GSR-TDMA : A Geometric Spatial Reuse-Time Division Multiple Access MAC Protocol for Multihop Underwater Acoustic Sensor Networks

The nonnegligible propagation delay of acoustic signals causes spatiotemporal uncertainty that occasionally enables simultaneous, collision-free packet transmission among underwater nodes (UNs).These transmissions can be handled by efficientlymanaging the channel access of the UNs in the data-link layer. To this end, Geometric Spatial Reuse-TDMA (GSR-TDMA), a new TDMA-based MAC protocol, is designed for use in centralized, multihop underwater acoustic sensor networks (UASNs), and in this case all UNs are periodically scheduled after determining a geometric map according to the information on their location. The scheduling strategy increases the number of UNs that send packets coincidentally via two subscheduling configurations (i.e., interhop and intrahop scheduling). Extensive simulations are used to investigate the reception success rate (RSR) and themultihop delay (MHD) of GSR-TDMA, and the results are compared to those of previous approaches, including C-MAC and HSR-TDMA. GSR-TDMA outperforms C-MAC; the RSR of GSR-TDMA is 15% higher than that of C-MAC, and the MHD of GSR-TDMA is 30% lower than that of C-MAC at themost. In addition, GSR-TDMAprovides even better performance improvements overHSR-TDMA; the RSR of GSR-TDMA is 50% higher than that of HSR-TDMA, and theMHDof GSR-TDMA is an order of 102 lower than that of HSR-TDMA at the most.


Introduction
A number of national or multinational projects have focused on developing underwater technologies for applications related to underwater exploration, observation, investigation, surveillance, construction, mining, or excavation [1,2].An underwater acoustic sensor network (UASN) is an enabling technology that can be used for these applications [1], and it is commonly used for underwater nodes (UNs) to purposefully sense and gather data and transfer that data to a land station via a surface station.Without loss of generality, a UASN is more challengeable due to the severity of the underwater environment than a radio frequency-(RF-) based terrestrial wireless sensor network (TWSN).The harsh underwater environment, which affects communications due to the extended multipath, refractive properties of medium, severe fading, and large Doppler shifts, causes high bit-error-rate and low throughput [3].
In addition, the use of acoustic signals results in a nonnegligible propagation delay that is 10 5 times higher than that of RF or optical signals [4,5].This long propagation delay can deteriorate the performance of the UASN (e.g., poor channel utilization, considerable latency, and frequent network failure).On the other hand, the propagation delay of the acoustic signals also leads to spatiotemporal uncertainty, which is a noticeable physical phenomenon.Although multiple acoustic signals destined to the same receiver are simultaneously sent by transmitters at different locations, collisions are not always expected due to the difference in the propagation delay of each signal [6].This phenomenon is opposite to that of a RF-based TWSN, where coincident transmissions inevitably cause collisions, regardless of their location.Hence, an underwater medium can be spatially reused, providing that the transmission time of each UN is efficiently scheduled by considering the spatiotemporal uncertainty, and this can be achieved with the use of an adequate medium access control (MAC) protocol in the datalink layer.
Underwater MAC protocols are broadly divided into contention-free and contention-based MAC protocols.In the case of multihop UASNs with periodic uplink and downlink traffic, contention-based MAC protocols implemented through random access (i.e., ALOHA) or reservation via control packets (i.e., carrier sense multiple accesscollision avoidance) can be ineffective due to the increase in collisions and redundant control signaling overhead [7][8][9][10].Contention-free MAC protocols include time division multiple access (TDMA), frequency division multiple access (FDMA), and code division multiple access (CDMA).FDMA is known to be the least favorable choice for a UASN because of limited bandwidth in the acoustic signals [11].CDMA can improve throughput by using different spreading codes, but the system used to implement CDMA can be complex, and CDMA also results in a near-far problem such that a dynamic power control is additionally required [4,12,13].In contrast, TDMA can be easily implemented by using simple hardware, and it is free of a near-far problem [14].Thus, in this paper we narrow our scope to contention-free TDMA-based MAC protocols.
In the literature, several TDMA-based MAC protocols that take advantage of the spatiotemporal uncertainty have been proposed [15][16][17][18].These MAC protocols are categorized into two types.One type finds an optimal solution by defining conflict-free constraints and formulating time scheduling.In [15], for example, the UNs execute multiple coincident transmissions with collision avoidance in a distributed manner by designing STUMP.A UN uses a Bellman-Ford distributed algorithm to find an optimal link according to its local neighbors' link schedules and propagation delay estimates.Simulation results show that STUMP outperforms TDMA, ALOHA, and T-Lohi in terms of the throughput.In [16], a TDMA-based MAC scheduling method was proposed for use in a single-hop fixed UASN.A BS formulates the MAC scheduling with four conflict-free constraints and determines the start time of all UNs to minimize interframe delays and maximize throughput.
The other type provides heuristic and conflict-free time scheduling.In [17], Cellular-MAC (C-MAC) considers a multihop UASN which consists of multiple hexagonal cells like a beehive.In C-MAC, one cycle consists of 7 time slots.At the initialization stage, a sink node determines the collisionfree time slot for all nodes by considering their location in a beehive-like network.The simulation results show that the throughput for C-MAC is higher than that for Slotted-FAMA.In [18], HSR-TDMA, which is a spatial reuse TDMA with CDMA, was proposed for use in a distributed multihop UASN.An HSR-TDMA time frame consists of multiple time slots whose number is the same as the number of network nodes.For example, node  becomes a slot node (i.e., a transmitting node) at time slot , and node 1 becomes a slot node at time slot 1.At time slot , node  calculates its hop counts from slot node  and determines whether it transmits or receives at time slot .This suboptimal approach enables nodes to operate in a collision-free manner with simultaneous transmissions, and simulation results show that HSR-TDMA outperforms TDMA.
In this paper, Geometric Spatial Reuse-TDMA (GSR-TDMA), which is a new heuristic TDMA-based MAC protocol, is designed for use in a centralized multihop UASN.In GSR-TDMA, the medium is spatially reused by predicting the propagation delays of all UNs according to the information on their location and then transmitting packets simultaneously without collisions.To do this, the UN regularly sends its location information and that of others, which is relayed by its previous hop and finally arrived to the UN, to a base station (BS) on the surface.Then, the BS, as a central controller, can build a geometric map that contains the location information of all UNs and can thus show the overall network topology.The BS uses the geometric map to determine the transmission time of all UNs, and the scheduling of GSR-TDMA consists of two subscheduling configurations (i.e., interhop and intrahop scheduling) which increase the number of UNs sending data coincidentally.The interhop scheduling enables multiple simultaneous transmissions with collision avoidance between the UNs in different hops, and the intrahop scheduling does so between the UNs at different locations in the same hop.
The virtue of using GSR-TDMA is that collision-free transmission scheduling for all UNs can be determined simply by using regularly updated location information without requiring any complicated algorithms.In other words, it is not necessary for GSR-TDMA to determine the optimal scheduling by considering several constraints.In addition, a change in the topology can be adaptively managed by regularly updating the geometric map.Thus, GSR-TDMA can improve the efficiency of channel-reuse and can thus outperform previous suboptimal methods, including C-MAC and HSR-TDMA.
The rest of this paper is structured as follows.In Section 2, GSR-TDMA is explained in detail.In Section 3, the performance of GSR-TDMA is investigated through a simulation, and the results are compared to those of previous approaches.In Section 4, this paper is concluded.

GSR-TDMA
As illustrated in Figure 1, GSR-TDMA includes several steps.The BS primarily sets or updates the geometric map.Then, the BS uses the geometric map to determine the interand intrahop scheduling.Finally, the BS sets all timing parameters, including the transmission time offsets of all UNs, the transmission cycle, and the cycle start time.

Setting the Geometric Map.
The geometric map is primarily set when the network is initialized, with the condition that the BS knows the information on the initial location of all UNs, and the BS periodically updates the geometric map after receiving all the location information gathered from the UNs that had been transmitted together with the data.The manner in which a geometric map is set is given as follows: (i) The BS locates the UNs in a 2D plane according to their location information.The BS locates itself in the center, and the UNs are spread around the BS in a 2D plane.(ii) The 2D plane is divided into several zones with the BS as the center.The zones include one circle and multiple rings, as shown in Figure 2. Throughout this paper, let us rename a zone as a hop.Both the radius of the circle and the thickness of a ring are given as the maximum communication range ().We attach a hop number, ℎ, to each hop according to the distance from the BS ( BS ) which is the multiple of .Hop 0 (ℎ = 0) is just the BS, and Hop 1 (ℎ = 1) is the circle including the UNs for which  BS is less than .Likewise, Hop 2 (ℎ = 2) is the ring that includes the UNs for which  BS is less than 2 but more than .
(iii) The BS maintains the hop number for all UNs in order to schedule their transmission time offsets.

Interhop Scheduling.
If the hop number (ℎ) difference between any two UNs is more than three, they are collisionfree in spite of performing simultaneous transmissions.This idea implies that all hops of the geometric map are categorized into three interhop groups (IHG  , 0 ≤  ≤ 2).As a result, collision-free transmissions are guaranteed among the several UNs that are located at different hops belonging to the same intergroup.An intergroup can be defined as a set of collision-free hops.Let us define  as the number of hops.
Using  and , IHG  can be expressed as ( There are two possible scheduling scenarios: one is where there is an uplink order (IHG 2 → IHG 1 → IHG 0 ), and the other is where there is a downlink order (IHG 0 → IHG 1 → IHG 2 ).The direction of the interhop scheduling depends on a target application.For an example, if the BS just periodically broadcasts a control packet to all UNs and the UNs mainly send the sensed data to the BS, the uplink interhop scheduling can be efficient.On the other hand, we can interchangeably decide the direction of the interhop scheduling according to the instantaneous frequency and the volume of the uplink and downlink traffic.

Intrahop Scheduling.
The intrahop scheduling involves all UNs that belong to the same hop, while the interhop scheduling involves all hops belonging to the same interhop group.The intrahop scheduling is applied to hops where collision-free and coincident transmissions of the UNs are available (ℎ ≥ 2).In the intrahop scheduling, a hop is divided into several subhops, as illustrated in Figure 3.The way to divide the hop into multiple subhops is given as follows: (i) Hop ℎ is divided into 2 ℎ subhops (Subhop 1,. .., Subhop 2 ℎ ).
(ii) A UN with the shortest  BS is selected as a reference UN in Hop ℎ.
(iii) A line between the reference UN and the BS (a reference line) is drawn vertical to the reference line.This results in four arcs per hop.
(iv) Each arc is divided into equal 2 ℎ−2 arcs around the BS in order to obtain 2 ℎ subhops.
(v) We define the subhop to be where a reference UN is located as a reference subhop.
(vi) As Hop 2 in Figure 3 exemplifies, half (2 ℎ−1 ) of all subhops can be collision-free in a hop because nonneighboring subhops, which are one subhop apart, are collision-free.Let us then define  as the subhop number.Starting with the reference subhop, all collision-free subhops are numbered as 1, 2,. . ., 2 ℎ−1 .These subhops belong to an upper subhop group (SHG  ).The other half are also collision-free and are numbered as 2 ℎ−1 + 1, 2 ℎ−1 + 2, . . ., 2 ℎ .These subhops belong to a lower subhop group (SHG  ).Based on the concept of subhops, the intrahop scheduling is given as follows: (i) In Hop 1 where collision-free and coincident transmissions for the UNs are unavailable, the transmission order of the UNs is determined in the  BS descending order.
(ii) In Hop ℎ (ℎ ≥ 2), SHG  sends first and SHG  does last.In a subhop, the transmission order of UNs is also given as  BS descending order.Figure 4 illustrates an example with the intrahop scheduling for hops belonging to IHG 0 in the case of the downlink ordered interhop scheduling.

Setting Timing Parameters.
Here we formulate two timing parameters by considering the inter-and intrascheduling, including the transmission time offsets for all UNs and the transmission cycle.The concept for the timing parameters is exemplified in Figure 5.The definitions of all parameters in order to define the timing parameters are given at the end of the paper.Let us consider a UN  that belongs to Subhop  in Hop ℎ.The UN  should wait during its waiting time, (ℎ, , ), and should then send packets during its service time, (ℎ, , ).Since the UN  can send packets right after several UNs that belong to the same subhop as the UN  but send packets earlier than the UN , the finished transmission, (ℎ, , ), is expressed as (ℎ, , ) is also represented as (3) Using ( 2) and ( 3), the time when all UNs belonging to Subhop  in Hop ℎ send packets can be expressed as (ℎ, ,  ℎ, ) + (ℎ, ,  ℎ, ), as illustrated in Figure 5. Since there are 2 ℎ−1 subhops in SHG  for Hop ℎ, the maximum for (ℎ, ,  ℎ, )+ (ℎ, ,  ℎ, ) in SHG  ,   (ℎ), is expressed as Similarly, the maximum for (ℎ, ,  ℎ, ) + (ℎ, ,  ℎ, ) in SHG  ,   (ℎ), is expressed as If we define the time for all UNs belonging to Hop ℎ in IHG  as   (ℎ) +   (ℎ), the maximum of   (ℎ) +   (ℎ) in IHG  , (), is represented as Using ( 2)-( 6), the transmission time offset of the UN  belonging to Subhop  in Hop ℎ in IHG  , (, ℎ, , ), can be finally obtained as The transmission cycle is the same as the time when one interhop scheduling is executed.Thus, the transmission cycle,  cycle , is expressed as   The BS informs all UNs of all timing parameters, including (, ℎ, , ),  cycle , and  0 , which is the initial time point for the transmission of the packet.Using these timing parameters, all UNs can access the channel for each cycle.Namely, the UN can transmit packets after waiting for (, ℎ, , ) starting from ( − 1) ×  cycle at cycle .

Simulation Results
In this section, the performance of GSR-TDMA is investigated through the use of simulations.The simulator is event-driven, and multiple events occur at the same time at one discrete simulation time point  (1 ≤  ≤ ), where  is the total duration of the simulation.In addition, 100 random experiments are executed for each case in order to obtain averaged performance results.The network conditions for the simulations are given as follows: (i) A fixed and centralized multihop network topology is used in which a BS is located at the center, and multiple UNs are deployed, as shown in Figure 2.
(iii)  is given as 3 ≤  ≤ 7 in order to see the effect of the number of hops.
(iv) Two UN distribution scenarios are considered according to UNs' distribution per hop.One is a simple scenario that the positions of UNs are uniformly distributed and the number of UNs gradually increases according to hops as  ℎ = 4 × ℎ (ℎ ≥ 1).The other is a scenario that UNs are randomly distributed so that the number of UNs per hop is also randomly given.
(v) The uplink and downlink routes between the BS and a UN are determined upon initializing the network.
(vi) In practice, corrupted packets are hardly recovered once acoustic signals are distorted underwater, and the transmitted packets cannot even reach their destination in the worst case.Thus, an error in the simulation is modelled as that where all packet transmissions, which are scheduled at error-occurring simulation time points, fail.We consider the error rate  to be the ratio of the amount of error-occurring simulation durations over .An error is randomly given to any UN at any , and  is given as  = 0 : 0.2 : 0.8.
The traffic conditions are given as follows: (i) Both uplink and downlink traffic are generated.
(iii) The number of packets served per one transmission or the size of the packet train (SN) is given as SN = 1 : 2 : 15.The length of a packet is of 1000 bits, and the data rate is given as 1000 bps.
Two performance parameters are considered, and these include the reception success rate (RSR) and the multihop delay (MHD).The RSR is the ratio of the number of packets received to that of packets transmitted.Two RSR parameters are used, one for uplink (RSR  ) and one for downlink (RSR  ).In order to define the RSR, let us define RN BS as the number of packets received at the BS sent by all UNs, TN UN is the number of packets transmitted from a UN  to a BS, TN BS is the number of packets transmitted from a BS to a UN , and RN UN is the number of packets received at a UN  sent by a BS at a UN , respectively.Then, the RSR is expressed for the uplink and downlink as The MHD represents the multihop end-to-end delay from the time the packet is generated at the source to the time the packet is received at the destination.Like the RSR, there are two MHD parameters, one for uplink (MHD  ) and one for downlink (MHD  ).Let us define UD  as the uplink end-toend delay from a UN  to a BS and DD  as the downlink endto-end delay from a BS to a UN .Then, the MHD for the uplink and downlink are expressed as UD  , for uplink, The simulation experiments are executed under the following four cases.
Case I.The experiment is error-free, and the number of hops () varies in order to investigate the effect of  when the positions of UNs are uniformly distributed and the number of UNs gradually increases according to hops.
Case II.The experiment is error-free, and the period of packet generation () varies in order to investigate the effect of  when the positions of UNs are uniformly distributed and the number of UNs gradually increases according to hops.
Case III.The experiment is error-occurring at fixed  and  in order to investigate the effect of  when the positions of UNs are uniformly distributed and the number of UNs gradually increases according to hops.
Case IV.The experiment is error-free, and the number of hops () varies considering random UN distribution and density in order to investigate the effect of random node distribution.
Case I. Figure 6 illustrates the RSR performance of the three MAC protocols, according to SN and , when  is fixed at 10.The results indicate that the RSR of GSR-TDMA is better than that of C-MAC, regardless of  and SN, for both the uplink and downlink traffic, with a maximum RSR margin of 15% (see Figure 6(b)).GSR-TDMA also outperforms HSR-TDMA in a large percentage of the cases, and the maximum RSR margin is almost 50% (see Figure 6(a)).Although the RSR of HSR-TDMA is better than that of GSR-TDMA, in the case of SN < 10 for  > 5, the margin is unremarkable (∼5%).The results also indicate that the three MAC protocols have little difference in terms of RSR (i.e., within 10%) as  increases.This occurs because the uplink and downlink traffic become heavy as the number of UNs increases with an increase in .This causes the RSR of the UNs far away from a BS to decrease, and the overall RSR performance is degraded.In terms of SN, we can intuitively expect for the RSR to be enhanced as SN increases.The results of the simulation indicate that the RSR improves and is then saturated at a certain value of SN.Thus, the value of SN (i.e., the size of the packet train) can be determined according to the values of  and .In addition, the use of GSR-TDMA is more favorable than that of the other two MAC protocols, in the case of the downlink traffic.failure.We also fix the other parameters, with  = 5 and  = 1, where GSR-TDMA outperforms HSR-TDMA and C-MAC in terms of RSR and MHD.The results indicate that the RSR severely deteriorates as  increases.There is no rebound in the performance among the three MAC protocols, and the performance superiority still holds, regardless of .The performance margin becomes insignificant as  increases due to the frequency of the transmission failures.These results still hold in the case of different values of  and .On the other hand, as  increases, the UNs that are far away from the BS are prone to suffer from transmission failures by going through several hops.Thus, the multihop end-to-end delays of the UNs close to a BS are mainly a concern to the extent that the averaged MHD  and MHD  finally decrease, as shown in Figures 9(c) and 9(d).
Case IV. Figure 10 illustrates the RSR performance of the three MAC protocols, according to SN and , when  is fixed at 10 and UNs are randomly distributed and the number of UNs according to hops is also random.As shown in Figures 10(a), 10(b), 10(d), and 10(e), the RSR of GSR-TDMA is mostly lower than that of C-MAC with slight margin when  is less than five.This is because the possibility of coincident TDMA scheduling among UNs in GSR-TDMA may decrease under UNs' random distribution and density.On the contrary, GSR-TDMA can be still advantageous when the number of hops is greater than five, as shown in Figures 10(c) and 10(f), showing that the RSR of GSR-TDMA is greater than that of C-MAC and HSR-TDMA.As illustrated in Figure 11, the uplink and downlink multihop delays of GSR-TDMA are still shorter than those of the other two MAC protocols under UNs' random distribution and density, the same as Cases I, II, and III.Based on the RSR and the MHD performances, it can be concluded that GSR-TDMA can be also more advantageous than the other two MAC protocols for Case IV.

Conclusions
GSR-TDMA is designed for use in a centralized multihop UASN that takes advantage of spatiotemporal uncertainty.For GSR-TDMA, collision-free transmission scheduling for all UNs is determined after setting a geometric map.The interhop and intrahop scheduling for GSR-TDMA can increase the number of UNs that send packets at the same time, and the extensive simulation in this work verifies these results.The simulation experiments are executed by varying the number of hops, the size of the packet train, and the period of packet generation.The results indicate that GSR-TDMA mostly outperforms C-MAC, irrespective of the conditions, except when the number of hops is less than five under UNs' random distribution and density.GSR-TDMA results in a 15% higher RSR and 30% lower MHD at maximum than C-MAC.In addition, GSR-TDMA outperforms HSR-TDMA in a large percentage of the cases, and GSR-TDMA provides better performance than HSR-TDMA (i.e., a 50% higher RSR and lower MHD by an order of 10 2 than that at maximum).In the case of the error-occurring case, the performance of the three MAC protocols is remarkably degraded as the error rate increases, and the performance of the three MAC protocols still holds, regardless of the conditions.Thus, it can be concluded that GSR-TDMA that transmits packet trains can be more favorable as a suboptimal solution than the two previous approaches used for a multihop UASN.

Figure 2 :
Figure 2: An example of a geometric map.

Figure 3 :
Figure 3: An example of dividing a hop into multiple subhops.

Figure 4 :
Figure 4: The concept of inter-and intrahop scheduling. h

Figure 5 :
Figure 5: The concept of determining the timing parameters.