1

Analyzing Multi-channel MAC Protocols forUnderwater Acoustic Sensor Networks

Zhong Zhou, Zheng Peng and Jun-Hong Cui and Zhjie Shi{zhongzhou, zhenpeng, jcui zshi} @engr.uconn.edu

Computer Science & Engineering, University of Connecticut, Storrs, CT, 06269, USA

Abstract

The focus of this paper is on the multi-channel MAC protocols for underwater acoustic sensor networks. Wemodel and analyze two generalized multi-channel MAC protocols: multi-channel access with Aloha on a dedicatedcontrol channel and multi-channel access with RTS/CTS on a dedicated control channel. Though the long delayfeature of underwater acoustic channels drastically increases the complexity of the theoretical analysis of theRTS/CTS protocol, we manage to develop tight upper bound and lower bound systems for it. Through simulations,we show that our theoretical analysis can closely estimate the system performance. We also conduct simulations tocompare the two investigated protocols. Our results demonstrate that the RTS/CTS protocol outperforms the Alohaprotocol in most cases, while the latter is more robust in dynamic network conditions.

I. INTRODUCTION

Recently there has been a rapid growing interest in building underwater acoustic sensor networks sincethey can bring significant benefits in a wide spectrum of applications, such as underwater environmentalobservation for scientific exploration, commercial exploitation, and coastline protection [2], [7], [4],[14], [10]. However, due to the unique characteristics of underwater acoustic channels (limited availablebandwidth, long propagation delay and extensive time-varying multi-path effects) and the harsh underwaterenvironments, building autonomous underwater acoustic sensor networks encounters grand challenges atalmost every level of the protocol stack, among which efficient medium access control (MAC) is one ofthe fundamental issues to solve.

In this paper, we investigate the MAC protocols for underwater acoustic sensor networks. Due to thelong propagation delays of acoustic channels (the speed of sound in water is about 1500 m/s, five ordersof magnitude lower than that of radio in air), directly adapting the MAC protocols designed for terrestrialradio sensor networks to underwater environments would be very inefficient. This new challenge for MACin underwater networks have recently inspired a significant amount of research efforts, see references [12],[23], [24], [8], [15], [13], [3], [19]. All these studies focus on single-channel network scenarios. To furtherimprove the system performance, however, we should consider multi-channel network settings, as theparallelism of multi-channel MAC protocols, can greatly improve network throughput, decrease channelaccess delay and lower energy consumption [22], [18], [11], [6]. For underwater acoustic networks, multi-channel MAC protocols have been firstly explored by Pompili et al. in [16] and Tan et al. in [20]. Bothof these two studies have showed the advantages of multi-channel MAC solutions. Further, even thoughacoustic channels traditionally have much lower available bandwidth compared with radio channels, theavailability of multiple channels in underwater acoustic sensor networks can be strongly justified by the

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fast development of underwater acoustic communication technologies, especially the recent high data-rateOFDM acoustic communication solution [9]. In the market, “AquaNetwork” modems from DSPCOMMcan provide multiple parallel CDMA (code division multiple access) channels to the upper layer [1] 1. .

In the literature, though multi-channel MAC protocols have been recently investigated for underwateracoustic sensor networks (as mentioned before), there are no theoretical analysis, specially on the collisionbehaviors, for such protocols yet. In this paper, for the first time, we model and analyze two generalizedmulti-channel MAC protocols: multi-channel access with Aloha on a dedicated control channel (“Multi-channel with Aloha” for short) and multi-channel access with RTS/CTS on a dedicated control channel(“Multi-channel with RTS/CTS” for short), for underwater acoustic sensor networks. Due to the complexityintroduced by long delays, we develop upper bound and lower bound systems for the Multi-channelwith RTS/CTS protocol. We conduct simulations to validate our theoretical analysis, and compare theperformance of the two investigated protocols. We hope that our results could provide useful guidelinesfor the future research in the area of multi-channel MAC protocols for underwater acoustic sensor networks.

The rest of this paper is organized as follows. In Section II, we describe the two multi-channel MACprotocols. Then in Section III, we present our assumptions and methodology. After that, we model andanalyze the two MAC protocols in Section IV and present performance evaluation results in Section V.Finally, we review some related work in Section VI, followed by our conclusions and future work inSection VII.

II. PROTOCOL DESCRIPTION

Different from single-channel MAC protocols, multi-channel access protocols utilize more than onedata channels for communication. In an underwater acoustic sensor network, nodes will exchange controlmessages in order to negotiate the channels for data transmission. Data packets will later be sent on theagreed channel. In the protocols discussed in this paper, a common control channel is dedicated for controlmessages and every node continuously monitors this channel.

A. Multi-channel with Aloha

This is the simplest multi-channel MAC scheme. As shown in Fig. 1, channels are divided into onecontrol channel and multiple data channels. When a node wants to send a data packet, it first selects achannel randomly from the available data channels. A control packet will then be sent on the controlchannel to inform the receiver of the selected channel for data transmission. After that, the data packetwill be sent on the select data channel without delay. No handshaking processes are required. As wecan see, the control channel essentially uses the random Aloha approach. This Multi-channel with Alohaprotocol can be treated as a generalized version of the protocol proposed in [16].

B. Multi-channel with RTS/CTS

This protocol is a combination of multi-channel access and the widely used RTS/CTS technique. Asshown in Fig. 2, there are one common control channel and multiple data channels. Like in the Multi-channel with Aloha protocol, every node continuously monitors the control channel. The difference is

1It should be noted that CDMA with pseudo-random codes may have non-zero cross-correlation. Thus channels are not completelyorthogonal. In this paper, to simplify analysis, we assume that all channels are orthogonal as in [6], [11].

3

Control

channel

Data

channel

Data

channel

Data

Data

Control Control

……

.

Fig. 1. Multi-channel with Aloha

Control

channel

Data

channel 1

Data

channel 2 …..

Data

channel m

RTS RTSCTS CTS

Data

Data

Fig. 2. Multi-channel with RTS/CTS

that the node with outgoing packets will sends a RTS (Request-to-Send) message to the control channel.The RTS message should include the sender/receiver id, the available channel set and the packet length.After correctly receiving a RTS message, the intended receiver will select one channel randomly fromthe available channel set based on its network condition. Then, the receiver will respond with a CTS(Clear-to-send) message to inform the sender of the selected data channel and tune to this channel. Uponreceiving this CTS message, the sender will send out its data packet on the selected data channel. Throughthis RTS/CTS exchange process, overhearing neighbors will know this transmission event and the useddata channel 2. This Multi-channel with RTS/CTS protocol is similar to the scheme presented in [6],which assumes that the propagation delay is negligible. However, due to the long propagation delays ofunderwater acoustic channels, the modelling and analysis process in this paper is quite different from thatin [6].

III. ASSUMPTIONS AND METHODOLOGY

A. Assumptions

Throughout the analysis in this paper, we make the following assumptions:

1) As in [6], [11], we consider a one-hop fully connected network with n nodes. And there are onecontrol channel and m data channels in the network.

2) The traffic at every node is an independent identical (iid) Poisson process with parameter λ.3) The bandwidth of the control channel is Rc, and the bandwidth of the data channel is Rd. Thus the

total bandwidth in the network is R = Rc + mRd. We assume R is fixed for a given network.

2In this paper, we only consider the one-hop network scenario. For multi-hop networks, one more control message is needed on the senderside to inform its own neighbors (which are not the receiver’s neighbors) of this communication event as in [18].

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4) The average length of a control packet is Lc. Thus the average transmission time for a control packetis Tc = Lc

Rc. For the Multi-channel with RTS/CTS protocol, the length of the RTS/CTS message is

LRTS = LCTS = Lc, and the transmission time for RTS/CTS message is TRTS = TCTS = Lc

Rc= Tc.

5) The average length of a data packet is Ld, then the average transmission time for the data packetis Td = Ld

Rd.

6) We ignore the energy consumption on data receiving and processing3. The average energy consump-tion for transmitting a single control packet is denoted as εc, and the average energy consumptionfor transmitting a data packet is represented as εd.

B. Methodology

We will model and analyze the two multi-channel access protocols in terms of throughput and energyconsumption, which are two important parameters for underwater sensor networks. Besides, we also willderive the optimal bandwidth allocation between the control channel and the data channels.

1) Throughput: In our analysis, for each protocol, based on its characteristic, we first derive theaverage probability of successfully transmitting one data packet, ps. Then, the average throughput η

can be presented as

η = nλLdps. (1)

2) Energy Consumption: For a single data packet to be successfully transmitted, averagely speaking,1ps

times of data transmissions are needed, if every data transmission is independent. Also keep in mindthat one or more control packets are needed for channel negotiation. We denote the average number oftransmissions for control packets used for each successful transmission of a data packet as α. Then theaverage (total) energy consumption per data packet can be written as

ε =1

ps

εd + αεc. (2)

3) Optimal Bandwidth Allocation: Since the total bandwidth in the network is fixed, there should existan optimal bandwidth allocation between the control channel and the data channels to maximize thethroughput. This can be obtained by solving the following optimization problem.

max η = nλLdps

s.t. Td =Ld

Rd

, Tc =Lc

Rc

,

mRd + Rc = R,

Ld > 0, Lc > 0. (3)

For the Multi-channel with Aloha protocol, Eq. (3) can be easily solved and we can get closed-formresults, while the Multi-channel with RTS/CTS protocol, Eq. (3) becomes quite complicated and can notbe solved directly. Thus, numerical methods can be used to obtain the optimal bandwidth allocation.Similar optimization models can be formulated to minimize the energy consumption. Due to the pagelimit, we ignore it for saving space.

3In underwater acoustic communication, data receiving and processing consume much less energy than data transmitting [5].

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IV. MODELLING AND ANALYSIS

A. Multi-channel with Aloha

In this scheme, the probability of successfully transmitting one packet can be denoted as

ps = P (AB) = P (A)P (B|A), (4)

where event A means that there are no collisions for the control packet in the control channel so thecontrol packet can be correctly received by its intended receiver 4, and event B means that there are nocollisions for the data packet on the selected data channel.

The packet arriving process for a node is an independent identical Poisson process with parameter λ.Consider a network with n nodes. The total traffic in the network can be viewed as a Poisson processwith parameter nλ.

If a control packet is transmitted at time tc, in order for this control packet to be received correctly,there should be no other control packets in the network during (tc−Tc, tc + Tc), where Tc is the durationof one control packet (as defined earlier). Now we can have

P (A) = e−2nλTc . (5)

For a data packet, even if its corresponding control packet has been successfully received, collisionscan still happen. If another sender selects the same data channel within a very short time, the data packetswill still get overlapped in the time domain and a collision occurs. Given a data packet, we use x todenote the number of other data packets which overlap with this data packet in the time domain (but theircontrol packets do not collide with each other). Then we have

P (x = k) =(2nλ(Td − Tc))

k

k!e−2nλ(Td−Tc). (6)

Under the condition of x = k, the probability that none of these k data packets selects the same channelas this packet is (m−1

m)k (since there are m data channels in the network and every node selects its own

data channel randomly and independently). Therefore, we can get

P (B|A) =∑

k∈(0,1,2,...)

P (x = k)× (m− 1

m)k (7)

=∑

k∈(0,1,2,...)

[(m− 1

m)k]

(2nλ(Td − Tc))k

k!e−2nλ(Td−Tc). (8)

Now we are ready to derive the average successful transmission probability for one data packet, ps:

ps = P (AB) = P (A)P (B|A)

= e−2nλTc × {∑

k∈(0,1,2,...)

[(m− 1

m)k]×

(2nλ(Td − Tc))k

k!e−2nλ(Td−Tc)}

= e−2nλTc × [e(−2nλ(Td−Tc)

m)] = e−

−2nλ(Td+(m−1)Tc)

m . (9)

4Throughout this paper, we assume that a packet will be successfully received by the receiver if there are no collisions for this packet.

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The average throughput η can be derived as

η = nλLdps = nλLde−2nλ(Td+(m−1)Tc)

m . (10)

Eq. (10) shows that the throughput of this protocol is not affected by the long-delay feature of underlyingacoustic channels (since no τ is involved in the throughput calculation).

For this Multi-channel with Aloha protocol, since every retransmission of a data packet is accompaniedby the retransmission of the corresponding control packet, we can get α = 1

ps. According to Eq. (2), the

average energy consumption per data packet thus can be derived as

ε =1

ps

(εc + εd) = e−−2nλ(Td+(m−1)Tc)

m × (εc + εd). (11)

From Eq. (10), we can see that the system throughput is jointly determined by the bandwidth of thecontrol channel as well as that of the data channels. To obtain the optimal bandwidth allocation, Eq. (3)can be converted to

max η = nλLde−2nλ(Td+(m−1)Tc)

m

s.t. Td =Ld

Rd

, Tc =Lc

Rc

,

mRd + Rc = Rt,

Ld > 0, Lc > 0. (12)

By using Lagrange method, we can get

Rc =R√

Lc√Ld +

√Lc

. (13)

B. Multi-channel with RTS/CTS

For this protocol, we will first analyze the behavior of the control channel and obtain the effective trafficto the data channels. Then, we will analyze the behavior of data channels and propose two tractable Markovmodels which can be served as the upper and lower bounds for the system performance.

1) Analyzing Control Channel: The control channel is basically a random channel with every successfulRTS packet leading to a CTS packet transmission. As shown in previous work [23], [3], the performanceof a pure random protocol is not affected by the long propagation delay. And it has been shown that thecompletion time of successful RTS/CTS dialogues can be accurately modelled by a Poisson process [21],[6].

Since every data packet is preceded by a RTS message, the RTS message destined to a node is thussubject to the same Poisson process as the input traffic. Let us denote the average collision probability onthe control channel as pc

c. Correspondingly, the CTS message on the control channel can be approximatedas a Poisson process with parameter (1 − pc

c)nλ. Since collisions might happen between any RTS andCTS messages on the control channel, pc

c then can be derived as

pcc = 1− e−2n(1+1−pc

c)λTc . (14)

Given Tc and λ, we can get pcc numerically. Since only successful RTS/CTS dialogues can result in data

transmissions on the data channels, the effective traffic in data channels can then be modelled as a Poissonprocess with parameter λe [6].

λe = (1− pcc)2nλ. (15)

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RTS

CTS

RTS

CTS

RTS

RTS

CTS

CTS

A

D

B

C

Fig. 3. Node interaction in Multi-channel with RTS/CTS

2) Analyzing Data Channels: Because of the long propagation delay, the RTS/CTS mechanism on thecontrol channel can not eliminate the collision on the data channels. For example, as shown in Fig. 3,node A has packets for node B and node C has packets for node D. Here, C sends out a RTS messageto D first. After D receives the RTS message from C, it will choose one channel from the availablechannels and respond to C with a CTS message. However, before the CTS message arrives at C, the RTSmessage of A arrives at B and B will select one channel from its current available channel set. Since atthis time, B does not know which channel has been selected by D to communicate with C, with certainprobability, B will select the same channel as D. In this case, collisions might happen on the selected datachannel. Thus, for a data packet at time t1, it may collide with a packet in the time range [t1− τ, t1 + τ ],where τ is the propagation delay. Then the collision window of one data packet in this protocol becomes2τ .

In terrestrial radio wireless networks, the analysis process for the multi-channel with RTS/CTS schemedirectly models the data transmission process as a Markov chain [21], [6]. In underwater acoustic sensornetworks, however, the long propagation delay of acoustic channels makes the data channel assignmentprocess a quite complicated distributed stochastic process: the channel selection decision by a node basedon its own perceived network condition may not be accurate. In fact, the data channel selection processfor long delay networks can no longer be modelled by a simple Markov process since the future state ofthe network is not only related to its current state, but also related to the state time τ before. To makethe analysis of such a complicated system tractable, instead of investigating the system directly, we tryto find its upper and lower bounds.

3) Lower Bound and Upper Bound: In this section, we first construct a “virtual” system so that itsperformance is equivalent to that of the original system. Then we develop lower and upper bounds forthe virtual system.

Virtual System: Let us imagine a system with m data channels, with each possessing the samebandwidth as the channels in the original system. Time is slotted into a series of 2τ intervals, whereτ is the propagation delay between two nodes. The input traffic to this system is a Poisson process withparameter λe = (1− pc

c)2nλ, which is the same as the effective traffic to the data channels of the original

system. But for this virtual system, packet collisions are confined to one slot only, which means that everypacket has no knowledge of other packets in its own slot and perhaps will select the same channel asthem. However, every packet knows all packets outside of its slot and thus collisions never happen forpackets from different slots.

8

.....

Channel 1

Channel 2

Channel m

Input :e Channel

allocation

2 4

Packet 1 Packet 2 Packet 3

0

Collision region Collision region

Fig. 4. Illustration of virtual system

0 42 6

………

0 42 6

………

Packet i

Collision region for packet i:

Packet i

Collision region for packet i: 2

2

Original system

Virtual system 1

Fig. 5. Comparison of original system and virtual system

Fig. 4 illustrates this virtual system. In this figure, packet 1 selects channel 1 for its transmission. Whilepacket 2, which is in its same slot, does not know this situation and perhaps will select the same channel1 as packet 1, as leads to collisions on channel 1. For packet 3, it is in the next slot. It knows packet 1and packet 2 and will not select the same channel as them. Here, it selects channel 2 for transmission,which is different from both packet 1 and packet 2.

As shown in Fig. 5, the only difference between this virtual system and the original system is that thecollision region of the packet at any time t1 is moved from [t1−τ, t1 +τ ] to [b t1

2τc2τ, b t1

2τ+1c2τ ]. Because

the effective input traffic of both systems is the same time-invariant Poisson process and the collisionregions of both systems are of the same length 2τ , the performance of this virtual system will be thesame as that of the original system.

The virtual system is still too complicated to analyze directly: three continuous random processes interactin the system. The first is the packet arriving process which is a Poisson process; the second one is thepacket leaving (channel recycle and reuse) process; and the third one is the channel allocation process inwhich one packet selects one channel randomly from its perceived available channel set. Fortunately, wecould derive lower bound and upper bound for the virtual system. Correspondingly, we could obtain thelower bound and upper bound for the original system.

Lower Bound System: We confine the virtual system as follows: the available channel set of everypacket will keep the same as that in the beginning of a slot. The channels that are released can be reusedduring this slot in the original virtual system. However, this will not happen in the confined system. Theyare only available to the packets in the next slot. Compared to the original virtual system, the number ofavailable channels for every packet in every slot is smaller because the released channels in this slot willnot be available to the packets in the same slot any more. Thus, this confined system will have higher

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collision probability than the original virtual system. It can be served as the lower bound of the originalvirtual system.

Upper Bound System: We revise the virtual system as follows: the release of channels occurs at thebeginning of a slot and thus these channels are available to all packets in this slot. Compared with theoriginal virtual system, the number of the available channels for every packet in one slot will be largerbecause all released channels will be available for all packets in the slot. Thus, this revised system musthave lower collision probability and can be served as the upper bound of the original virtual system.

Solving Lower Bound System: For the virtual lower bound system, we set the system state as thenumber of the available channels for the current slot. And we use Pst = (p0, p1, ..pi, .., pm) to denote thesystem stationary probability, where pi means that there are i channels available for the current slot. Wehave proved that this virtual lower bound system can be accurately modelled by discrete time Markovchains. We have also calculated its stationary probability vector Pst and the average data packet collisionprobability pcol. The detailed proof and calculation are omitted in this paper due to page limit. Interestedreaders can refer to VIII-A.

The overall packet success probability can thereby be denoted as

ps = 1− pcol − p0, (16)

where p0 is the average probability that there is no channel available for the system, the condition whenthe system can not support any data transmissions.

Now, according to Eq. (1), the system average throughput can be calculated as

η = (1− pcol − p0)nλeLd. (17)

Considering the RTS/CTS exchange process on the control channel as well as the collision behaviors onthe data channels, we can get the average number of transmissions of control packets for one successfullytransmitted data packet α as

α =2

ps(1− pcc)

. (18)

Accordingly, the average energy consumption per data packet for this system can be written as

ε =2εc

ps(1− pcc)

+1

ps

εd. (19)

The upper bound system can be solved in a similar way. Here, we ignore it for space saving.Handling Various Delays: With the increase of the propagation delay, the system’s collision region

will increase and its performance will degrade. Thus, for a network with various propagation delays fallingwithin [τmin, τmax], we can use τmax as a parameter to get its lower bound and use τmin to get its upperbound. In Section V, through simulations we will show that these bounds are tight in most cases.

V. PERFORMANCE EVALUATION

To assess the performance of the multi-channel MAC protocols, a series of simulations have beencarried out. In this section, we will first validate our theoretical analysis by simulation results. Thenwe systemically compare the two investigated protocols in different network conditions. For presentationbrevity, in the results, we use “Aloha” to denote the Multi-channel with Aloha protocol and use “RTS/CTS”to denote the Multi-channel with RTS/CTS protocol.

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A. Simulation Settings

In our simulations, 50 nodes are randomly distributed in a one-hop fully connected network. Unlessspecified otherwise, the following parameters will be used throughout our simulations. We assume thepropagation speed of the acoustic signal is 1500m/s and distance between any nodes follows a uniformdistribution between 400 meters and 500 meters. Thus, the propagation delay between any two nodeshas a uniform distribution between 0.27 second and 0.33 second. The average data packet and controlpacket length are 200 bytes and 10 bytes respectively. There are 16 data channels in the network. Thepower consumption of each node in transmitting mode is 2Watt and no power control strategies are used.To make a fair comparison, we normalize the throughput to the default average length of data packets(200 bytes). The average energy consumption is presented as the overall average energy consumption forevery successful transmission of 200 bytes data (the default average length of a data packet). The overallbandwidth in the network is fixed to 17 kbps. If C kbps bandwidth is allocated to the control channel,then each of the remaining m data channels will get a bandwidth of 17−C

mkbps.

B. Validating Theoretical Analysis

1) Optimal Bandwidth Allocation for Multi-channel with Aloha: In this set of simulations, we set theinput traffic of every node to be 0.05, 0.1 and 0.2 packets per second respectively. The bandwidth ofthe control channel increases from 1 kbps to 7 kbps. Fig. 6 shows that an optimal bandwidth allocationbetween the control and the data channels does exist. It is 3 kbps and does not change with the inputtraffic. However, as shown in Fig. 7, the optimal bandwidth for the control channel changes with the datapacket length. And the theoretical results are very close to the simulation results, which indicates that ourtheoretical analysis can estimate the system performance very well.

1 2 3 4 5 6 71

1.5

2

2.5

Bandwidth of the control channel(kbps)

Thr

ough

put

λ=0.1λ=0.2λ=0.05

Fig. 6. Throughput with varying control channel bandwidth for “Aloha”

2) Upper and Lower Bounds for Multi-channel with RTS/CTS: In this set of simulations, we verifyour theoretical upper and lower bounds. The upper and lower bounds are obtained by solving the Markovmodels in Section IV-B. And we also compare our results with the theoretical results of the ideal casewhich does not consider the propagation delay. These ideal theoretical results can be obtained by usingthe method from [6] and are referred to as “ideal case without delay” in the results.

We set the input traffic λ to 0.2 packets per second and plot the results in Fig. 8. From this figure, wecan clearly see that our theoretical upper and lower bounds are quite tight. Further, compared with the

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Data Packet

Length (Bytes)

Simulation

results (Kbps)

Theoretical

results (Kbps)

100

200

300

4.0854

3 3.106

2.6 2.624

Fig. 7. Optimal bandwidth allocation for “Aloha”

0 5 10 15 20 25 30 35

1.4

1.6

1.8

2

2.2

2.4

2.6

2.8

3

Number of channels

Actual system

Lower bound

Upper bound

Ideal case without delay

(a)

0 5 10 15 20 25 30 351

2

3

4

5

6

7

8

9

10

11

Numbers of channels

Actual system

Lower bound

Upper bound

Ideal case without delay

(b)

Fig. 8. Comparison of bounds and actual system for “RTS/CTS” (with varying number of data channels). (a) Throughput ; (b) Averageenergy consumption.

theoretical results for the ideal case without delay, our theoretical bounds are much more accurate in longdelay underwater acoustic networks.

Another trend we can observe from Fig. 8 is that the throughput increases significantly with the liftingnumber of data channels and the average energy consumption decrease monotonically. Further, with theincrease of the number of data channels, the system will approach the ideal case of zero propagation delayand archive better throughput and energy efficiency. For example, when the number of data channels is4, the throughput gap between the actual system and the ideal system is 1.1. When number of channelsincrease to 32, this gap is reduced to 0.2. This result suggests that the impact of long propagation delayscan be partly alleviated by increasing the number of data channels.

0.1 0.2 0.3 0.4 0.5 0.62

2.1

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

Propagation delay(Seconds)

Thr

ough

put

Actual systemLower boundUpper boundIdeal case without delay

(a)

0.1 0.2 0.3 0.4 0.5 0.63

4

5

6

7

8

9

Propagation delay(Seconds)

Ave

rage

ene

rgy

cons

umpt

ion

(Jou

ls)

Actual systemLower boundUpper boundIdeal case without delay

(b)

Fig. 9. Performance with propagation delay when λ = 0.2

In Fig .9, we change the average propagation delay from 0.1 second to 0.6 second. In this case,the average distance between nodes varies from 150m to 900m. As expected, the network throughput

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decreases rapidly with the increase of propagation delay and the average energy consumption increasescorrespondingly. This is because the longer the propagation delay is, the higher the collision probabilityon data channels would be, which degrades the network performance. Our theoretical upper and lowerbounds become looser when the propagation delay is high, but still much better than the ideal case whichdoesn’t take the propagation delay into consideration.

In Fig .10, we change the average input traffic of every node λ from 0.01 to 0.6 bytes per second.Initially, the network throughput increases with the the input traffic. The throughput reaches its maximalvalue when λ = 0.2 bytes per second. Afterwards, with the further increase of input traffic, the throughputwill decrease because of the increase of the collision probability in the network. Simulation results provethat in most cases, our theoretical upper and lower bound are quite tight, they are much closer to thesimulation results than the ideal results which neglect the impacts of the propagation delay.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.70

0.5

1

1.5

2

2.5

3

λ

Thr

ough

put

Actual systemLower boundUpper boundideal system without delay

(a)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.72

4

6

8

10

12

14

16

λ

Ave

rage

ene

rgy

cons

umpt

ion

(Jou

ls)

Actual systemLower boundUpper boundideal system without delay

(b)

Fig. 10. Performance with input traffic

In Fig. 11, we increase the bandwidth of the control channel from 1k bps to 11 bps. As is shown in thefigure, the optimal bandwidth allocation does exist to maximize the system performance. Different fromrandom case in Section V-B, these optimal values are different for different input traffics. For example,when λ = 0.05 packets per second, the optimal bandwidth for the control channel is 6 kbps, while whenλ equals 0.1 packets/second, the corresponding value becomes 7 kbps.

Because of the system complexity, we can not get a closed form solution for the optimal bandwidthallocation between the control channel and the data channels. However, according to our study in Sec-tion IV-B for different bandwidth allocation, by solving and comparing a series of system upper and lowerbounds, we can estimate the optimal bandwidth allocation numerically. Because of the tightness of bothbounds, our estimation will be quite accurate in practice.

C. Comparing “Aloha” and “RTS/CTS”

In this section, we compare the two investigated protocols under different network conditions. Un-less specified otherwise, we set the bandwidth of the control channel to 3 kbps, the input traffic 0.1

packet/second and the number of data channels 16.1) Effects of the Number of Data Channels: Fig. 12 shows that when the input traffic is relatively

low (in this case, λ = 0.1 packet/second), if the number of the data channels is small (less than 6),the Multi-channel with Aloha protocol can achieve higher throughput. However, this is not without a

13

2 4 6 8 100.5

1

1.5

2

2.5

3

3.5

4

4.5

Bandwidth of the control channel(kbps)

Thr

ough

put λ=0.05

λ=0.1λ=0.2

(a)

2 4 6 8 104

5

6

7

8

9

10

11

12

13

Bandwidth of the control channel (kbps)

Ave

rage

ene

rgy

cons

umpt

ion

(Jou

ls)

λ=0.05λ=0.1λ=0.2

(b)

Fig. 11. Performance with the bandwidth of control channel

(a) (b)

Fig. 12. Performance comparison with varying number of data channels. (a) Throughput; (b) Average energy consumption.

cost: it has higher average energy consumption too. With the increase of the number of data channels,the Multi-channel with RTS/CTS protocol increases network throughput significantly and becomes thewinner. Meanwhile, its average energy consumption also decrease monotonically, which makes it moreenergy efficient.

2) Effects of Input Traffic: We change the input traffic of every node from 0.01 to 0.5 packet persecond. The results are plotted in Fig. 13(a). From this figure, we can observe that when the input trafficis relatively low (less than 0.1), the two protocols provide almost the same throughput. With the increaseof the input traffic, “RTS/CTS” achieves much better throughput. This is reasonable since for “Aloha”,with an increase of the input traffic, collision probabilities on both control channel and data channels willincrease monotonically. On the other hand, for “RTS/CTS”, the collision on the data channels has beenpartly suppressed by the RTS/CTS exchange on the control channel. From Fig. 13(b), we can also observethat in most cases, “RTS/CTS” is more energy efficient.

3) Effect of the Length of Data Packets: We increase the average length of data packets from 100 bytesto 1200 bytes. The results are plotted in Fig. 14(a). This figure shows that with the increase of data packetlength, the system throughput will increase monotonically for the Multi-channel with RTS/CTS protocol.The reason is, in this protocol, the control channel is not affected by the length of data packets. Whilethe longer a data packet is, the more data will be transmitted in the data channels for each successful

14

(a) (b)

Fig. 13. Performance comparison with varying input traffic λ. (a) Throughput; (b) Average energy consumption.

(a) (b)

Fig. 14. Performance comparison with varying length of data packets. (a) Throughput; (b) Average energy consumption.

RTS/CTS exchange in the control channel. Thus higher throughput will be achieved with longer datapacket length.

For the Multi-channel with Aloha protocol, when the packet length is low (less than 300 bytes), thenetwork throughput has limited increase, but decreases monotonically afterwards. This is because, for thisprotocol, the length of data packets has double effects. On one hand, longer data packets may contributeto higher collision probability on the data channels, which might lead to the decrease of the throughput.On the other hand, potentially, with longer data packets, one successful data packet transmission willcontribute more throughput than the case with shorter data packets. When the average length of datapackets is short, the second factor dominates the first, therefore the network throughput will increase. Butwith the increase of data packet length, the first factor plays a major role and thus the network throughputwill decrease.

From Fig. 14(b), we can also observe that for both protocols, the average energy consumption decreaseswith the increase of the average data packets length, which means that the longer the data packet, thehigher the energy efficiency. Thus, in practice, we may increase the length of data packets for high energyefficiency.

4) Effects of Propagation Delay: In this set of simulations, we change the average propagation delayfrom 0.1 second to 0.6 second. This means the average distance between any nodes varies from 150m to

15

(a) (b)

Fig. 15. Performance comparison with varying propagation delay. (a) Throughput; (b) Average energy consumption.

900m. Fig. 15 plots the results and demonstrates that the performance of the Multi-channel with RTS/CTSprotocol degrades a lot with the increase of the propagation delay. On the contrary, the performance ofthe Multi-channel with Aloha protocol is not affected by the propagation delay. This indicates “Aloha”is more suitable for mobile networks with dynamic propagation delay and can provide a relatively stableperformance to the upper layer.

5) Summary: Now we summarize the performance comparison results as follows.

• The Multi-channel with Aloha protocol is simple and easy to implement. Its performance is notaffected by the long delay feature of underlying acoustic channels. It can provide stable performanceto the upper layer even in mobile networks. Because of its random features, the probability ofpacket collision will soar when the average data packet length is long and the input traffic is large.Consequently, both throughput and energy efficiency will degrade significantly. Thus, “Aloha” issuitable for the network with light traffic and short data packet.

• The Multi-channel with RTS/CTS protocol always achieves relatively high energy efficiency becauseof the RTS/CTS mechanism, which confines the collision region to 2τ . System throughput alsoincreases significantly with the average length of data packets. It outperforms the Multi-channel withAloha protocol considerably when the input traffic is high. Thus, “RTS/CTS” is a better choice forthe network with relatively high traffic and long data packets.

VI. RELATED WORK

In this section, we first summarize some recent MAC layer protocols for underwater acoustic sensornetworks. Next, we briefly review some related work on multi-channel MAC protocols for terrestrial radiowireless networks. After that, we discuss some research on multi-channel MAC protocols for underwateracoustic sensor networks and show their differences from our work.

Recently, efficient MAC protocols for long-delay underwater acoustic sensor networks have receivedsignificant research attention. For example, in [15], to improve system performance, the authors minimizethe duration of a hand-shaking process by taking advantages of receiver’s tolerance to interference whentwo nodes are closer than the maximal transmission range. In [?], time is divided into slots with lengthof the maximal propagation delay. Transmissions are initiated at the beginning of slots. With strictsynchronization, this scheme can greatly reduce the collision probability and is energy efficient. In [24],

16

the authors propose that before data transmission, propagation delay measurement and channel reservationare made in advance to reduce the packet collision probability. In [13], the authors focus on the energyefficiency of the MAC protocol, data transmission is efficiently scheduled despite of the long propagationdelay of acoustic channel in their proposed protocol. The authors of [3] study the Aloha-based protocols inunderwater networks and propose two enhanced schemes, which take advantage of long propagation delays.All of the above work are for the single channel network scenario. While for acoustic communication,CDMA-like technologies can be used in the physical layer to enable concurrent transmission on multiplechannels. For example, “AquaNetwork” modem from DSPCOMM company can provide multiple parallelCDMA channels to the upper layer [1]. Ideally, compared with single channel schemes, multiple channelschemes can improve the system throughput and energy efficiency. Thus motivates our research of multi-channel MAC schemes for the long-delay underwater network scenario.

Multi-channel MAC protocols have long been investigated for terrestrial radio wireless networks. In [22],the authors propose a receiver initiated multi-channel MAC protocol based on frequency hopping formulti-hop wireless networks. Strict synchronization among nodes is needed for this protocol. The authorsof [18] propose a multi-channel MAC protocol with a single transceiver. They identify the multi-channelhidden terminal problem and solve it with a synchronized MAC protocol which splits the time into channelnegotiation phase and data transmission phase. In [6], the authors analyze the performance of multi-channelMAC protocols with Aloha-like reservation on a dedicated control channel for wireless networks. In [11],the authors analyze and compare four different multi-channel MAC protocols for single-hop wirelessnetwork. Their analysis and simulation results show that different protocols have different properties andthus are preferred in different network scenarios. All these studies are performed for radio communicationwhere propagation delay is negligible. Their models and analysis processes can not be applied directly inthe long-delay underwater environments.

Multi-channel schemes for underwater acoustic sensor networks have also aroused significant researchinterest recently. For example, in [17], a hierarchical multi-channel MAC protocols is proposed forclustered underwater networks where TDMA is used for the intra-cluster communication and CDMAis used for the inter-cluster communication. Strict synchronization among all nodes is needed in thisscheme. In [16], the authors propose a random CDMA MAC protocols for underwater networks. In thisscheme, one CDMA channel is dedicated as a control channel for control messages and every senderrandomly chooses one of the CDMA channels for data transmission. This protocol can be treated as oneinstantiation of our generalized scheme of multi-channel with Aloha. The authors in this paper focustheir research on the optimal power control strategies in the physical layer. In [20], the authors utilizeCDMA as the underlying multiple access technique. A RTS/CTS handshaking scheme is employed forevery channel before actual data transmission. In this scheme, CDMA spreading codes are distributedbefore hand by some predefined algorithm and every node is assumed to get a unique spreading codeamong its one-hop neighbors. Summarizing all these research efforts on multi-channel MAC protocolsfor underwater acoustic networks, none of them have theoretically modelled and analyzed the collisionbehaviors and system performance, such as throughput and energy efficiency, which is the focus of ourpaper.

17

VII. CONCLUSIONS AND FUTURE WORK

In this paper, we investigate multi-channel MAC protocols for long delay underwater acoustic sensornetworks. Two generalized protocols: Multi-channel with Aloha and Multi-channel with RTS/CTS aremodelled, analyzed and compared. Through the long-delay feature of underwater acoustic channel greatlycomplicates the theoretical analysis for the Multi-channel with RTS/CTS scheme, we have successfullydeveloped tight upper bound and lower bound. Though simulations, we show that our theoretical analysiscan closely estimate the system performance. Further, our simulation results demonstrate that in mostcases, although “Aloha” simplifies the protocol design, it can not provide good system performance interms of both throughput or energy efficiency. Intricate control such as RTS/CTS like channel reservationcan significantly augment the system performance even in long delay underwater environments. On theother hand, ”Aloha” can achieve stable performance with varying propagation delays, which suggests thatit is more suitable for dynamic network conditions .

Future Work: We would like to pursue our work in three directions: 1) Explore more complicatedmulti-channel MAC protocols for long-delay underwater environments. For example, combine the delaymeasurement techniques, such as those in [24], [13] with multi-channel protocols to improve the systemperformance. 2) Investigate multi-channel MAC protocols in multi-hop underwater network environments.3) Implement multi-channel MAC protocols in real underwater sensor network testbeds and investigatepractical design parameters.

REFERENCES

[1] Aquanetwork: Underwater wireless modem with networking capability. In http://bwww.dspcomm.com/products aquanetwork.html.[2] Ian F. Akyildiz, Dario Pompili, and Tommaso Melodia. Underwater Acoustic Sensor Networks: Research Challenges. Ad Hoc Networks

Journal (Elsevier), 3(3):257–281, March 2005.[3] Nitthita Chirdchoo, Wee-Seng Soh, and Kee Chaing Chua. Aloha-based MAC protocols with collision avoidance for underwater

acoustic networks. In Proceedings of INFOCOM’07, Mini-Symposium), pages 2271 – 2275, 2007.[4] Jun-Hong Cui, Jiejun Kong, Mario Gerla, and Shengli Zhou. Challenges: building scalable mobile underwater wireless sensor networks

for aquatic applications. IEEE Network, Special Issue on Wireless Sensor Networking, 20(3):12–18, May 2006.[5] Lee Freitag, Matthew Grund, Sandipa singh, James Partan, Peter Koski, and Keenan Ball. The WHIO micro-modem: An acoustic

communications and navigation system for multiple platforms. In Proceedings of MTS/IEEE OCEANS, volume 2, pages 1086–1092,June 2005.

[6] Yunghsiang S. Han, Jing Deng, and Zygmunt J. Haas. Analyzing multi-channel medium access control schemes with ALOHAreservation. IEEE Transaction on Wireless Communications, 5(8):2143–2152, August 2006.

[7] John Heidemann, Wei Ye, Jack Wills, Affan Syed, and Yuan Li. Research Challenges and Applications for Underwater SensorNetworking. In Proceedings of IEEE Wireless Communications and Networking Conference, pages 228–235, Las Vegas, Nevada, USA,April 2006.

[8] Kurtis B. Kredo and Prasant Mohapatra. A Hybrid Medium Access Control Protocol for Underwater Wireless Networks. In Proceedingsof ACM WUWNet’07, September 14 2007.

[9] B. Li, S. Zhou, M. Stojanovic, L. Freitag, and P. Willett. Multicarrier communication over underwater acoustic channels with nonuniformDoppler shifts. IEEE Journal of Oceanic Engineering, 33(2), April 2008.

[10] Lanbo Liu, Shengli Zhou, and Jun-Hong Cui. Prospects and problems of wireless communications for underwater sensor networks.Wiley Wireless Communications and Mobile Computing, Special Issue on Underwater Sensor Networks, August 2008.

[11] Jeonghoon Mo, Hoi-Sheung Wilson, and Jean Walrand. Comparison of multichannel mac protocols. IEEE Transaction on MobileComputing, 7(1):50–65, January 2008.

[12] Marcal Molins and Milica Stojanovic. Slotted FAMA: A MAC protocol for underwater acoustic networks. In Proceedings of the IEEEOceans Conference, pages 1–7, May 2006.

[13] Min Kyoung Park and Volkan Rodoplu. UWAN-MAC: an energy-efficient mac protocol for underwater acoustic wireless sensornetworks. IEEE Journal of Oceanic Enegineering, 32(3):710–720, July 2007.

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[14] J. Partan, J. Kurose, and B. N. Levine. A survey of practical issues in underwater networks. In Proceedings of ACM WUWNet’06,Los angeles, CA, USA, September 2006.

[15] Borja Peleato and Milica Stojanovic. Distance aware collision avoidance protocol for ad-hoc underwater acoustic sensor networks.IEEE Communication Letters, 11(12):1025–1027, December 2007.

[16] Dario Pompili, Tommaso Melodia, and Ian F. Akyildiz. A distributed cdma medium access control for underwater acoustic sensornetworks. In Proceedings of Mediterranean Ad Hoc Networking Workshop, 2007.

[17] Francisco Salva-Garau and Milica Stojanovic. Multi-cluster protocol for ad hoc mobile underwater acoustic networks. In Proceedingsof the IEEE Oceans Conference, pages 91–98, 2003.

[18] Jungmin So and Nitin Vaidya. Multi-channel mac for ad hoc networks: Handling multi-channel hidden terminals using a singletransceiver. In Proceedings of ACM MobiHoc, pages 222–233, May 2004.

[19] A. Syed, Wei Ye, and John Heidemann. T-Lohi: A New Class of MAC Protocol for Underwater Acoustic Sensor Networks. In IEEEINFOCOM’08, 2008.

[20] Hwee-Xian Tan and Winston K. G. Seah. Distributed cdma-based mac protocol for underwater sensor networks. In Proceedings ofthe 32th IEEE Conference on Local COmputer Networks, pages 26–36, 2007.

[21] Fouad A. Tobagi and Leonard Kleinrock. Packet switching in radio channels: Part III-polling and (dynamic) split-channel reservationmultiple access. IEEE Transaction on Communications, 24(8):832–845, August 1976.

[22] Asimakis Tzamaloukas and J. J. Garcia-Luna-Aceves. A receiver-initiated collision-avoidance protocol for multi-channel networks. InProceedings of INFOCOM, pages 189–198, 2001.

[23] Peng Xie and Jun-Hong Cui. Exploring random access and handshaking techniques in large-scale underwater wireless acoustic sensornetworks. In Proceedings of MTS/IEEE OCEANS, September 2006.

[24] Peng Xie and Jun-Hong Cui. R-MAC: An Energy-Efficient MAC Protocol for Underwater Sensor Networks. In Proceedings ofInternational Conference on Wireless Algorithms, Systems, and Applications (WASA’07), Chicago, Illinois, USA, August 1 - 3 2007.

[25] Zhong Zhou, Zheng Peng, and Jun-Hong Cui. Analyzing multi-channel mac protocols for underwater acoustic sensor networks. UCONNCSE Technical Report: UbiNet-TR08-02, August 2008. URL: http://www.cse.uconn.edu/∼jcui/publications.html.

VIII. APPENDIX

A. Solving Lower/Upper Bounds for Multi-channel with RTS/CTS

In the lower bound virtual system, the system state is set as the number of the available data channelsin a slot. We use xi to denote the system state in slot i. The next state xi+1 will be shown to be onlyrelated to the current state xi.

The one-step transition probability from state xi = y0 to xi+1 = y1 can be denoted as

P (xi+1 = y1|xi = y0) = P (xi+1 − xi = y1 − y0|xi = y0). (20)

We set Y to be the number of channels that have been used by the newly arrived packets in slot i and X

to be the number of channels that have been released (due to the end of packet transmissions) in slot i.Then, we can get

xi+1 − xi = X − Y. (21)

If xi = y0 and there are s incoming packets during the ith slot, the probability that these packets occupyexactly k channels can be written as

P (Y = k|s, xi = y0) =k∑

j=0

(−1)(k−j)(

kj

)(

j

y0

)s; k ≤ s (22)

.

19

Then the distribution of Y when xi = y0 can be calculated as follows,

P (Y = k|xi = y0)

=∑

s≥k

P (s)P (Y = k|s, xi = y0)

=∑

s≥k

[(2λeτ)s

s!e−2λeτ

k∑j=0

(−1)(k−j)(

kj

)(

j

y0

)s]

=∑

s≥k

k∑j=0

[(−1)(k−j) (2λeτ)s

s!e−2λeτ

(+kj

)(

j

y0

)s]

= e−2λeτ

k∑j=0

(−1)k−j(

kj

)(e−2λeτ j

y0

−∑

s<k

(2λeτ)s

s!e−2λeτ (

j

y0

)s)

We set µ = 1Td

, where Td is the average transmission time for one data packet. When the packet lengthis subject to an independent exponential distribution, the distribution of X then can be calculated as

P (X = k|xi = y0) = (m−y0k )(1− µe−2µτ )k×

(µe−2µτ )(m−y0−k) 0 ≤ k ≤ m− y0 (23)

Now can get

P (xi+1 = y1|xi = y0) = P (xi+1 − xi = y1 − y0|xi = y0)

=

y0∑

k=0

P (Y = k|xi = y0)P (X = k + (y1 − y0)|xi = y0)

=

y0∑

k=0

e(−2λeτ){k∑

j=0

[(−1)k−j(

kj

)(e−2λeτ j

y0−

∑

s<k

(2λeτ)s

s!(

j

y0

)se(−2λeτ))]} × (m−y0

k+(y1−y0)

)×

(1− µe−2µτ )k+(y1−y0) × (µe−2µτ )m−k−y1 ;

m− y0 ≥ k + (y1 − y0). (24)

Eq. (24) gives us the one-step transition probability of lower bound system from state y0 to y1. Wecan clearly see that it is only related to the current system state. Next we can get the one step transitionmatrix PT , based on which we can easily calculate the system stationary probability Pst and the collisionprobability Pcol. Interested reader can refer to our technical report [25] for more details. In a similar way,we can prove that the upper bound system can also be modeled with a discrete time Markov chain andthen we can calculate its stationary probability and average collision probability.

For the lower bound system, the stationary probability Pst then can be calculated as

PstPT = P

|Pst| = 1.(25)

20

If the system is in state 0, which means that there is no channel available for packets in this slot andthus all packets will backoff 5. If the system is in state i, packets in this slot will select one channelrandomly from all available i channels. Collisions might happen if multiple packets in the same slot selectthe same channel . The packet collision probability when system is in i state can be denoted as

P (collision|x0 = i) = 1−inf∑

k=0

(2λeτ)k

k!e(−2λeτ)(

i− 1

i)k

= 1− e−2λeτ

i (26)

And the average packet collision probability pcl can be denoted as

pcl =m∑

i=1

P (collision|x0 = i)P (x0 = i)

=m∑

i=1

P (x0 = i)(1− e−2λeτ

i ), (27)

In the same way, we prove that the upper bound system can be accurately modeled by a discrete Markovchain and we can also calculate its the stationary probability and average collision probability.

5Here, we don’t investigate the backoff strategies for the multi-channel MAC protocols and left it as our future work