Collaborative Multiple Access And Energy-Efficient Resource Allocation in Distributed Maritime Wireless Networks

Xueyan Cao,Hongming Zhang,Mugen Peng

State Key Laboratory of Networking and Switching Technology,Beijing University of Posts and Telecommunications,Beijing 100876,China

Abstract:With the rapid increasing of maritime activities,maritime wireless networks(MWNs)with high reliability,high energy effciency,and low delay are required.However,the centralized networking with fxed resource scheduling is not suitable for MWNs due to the special environment.In this paper,we introduce the collaborative relay communication in distributed MWNs to improve the link reliability,and propose an orthogonal time-frequency resource block reservation based multiple access(RRMA)scheme for both one-hop direct link and two-hop collaborative relay link to reduce the interference.To further improve the network performance,we formulate an energy effciency(EE)maximization resource allocation problem and solve it by an iterative algorithm based on the Dinkelbach method.Finally,numerical results are provided to investigate the proposed RRMA scheme and resource allocation algorithm,showing that the low outage probability and transmission delay can be attained by the proposed RRMA scheme.Moreover,the proposed resource allocation algorithm is capable of achieving high EE in distributed MWNs.

Keywords:maritime wireless networks;distributed multiple access;resource allocation;energy effciency maximization

I.INTRODUCTION

1.1 Background

With the deployment of the ffth-generation(5G)and the sixth-generation(6G)communication to improve the network performance and coverage for a wide range of applications,a global space-air-ground-sea integration network is desired[1].Hence,the maritime wireless network(MWN)is growing an area of interest for both academia and industry point-ofview,which contains multiple communication devices such as ships,buoys,and beacons,and adopts various advanced communication techniques[2].Currently,the MWNs rely on the satellite communication,shored base station(BS)communication,and veryhigh-frequency(VHF)communication over the sea.The satellite communication represented by the stateof-the-art Global Maritime Distress and Safety System(GMDSS)[3]with high rate and seamless coverage subjects to high access cost and communication delay.The shored BS communication suffers from the limited offshore coverage and diffculty of BS site selection.The VHF communication with the maximum data rate 9.6 kbps merely cannot provide broadband services.

However,with the unprecedented growth of oceanrelated activities,e.g.,fshery,maritime traveling,resource exploration,environment monitoring,etc.,diversiform maritime traffc put forward higher requirements,which necessitate more robustness 6G MWN architecture,reliable networking and transmission technique.Specifcally,the traffc transmission delay should be one-tenth of 5G and the energy effciency(EE)should ten times as much as 5G[4].Hence,there exists an imperious need to establish an MWN with satisfactory quality of service(QoS)performance and user experience to provide ultra-high speed and low delay communication,in a low-cost and high-reliability way.

Unlike the terrestrial wireless communication networks,where the densely distributed users are controlled by the BS intensively,the distribution of users over the sea is limited to the location of mobile devices,and the devices near or far from the coast are distributed differently,which is identifed as the network heterogeneity.Moreover,the wicked marine environment with high humidity,strong wind and waves restricts the deployment of fxed communication infrastructure,and the devices far from the coast are lack of centralized control.Hence,the centralized networking and resource management are not suitable for MWNs,which can be identifed as the environmental particularity.Based on these characteristics,there are two challenges in MWNs development.The frst one is the link interference problem due to the dynamic wireless channel,uneven node distribution,and limited resource,and the second one is the link unreliability problem caused by the high path loss in a longrange transmission.

In response to these issues,the distributed multiple access scheme with resource scheduling is desired.At present,the IEEE 802.16 based time division multiple access(TDMA)medium access control(MAC)protocol with possible resource waste in centralized networks,and the contention-based distributed coordinated function protocol with back-off delay,interference,and collision,are unsuitable for the distributed MWN with the limited resource.Hence,we adopt the reservation-based multiple access scheme,where the available resource can be reserved in an equitable way and the data can be sent in a collision-free manner.Additionally,the deep fading of the wireless channel or random interference in MWNs lead to the link failure and unreliability,which can be alleviated by the collaborative relay communication via introducing the space and/or time diversity among maritime devices[5].It fts well in ship-to-ship communications with the demands of long range and high reliability by not only extending the coverage and reducing the power consumption of transmitter,but also offering the high diversity gain and reliability by multi-hop multi-link transmission[6,7].

In conclusion,as the key technology of maritime networking,the integration of collaborative relay communication and reservation-based resource scheduling is possible and promising for 6G MWN construction under the heavy burden of limited resource.On one hand,the resource allocation without collision speeds up the selection of relays and benefts for the diversity gain of collaborative relays.On the other hand,the multi-relay aided communication reduces the resource waste and retransmission collision.However,this integration is not simply superimposed.Specifcally,the introduction of the collaborative relay communication enlarges the diffculty of the interference management and resource scheduling among multiple available collaborative relays.First,which point acts as the collaborative relay and when does it trigger the collaborative relay mode are primary issues.Then,given the collaborative relays set,how can energy-constrained relays process the data without the centralized control and coordination under the limited resource in a collisionfree manner is an another signifcant problem.Aiming at these problems,we will unfold the research on the collaborative relay selection,multiple access procedure of MAC protocol,and resource allocation algorithm for distributed MWNs in the following sections.

1.2 Related Works

The study of maritime wireless communication technologies has attracted great research attentions.In terms of the network structure,to achieve the long range ship-to-ship and ship-to-shore communication,radios such as Worldwide Inter-operability for Microwave Access(WiMAX),medium frequency(MF),high frequency(HF),VHF,IEEE 802.16m,and Long-Term Evolution(LTE)were exploited as major longrange communication techniques in maritime networks.In[8],authors designed a cognitive maritime wireless network and a maritime access network,and Joet al.in[9]introduced the LTE-based maritime network,which is an ongoing research project in South Korea.Furthermore,Yanget al.introduced the project of wireless broadband access for Singapore Seaport,which achieves the wireless broadband access rate of up to 5 Mbps based on WiMAX technology with limited coverage[10].Moreover,a promising scheme called delay tolerant networks(DTNs)in maritime communication with packet store-carryforwarding scheme arose[11],where each mobile device transmits the packet to others once there exists an opportunity,otherwise,it stores and carries persistently.However,the large transmission delay and centralized control lead to the low transmission effciency.

Additionally,the MAC protocol consisting of multiple access and resource scheduling scheme plays an important role in distributed MWNs.Previous works focus on the TDMA and contention-based MAC protocol in mesh MWNs and ad hoc MWNs.Tainakaet al.showed a multi-hop network with contention access in[12],and Liuet al.proposed a cross-layer scheduling algorithm with TDMA protocol[13].Furthermore,a self-organized TDMA protocol was proposed for Automatic Identifcation System(AIS)in marine systems.Recently,relay communication techniques have also been extended to oceanic scenarios for improving the effciency and the reliability of maritime broadband services[2,8].Authors design a multi-hop ship-to-shore MWN,which relies on mobile ships and buoys to act as relay mobile equipments.Taking the relay communication and network performance enhancement into consideration,Duanet al.proposed a cooperative multi-cast communication network with a BS ashore and several offshore relays,which relys on joint beamforming optimization and relay design[14].Further,authors introduced a sophisticated relay selection scheme in[15],where the mobility of relays was considered and a location-aware distributed relay selection method was proposed to enhance system EE.In terms of the collaborative relay communication,an interference-aware relay selection scheme was proposed in[6]for two-hop relay networks with multiple transmission links assisted by a relay selected from the candidates.In addition,Hasnaet al.studied the optimal power allocation for relay transmissions under the generated Rayleigh fading channels in[7].However,the mentioned papers do not consider the distributed resource scheduling coupled with collaborative relay communications for MWNs lacking of centralized control and suffcient energy.

1.3 Contributions

Motivated by these observations,in this paper,we construct a distributed MWN with multiple ship access points(SAPs)being access points and relays.To achieve the long-range communication without the centralized control,we introduce the collaborative relay communication in multi-hop link.Further,to enhance the resource utilization and system performance of multiple access,we propose a resource reservation based scheduling scheme coupled with an energyeffciency maximization optimization problem.However,the integration of resource allocation strategy and the collaborative relay multiple access scheme are coupled rather than simply superimposed,which is signifcantly challenging.To sum up,our contributions of this paper are summarized as follows:

·We focus on the distributed collaborative multiple access for MWNs,where the collaborative relay communication is introduced to improve link reliability and the resource block(RB)reservation is adopted for collision avoidance.To achieve the effcient networking,we further propose an EE maximization resource scheduling algorithm jointly integrated with the proposed collaborative multiple access rather than simply superposition.

·We frst design a distributed MAC frame structure,where the orthogonal time-frequency RBs are operated on a frame-by-frame basis adaptively for various traffc types.Then,we propose a resource reservation based multiple access(RRMA)scheme based on three-way-handshake scheduling for one-hop multiple access,and extend it to a three-phase scheduling for multi-hop collaborative multiple access,including collaborative relay selection,RB reservation,and data transmission.

·To reduce the energy consumption of collaborative relay communication in MWNs,we formulate an EE maximization problem under the SNR constraint,and propose an iterative resource allocation algorithm.Extensive simulations show that the low outage probability and transmission delay can be attained by the proposed RRMA scheme,and the high EE can be obtained by the proposed resource allocation algorithm,both of which show the feasibility and effciency.

II.SYSTEM MODEL

In this paper,we consider a maritime wireless network,which serves a number of mobile devices like ships,beacons and buoys.As shown in Figure 1,each SAP is equipped with the radio and control modules,which not only acts as the access point for serving maritime users but also the relay for forwarding data to other SAPs.Moreover,the set of SAPs is denoted asK={s1,...,sK},whereKSAPs are randomly distributed following Poisson distribution with densityρs.When the destination SAP locates in the transmission range of the source SAP,the source SAP intends to send a confdential message via the predefned physical layer secure communication technique to the destination SAP directly.Otherwise,the collaborative relay communication mode is triggered,where multiple SAPs can help to forward the traffc data of the source SAP in a collision-free manner.Taking the diffculty of data processing and large total delay into consideration,the amplify-and-forward(AF)protocol is properly adopted by each relay SAP via simple linear amplifcation.However,the decode-and-forward(DF)will also be applied in the multi-hop transmission through the deep fading.Furthermore,due to the lack of centralized control,the MAC scheduling and resource allocation optimization become challenging.

Figure 1.An architecture of maritime wireless network.

2.1 Channel Model

In this paper,the general maritime two-ray signal propagation model is adopted to describe the channel gain of each transmitter-receiver pair[16],where the large-scale fading coeffcient can be expressed as

2.2 Transmission Model

A collaborative relay link between two SAPs is considered,where the source SAPsasends the data packet to the destination SAPsbvia multiple collaborative relay SAPs.In order to improve the resource utilization,the total available bandwidthWis divided intoCorthogonal subchannels,where one subchannel in one mini-slot represents an RBr ∈R={1,...,R}each with bandwidthB=W/C.In each data transmission,the SAP that generates the data packets is called the active SAP.For simplifcation,denote the index of SAPsaasa,and similarly hereinafter.Denote the binary indexξak=1 if the neighbor SAPkof the active SAPaacts as a collaborative SAP ofa,otherwise,we can haveξak= 0.Moreover,denote the binary indexwhen the link betweenaandkreserves the RBr,otherwise,we can haveHence,the received signal-to-noise-ratio(SNR)on RBrof each collaborative SAPkfromais expressed as

Note that the amplifcation of noise in AF protocol will infuence the received signal quality when the data transmission needs multiple hops(e.g.,Nhops),which leads to low transmission effciency.Hence,to achieve the trade-off between the energy consumption and the transmission performance,the(N-1)-th hop SAPs should use DF protocol,where the SAPs decoded successfully can forward the data with the same code mode to the destination.Take the three-hop relay transmission as an example,the frst-hop SAPs use AF protocol for energy saving and the second-hop SAPs use DF protocol.The received SNR on RBrof the destination SAPbfrom all second-hop collaborative SAPs is expressed as

2.3 Traffic Model

In this paper,we consider the non-real-time(NRT)traffc and real-time(RT)traffc in data transmission,and propose two models to meet the transmission requirement.

The NRT traffic and Poisson model:The NRT traffc refers to the background traffc such as the email,message and fle downloading,all of which request for high throughput.We apply the Poisson arrival model with arrival ratersfor NRT traffc,where the traffc arrival procedure is stable and independent of the service process.The number of the arrived traffc relates to the generating probability,which obeys the Poisson distribution as.

The RT traffic and ON/OFF model:The RT traffc refers to the conversation traffc such as emergency call,video call,and navigation updating traffc,all of which request for high real-time and reliability.Considering the suddenness and randomness,the ON/OFF model is applied for RT traffc,where the source device alternates between sending state of ON mode and silent state of OFF mode.The traffc will be sent at a fxed same rate as NRT traffc of ON mode,and this model is actually determined by the length distribution of ON and OFF period,which are independently and identically distributed.

Defne that the priority of the RT traffc is higher than that of the NRT traffc.Note that the mobility effects are not considered and all traffc packets can be transmitted within the considered period without retransmission.Hence,as shown in Figure 1,each SAP has a reasonable buffer capacity[17]and the order of packet transmission depends on the priority and arrival order.For the same traffc type,a new packet is buffered until the previous are fnished,i.e.frst in frst out,and the high-priority traffc should be sent frstly to guarantee the real-time transmission.

Figure 2.The frame structure of the proposed scheme.

III.THE PROPOSED DISTRIBUTED MULTIPLE ACCESS SCHEME

Due to the lack of the centralized control,we propose a distributed multiple access scheme,which comprises of the frame structure and the distributed multiple access procedure.In the following section,we just illustrate the performance analysis of one-hop and twohop transmission for simplicity[18],which can be extended to multi-hop transmission with modifcation.

3.1 Description of MAC Frame Structure

A hybrid MAC protocol for MWNs is adopted by considering the operation on a frame-by-frame basis,which is shown in Figure 2.The time domain resource is divided into frames with constant duration based on IEEE 802.16 series.Each frame contains two kinds of sub-frames,namely control sub-frame and data sub-frame.A control sub-frame withMCslots(1≤MC≤15)[17]is used to transmit control messages in a contention-based manner.A data sub-frame withMDmini-slots is used to transmit the data packet in a reservation-based scheduling manner.The control sub-frame has two forms: network control sub-frame and scheduling control sub-frame,both of which cannot coexist.In the network control subframe,there areN1network confguration(NCFG)slots for sending the network confguration messages periodically,andMC-N1network entry(NENT)slots for sending the access license messages to the new arrived SAPs.In the scheduling control sub-frame,there areN2centralized scheduling(CSCH)slots for sending the scheduling messages in centralized networks,andMD-N2distributed scheduling(DSCH)slots for sending the scheduling messages in distributed networks.The values ofMCandMDdepend on the network topology and modulation coding mode.

In this paper,we propose a time-frequency resource reservation based collaborative MAC protocol.There are only DSCH slots in the scheduling control subframe,so we haveN2= 0.In particular,the DSCH slots are contended among all potential contended SAPs via scheduling information exchange of the predefned distributed election algorithm[19].Then,the three-way-handshake distributed scheduling is used to reserve time-frequency resource via “request-grantgrant confrm” three steps.Finally,the data packets are sent on the reserved resource without collision and interference.As shown in Figure 3(a),one SAP occupies the whole bandwidth in one mini-slot in TDMA scheme with low resource utilization.Different from(a),the orthogonal subchannels in each mini-slot make up RBs in Figure 3(b)with resource utilization improvement.The horizontal frequency axis denotes the subchannel sequence,i.e.,RB,in each mini-slot,and the vertical axis is the power allocated for each RB by each SAP.

3.2 Time-Frequency Resource Reservation Based Multiple Access Procedure

Before the data transmission,a proper routing protocol is adopted to choose the path from the source to the destination of each data packet[20].Moreover,each SAP periodically broadcasts acknowledge(ACK)message and DSCH message,which contains the scheduling and resource allocation information of its one-hop neighbors as well as its own.As such,each SAP can obtain the scheduling information of its twohop neighbors for collision avoidance,and calculate the next transmission time.Specifcally,the procedure of three-way-handshake containing three scheduling messages is shown in Figure 4[21].Note that the DSCH-Grant:1 message and the DSCH-Grant:0 message should also broadcast to neighbors to update the availabe resource,and the traffc priority can be guaranteed by priority comparison before grant.Two cases of distributed scheduling are shown in the following.

Figure 3.(a)The architecture of mini-slot multiple access.(b)The architecture of time-frequency RB multiple access.

Figure 4.The description of three-way-handshake procedure and the format of each distributed scheduling message.

One-hop multiple access procedure:When an active SAPs1generates a data packet transmission request to its one-hop neighbor SAPs3,which is shown in Figure 5(a),it frst contends the DSCH slots by distributed election algorithm to operate the three-wayhandshake procedure.Then in grant step,s3selects its available RBs from the requested RBs in DSCHRequest message as a grant reply tos1,which contains the sequence number of starting frames,persistence frames,data mini-slots,and RBs.In order to guarantee the priority of traffc,s3will release all its RBs to form the available RB set if the traffc sent bys1is prior to its.In grant confrm step,s1calculates the optimal RBs and transmitting power by the following resource confguration algorithm shown in Section IV,and broadcasts the DSCH-Grant:0 message to neighbors.Finally,s1sends the data packet on the reserved time-frequency resource by optimal transmitting power.

Two-hop collaborative multiple access procedure:When an active SAPs1generates a data packet transmission request to the SAPs5two-hop far from it,which is shown in Figure 5(b),multiple relay SAPs are required to help to establish communication links between these two SAPs.However,the time-varying channel quality in maritime environment raises the outage probability and reduces the reliability of twohop single relay link.Under this circumstance,we propose a multi-relay collaborative access and resource scheduling procedure,which is divided into three phases in the following.

Figure 5.An example to illustrate the operation procedure of the proposed scheme.

·Phase 1:The frst phase is collaborative SAPs selection and data broadcasting.First,s1selects the collaborative SAPs under the limitation of priority and available resource.Then,s1operates request-grant-grant confrm steps,where the grant and ACK message are sent by collaborative SAPs to the active SAP and neighbors to exchange scheduling information for collision-free transmission.Finally,s1confrms available RBs and sends the packet copies to relays by optimal transmitting power on each RB.

·Phase 2:The second phase is data processing.In this phase,the AF protocol is adopted for collaborative relay SAPs3and SAPs4in a lowcomplexity way.By adjusting the transmitting power or amplify coeffcient and reserved RB by optimal resource confguration,the data can be forwarded with high quality and low delay.

·Phase 3:The third phase is collaborative multiple access and data forwarding.In this phase,s3ands4contend the DSCH slots and send the data tos5on the reserved RB,respectively,by the threeway-handshake mechanism and optimal resource confguration algorithm.Unlike the TDMA,more SAPs can send the packets simultaneously without interference through the time-frequency RBs reservation.

3.3 Collaborative SAP Selections

In the phase 1 of the two-hop collaborative multiple access procedure,the active source SAP should select the proper collaborative relays,where the AF protocol is adopted during data forwarding fromadirectly with amplify coeffcient.Taking the traffc priority into consideration,we propose a collaborative SAP selection procedure among all potential collaborative SAPs in each transmission.Denote the available RB set and requested RBs of SAPaasRaandthe one-hop neighbor SAPs set ofaasKa,the priority identiferφa=Ras the RT traffc,andφa=Nas the NRT traffc.In grant step,if the neighbor SAPk ∈Kareceives a prior transmission request bya,i.e.,φa=Randφk=N,kreleases all its occupying RBs as available RB set,i.e.,Rk=R,and replies the grant message.Otherwise,the SAPkchooses the intersection fromandRkas the available RBs to reply a confrm toa.The collaborative SAPs should broadcast the ACK messages after priority determination so that the neighbor can acquire the collaborative information clearly.To sum up,the collaborative SAP selections procedure is shown in Algorithm 1.

IV.ENERGY-EFFICIENT DISTRIBUTED RESOURCE ALLOCATION

Orthogonal RBs partition improves the frequency resource utilization and speeds up the three-wayhandshake scheduling to reduce the transmission delay.In order to further improve the system performance,we propose an EE resource allocation method under the wireless resource and energy limitation.

In this section,the EE is defned as the total average number of bit/Joule successfully delivered to the others,which is given by[22]

whereNtotalis the number of transmitted bits,Etotalis the energy consumption,andTis the focused transmission time.The above equation can be simplifed to the ratio of transmission rateUtotalto the power consumptionPtotal,whereUtotalis the total transmission rate successfully andPtotalcontains total power of all SAPs.Based on the Eq.(4),the transmission rate on RBrfromatobin our system can be expressed as

and the total rate can be given by

where the sum item represents the transmitting power of the active SAPsand collaborative relay SAPs withκbeing the power amplifer effciency factor,PCTandPCRare the constant sum of transmitting and receiving circuit powers of all SAPs.Hence,the overall EE in our proposed collaborative relay system is expressed as

Algorithm 1.Collaborative SAP selections.1: Initialize: active SAP a,distributed neighbor SAPs k ∈Ka,priority identifer φa,φk,available RB set Rk of k,requested RBs ˆRa of traffc from a 2: Output: collaborative vector Na = {ξak} and collaborative relay set Na of a 3: for each neighbor k ∈Ka do 4: if φa =N then 5:k determines the available RBs set Rk =Rk ∩ˆRa 6: else if φk =N then 7:k releases all RBs as available RBs,i.e.,Rk =R 8: else 9:k determines the available RBs set Rk =Rk ∩ˆRa 10: end if 11: if Rk =Ø then 12:k ignores this request and updates ξak =0 13: else 14:k replies the ACK and DSCH-Grant:1 message to a with Rk 15:a updates ξak =1 and broadcasts ACK to the neighbors 16: end if 17: end for

4.1 Problem Formulation

To guarantee the transmission,the SNR thresholdγthis treated as the SNR-constrained QoS requirement.Taking the maximum transmitting power,resource limitation,and the SNR-constrained QoS requirement into consideration,we formulate the EE maximization resource allocation optimization problem as

where the optimization variables are transmitting powers P and the RB allocation strategy A of each transmission link.Eq.(13)is the optimization objective.Constraint(13a)represents the limitation of RB allocation variables.Constraints(13b)-(13c)represent the maximum limited transmitting powerPmaxof each SAP.Constraint(13d)represents that each RB can only be occupied by one link.Constraint(13e)represents the SNR-constrained QoS requirement.

After determining the collaborative variableξakvia Algorithm 1,the optimal RB and power allocation should be solved under the acquired perfect channal state information of each RB and the given collaborative SAPs setNa.It can be clearly seen that the objective function in Eq.(13)is a non-convex fractional form[24],which motivates us to transform it into an equivalent parametric programming and solve it effciently by the Dinkelbach method[22].

For the sake of notational simplicity,we defneGas the set of feasible solutions of the optimization problem in(13).Without loss of generality,we defne the maximumwhereU(P*,A*)andP(P*,A*)are the transmission rate and power consumption under the optimal power and RB allocation strategy.According to theProposition 1in[25],the fractional programming with the given collaborative relay setNacan be related to the equivalent parametric programming as

whereqis the coeffcient of total power consumption,P(P,A)＞0,andU(P,A)andP(P,A)are continuous functions.The equivalence means that both problem formulations lead to the same resource allocation policies.Note that the optimal coeffcientq*,

can be achieved if and only if the following condition,

holds,where{P*,A*} ∈Gis the optimal solution to Eq.(13).Hence,the optimization problem(13)can be transformed as

Note that Eq.(17)is a tractable feasibility problem.Based on the optimal condition related to the problem transform,if we can fndq*,the objective function of the fractional form in Eq.(13)can be transformed into the subtractive form Eq.(17).As a result,we can focus on the equivalent objective function in the rest of the paper.

4.2 Proposed Iterative Algorithm for Energy Efficiency Maximization

Sinceq*cannot be directly obtained,an iterative algorithm is proposed to updateqwhile ensuring that the corresponding solutions P and A remain feasible in each iteration.The convergence can be proved,and the optimal resource allocation for Eq.(17)can be derived.The proposed iterative Algorithm 2 ensures thatqincreases in each iteration,where max{U(P,A)-qP(P,A)}is verifed as a decreasing function ofq.Hence,the optimal solution to maximize EE can be achieved via two nested loops.The outer loop updatesqj+1byU(Pj,Aj)andP(Pj,Aj)from the last iterationj,and the inner loop calculates the power strategy Pjand RB allocation strategy Ajunder the given parameterqjby the following inner-loop optimization problem

whereqjis the updated parameter in the outer loop.Note the global optimal solution can be guaranteed by difference of convex(DC)programming,i.e.,{U(P,A)-qjP(P,A)}which can be explored in[26].The detailed solving procedure is shown in Algorithm 2.

The problem Eq.(18)is a non-convex problem,which cannot be solved directly.In this part,we adopt the Lagrange dual decomposition method to achieve the sub-optimal solution of power and RB allocation strategy.The Lagrange function for the transformed optimization problem Eq.(17)under the givenqjis

whereβ={β1,...,βK}is the Lagrange multiplier related to the transmitting power limitation,µ={µ1,...,µR}is the Lagrange multiplier related to the RB allocation limitation,andθis the Lagrange multiplier related to the SNR-constrained QoS requirement.

Then,the dual optimization function can be given by

and the dual optimization problem can be given by

It is obvious that the dual optimization problem is convex.Hence,we adopt the dual decomposition method to divide the dual problem(21)intoRindependent sub-optimization problems.With the Karush-Kuhn-Tucker(KKT)condition,the optimal power allocation is derived by

wherekis also suitable fora,[x]+=max{0,x},andis the equivalent channel gain.Then,we substitute the optimal power allocation obtained by(22)into the decomposed optimization problem(20),and we can have

wheref(A,P*)is the function of RB allocation variable under the optimal power.Denote a matrix F withRrows and 1+columns to represent the value off.By ranking the rate value of each column,the optimal RB allocation indicator A for the given dual variables can be expressed as

Note that each link fromsitosjcan occupy multiple RBs,so the criterion(24)should be operated several times until the demands of requested traffc are met.

Then,we adopt the sub-gradient method[27]to solve the dual problem by updating the Lagrange mul-tipliers

whereνrepresents the positive iterative step size,iis the iterative step.The values ofβk,µr,θupdate with the increasing of iteration number,which can update the optimal power and RB allocation.When the stop condition is met,the iteration stops.The optimal power P*and RB confguration A*are the optimal resource confguration strategy and the maximum EE can be obtained by Eq.(15).

V.NUMERICAL RESULTS

In this section,we test the performance of RRMA scheme and energy-effcient resource allocation algorithm.In particular,there are various tests with the traditional resource allocation schemes for comparison.Other parameters are summarized in Table I,unless otherwise specifed.

Table 1.Message format.

In the tests,the SAPs are distributed over the sea within 5×5 km2,which is shown in Figure 6.We consider that the available coverage range of each SAP is 2 km taking the channel gain and antenna gain into consideration.The channel gain is set as the signal propagation function to each SAP and it is assumed unchanged within one frame.In addition,before access and data transmission,the traffc of SAPs should be categorized into various priorities,i.e.,RT traffc or NRT traffc.Without loss of generality,we assume that each traffc with high priority should be transmitted within 2 frames,and the traffc with low priority should be transmitted within 4 frames.

Figure 6.The topology of the maritime wireless network.

Figure 7.The access success probability of FTMA and the proposed RRMA with the increasing number of SAPs.

Figure 8.The outage probability of FRMA and the proposed RRMA with the increasing number of SAPs.

Algorithm 2.Iterative energy-efficient resource allocation algorithm.1: Initialize: the maximum inner loop times Imax,the maximum outer loop time Jmax,converged threshold ϵ,and the initial value q(1) = 0, i ←1,j ←1 2: Output: {P*,A*}and q* = U(P*,A*)P(P*,A*)3: for 1 ≤j ≤Jmax do 4: for 1 ≤i ≤Imax do 5:Obtain the collaborative SAPs set of SAP a 6:Calculate the local optimal Pj,Aj under the qj by min β,µ,θ g(β,µ,θ)= min β,µ,θ max P,A L(P,A,β,µ,θ s.t.βk ≥0,µr ≥0,θ ≥0 7:Update the Lagrange multipliers by(25)8: end for 9: Obtain U(Pj,Aj)and P(Pj,Aj)10: if U(Pj,Aj)-qjP(Pj,Aj)≤ϵ then 11:Set{P*,A*}={Pj,Aj},q* =qj 12:break 13: else 14:Calculate the coeffcient qj+1 by qj+1 = U(Pj,Aj)P(Pj,Aj).15: end if 16: end for)

5.1 Traffic Access Success Probability

In this subsection,the trend of traffc access success probability with the number of SAPs is tested under the proposed RB reservation based multiple access(RRMA)and the fxed time slot based multiple access(FTMA)referring to IEEE 802.16 based TDMA MAC protocol in[17].Defne that the traffc access is successful if the traffc packet is received completely and decoded correctly by the destination SAP,and the traffc access success probability is denoted as the proportion of traffc accessed successfully at the destination SAP.We adopt the FTMA scheme as a benchmark to verify the access performance for two reasons.On the one hand,the assumption of ship mobility in two schemes are similar.On the other hand,the access success probability is infuenced by transmission effciency within a targeted time,which can be improved by the orthogonality partition and proper scheduling of resource in RRMA compared with the FTMA.In the FTMA procedure,the active SAP sends the data packet in the data slots,which are the same as the contended DSCH slots by the election algorithm,and the strategy will not change until there exists link outage or point failure.The new active SAP should select the residual data slots without dynamics and adaption.However,the proposed RRMA is beneft from the orthogonal RB partition and reservation,which improves the QoS and access probability.

Assume all the traffc have the same size and type,and the demands of persistence frames is 2.Figure 7 shows that with the increasing number of SAPs,the traffc access success probability of two schemes have different degrees of reduction due to the insuffcient even saturated resources when more SAPs join in.However,through orthogonal subchannels division,more RBs can be accessed by different SAPs within the same data mini-slot in our proposed RRMA scheme,which speeds up the transmission procedure.Meanwhile,the increasing number of SAPs leads to more potential collaborative SAPs of collaborative relay selection in our proposed RRMA scheme,which can alleviate the degree of performance degradation.

5.2 Traffic Outage Probability

In this subsection,the trend of traffc outage probability with the increasing number of SAPs is tested under different multiple access schemes.To verify the effect of on-demand resource reservation,we adopt the fxed RB based multiple access(FRMA)as a benchmark,where the transmitting power and RB allocation of each SAP are fxed after frst control sub-frame[28].It may lead to the insuffciency of the requested resource and poor channel state of the chosen RB,which cause the high energy consumption and delay.

Figure 8 shows that the outage probabilities of NRT traffc in two schemes are increasing with the number of SAPs due to the possible collision or incomplete transmission.However,the outage probabilities of RT traffc in two schemes are low due to the priority guarantee.In addition,it is seen that due to the adaptive adjustment to the demands,the outage probability of our proposed RRMA scheme is dominantly lower than that of FRMA,which leads to the unexpected RB wastes and traffc packet loss if the subchannel quality is poor,and the transmitting power is much lower than the demands.

Figure 9.The traffic transmission delay of FTMA,CTMA and the proposed RRMA with the increasing number of SAPs.

Figure 10.The traffic transmission delay of FTMA and the proposed RRMA under different arrival rates.

Figure 11.The collaborative transmission energy efficiency of FRMA and the proposed RRMA under different QoS requirements.

5.3 Traffic Transmission Delay

In this subsection,the average transmission delays of 12 SAPs are tested under the FTMA within the whole frequency resource,contention based time slot multiple access(CTMA)and our proposed RRMA,where the backoff time in CTMA and the retransmission or outage in FRMA would increase the delay.The CTMA is a widely used MAC protocol in IEEE 802.11,where the active SAP monitors whether the frequency resource is idle or not and then selects to access after backoff timer stops[12].Unless the parameters mentioned above,we set the contention window range is[31,100],the interframe space time is 2 ms.For fair comparison,we choose the time duration of one mini-slot in our scheme to be equal to the smallest time unit in IEEE 802.11 with the same preamble overhead.

In the test,two traffc types are considered in FTMA and our proposed RRMA.Note that there exists no priority in CTMA since it is unable to differentiate services and QoS guarantee for different traffc types.Defne the traffc transmission delay of one type traffc as the time from the active SAP to the destination at the frst time.In addition,we set the requested RBs of RT and NRT priority traffc are half of|R|,and the requested mini-slots in fxed slot access of NRT and RT priority traffc are|MD|.Figure 9 shows that with the increasing number of SAPs,the traffc transmission delay increases rapidly due to the high probability of collision and limited RBs.It is clear that the CTMA has the largest growth rate,which suffers from serious collisions due to the frequent contention.Beyond that,our proposed RRMA achieves the lowest traffc transmission delay of both RT traffc and NRT traffc among three schemes.In the FTMA scheme,the traffc transmission only takes up a portion of the bandwidth resource or has no traffc,which leads to the frequency waste.However,more than one SAP can access in one data mini-slot with the collaborative transmission in our proposed RRMA scheme,which speeds up the data packet transmission and the transmission procedure with lower delay than that in other schemes.Additionally,the transmission delay of RT traffc is lower than that of NRT traffc due to the strict demands and priority guarantee of RRMA scheme.

In Figure 10,we test the transmission delay of the proposed RRMA scheme and FTMA scheme under different traffc arrival ratesrsof NRT traffc.It is clear to see that with the increasing number of SAPs,the transmission delay of two schemes are increasing underrs= 10 packets per second andrs= 5 packets per second.For the same traffc arrival rate,the transmission delay of our proposed RRMA scheme is smaller than that of FTMA scheme.On the other hand,for any multiple access scheme,the growth of the arrival rate leads to the increasing of transmission delay,and the gap is enlarging with the increasing number of SAPs under the limited available resource.

5.4 Energy Efficiency Optimization

Finally,we simulate the collaborative transmission EE of the FRMA and the proposed RRMA.The maximum transmitting power is adopted in FRMA.In Figure 11,it is clear to see that within the fnite iterations,the optimal EE can be obtained,which verifes the effciency of iteration optimization algorithm.In addition,without considering the demand of traffc and channel quality,the EE of our proposed RRMA is higher than that of FRMA signifcantly.Moreover,the larger the threshold,the lower the EE due to the larger probability of decoding failure of the destination SAP.

VI.CONCLUSION

In this paper,we propose a distributed multiple access method for a distributed MWN with multiple SAPs far from the land.First,we design a time-frequency resource reservation based multiple access procedure for one-hop direct link and two-hop collaborative relay link.Then,to improve resource utilization and system performance,we formulate a resource allocation optimization problem for EE maximization,and propose an iteration based resource allocation algorithm.Finally,numerical results show the feasibility and effciency of RRMA and optimal resource allocation algorithm.

ACKNOWLEDGEMENT

This work was supported in part by the National Natural Science Foundation of China under Grant 62001056,61925101,U21A20444,in part by the Fundamental Research Funds for the Central Universities under Grant 500421336 and Grant 505021163.