarder node, and line 7 includes in the path.
Vi Numerical Results
We consider a square network area with varying side lengths (SL). Throughout simulations, the source and the sink nodes are located at reference points of and , respectively. The remaining
nodes are uniformly distributed over thenetwork area. Obtained results are averaged over random realizations. Unless it is stated explicitly otherwise, we use the parameters listed in Table I which is mainly drawn from . Before presenting the numerical results, let us illustrate the operation of SectOR in comparison with a TUR benchmark which is solved Dijsktra’s shortest path (DSP). Unlike the SectOR, the DSP calculates the shortest path based on the available global topology information of the entire network. Therefore, the DSP sets the divergence angle at minimum to reach maximum range with low error performance.
Before delving into the numerical results, let us provide a better insight into how SectOR protocol works. In Fig. 5, black solid lines represent the route calculated by the TUR. Blue/red/green colored sectors correspond to the search space, maximum divergence angle with the minimum range, and minimum divergence angle with the maximum range, respectively. Yellow colored sectors depict the candidate sets obtained by the proposed candidate selection. Fig. 4(a) shows an instance where the DP metric yields the same path with the TUR benchmark. Fig. 4(b) is a clear example of how the SectOR can leverage the proposed candidate selection method to find out potential CSs to reach the destination. Notice that the fourth hop starting from node 32 cannot find any feasible CS if the pointing vector is aligned to the sink node. Therefore, node 32 points the transceiver toward the only node (node 47) that lies within the SS, which is shown by cyan colored sector. By doing so, the SectOR was able to reach to the sink node via node 47. A better example of this case is shown in Fig. 4(c) where the second and third hop is handled by nodes 14 and 12 as there are no nodes within the feasible region of coverage. Finally, Fig. 4(d) demonstrate the negative impact of the lack of global topology information on the routing performance. Even though the path is routed over node 24 by changing the pointing vector node 22, the local SectOR was not able to reach to the destination.
In the remainder, we present key performance metrics for various network side length, i.e., network size. Since we keep number of nodes constant, increasing side lengths also account for decreasing the node density. Fig. 6 demonstrate the impacts of node density on the probability of finding a path from source to destination. Since TUR and GOR-EXNT have a global network view, they were always able to find a feasible path. On the contrary, LOR methods have a lower probability of path discovery as the node density decreases. In particular, LOR-DP and LOR-EDP perform slightly better than LOR-ExNT because they try to reach the destination in a lower number of hops, which naturally helps them find a feasible path. On the contrary, LOR-ExNT fails to reach the destination while following paths with less number of ExNT.
Fig. 7 demonstrates the fact that E2E-PDR reduces with increasing network sparsity. The first thing to observe is that TUR and LOR-DP perform worse than others, which is mainly because of the fact that they are agnostic to the underwater channel hostility and merely consider the distance as their performance metric. By considering the channel condition along with the distance, LOR-EDP delivers a much better performance than its counterpart LOR-DP. On the other hand, LOR-ExNT delivers a higher PDR as ExNT metric is inversely proportional to the PDR. Lastly, GOR-ExNT is the best as it has the global network view. Fig. 8 visualizes the fact that E2E-ExNT increases with decreasing network density. Again, TUR and LOR-DP delivers a poor performance as they only account for the distance. On the contrary, LOR-EDP and LOR-EDP improves the E2E-ExNT, which is beaten by the GOR-ExNT at the cost of a higher computational complexity and communication overhead.
Fig. 9 compares the traveled total distance by different schemes. As expected, TUR gives the shortest distance as the DSP is optimal. TUR is followed by LOR-DP and then LOR-EDP as they account for distance progress. However, LOR-ExNT performs worst as they follow a longer path with higher number of hops for the sake of a minimum ExNT. Although GOR-EXNT is the worst case under higher densities, it reaches a performance level closer to LOR-DP and LOR-EDP.
Fig. 10 and Fig. 11 show the E2E energy consumption and delay versus varying network size. The LOR-DP yields highest energy consumption and delay for the sake of the shortest path. The TUR provides second worst case performance. LOR-EDP and LOR-ExNT improves the energy and delay performance significantly, which is again beaten by the GOR-ENG and GOR-DEL, respectively.
In this paper, we developed a sector-based opportunistic routing protocol for UOANs. OR is especially suitable for UOWCs as hostile aquatic channel impairments can disrupt the established link connectivity. By leveraging the broadcast nature of the communication, backing up the broken link connectivity by engaging other users who also received the lost packet may improve the system performance in a significant extend. The proposed SectOR protocol exploits the sector-shaped coverage region of the light source and finds the path exploiting the local or global topology information in a distributed manner. Numerical results show that it can reach the performance level of a unicast optimal routing especially for high node density levels.
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