Power Allocation Scheme for Non-Orthogonal Multiple Access in

sensors Letter

Power Allocation Scheme for Non-Orthogonal Multiple Access in Underwater Acoustic Communications Jinyong Cheon and Ho-Shin Cho * School of Electronics Engineering, Kyungpook National University, Daegu 41566, Korea; [email protected] * Correspondence: [email protected]; Tel.: +82-53-950-7577 Received: 11 September 2017; Accepted: 23 October 2017; Published: 27 October 2017

Abstract: In this paper, we propose a power allocation scheme for non-orthogonal multiple access (NOMA) in underwater acoustic sensor networks (UWASNs). The existing terrestrial sum-rate maximization (SRM) power allocation scheme suffers from the degradation of the overall sum-rate in UWASNs due to wasteful resource created by unequal transmission times between each transmission path. To address this issue, we propose the equal transmission times (ETT) power allocation scheme, which can prevent wasteful resource generation by guaranteeing equal transmission times between each transmission path. ETT considers the number of packets waiting for transmission in the sender’s buffer for creating equal transmission times. Numerical results show that the proposed ETT outperforms SRM in terms of the overall sum-rate, while having nearly identical maximum sum-rate to the SRMs. Keywords: power allocation; non-orthogonal multiple access (NOMA); underwater acoustic sensor networks (UWASNs)

1. Introduction Among the envisioned medium access control (MAC) protocols for the fifth generation of mobile communication, the non-orthogonal multiple access (NOMA) protocol is one of the most promising candidate techniques, as it has been shown to increase cell capacity. To support multiple users, the NOMA protocol allocates two-dimensional time-frequency resources that are superposed and transmitted to multiple users whose channel gain differences are very large. Each receiver node can decode an individual packet from packets that are superposed in the power domain, by using the method of successive interference cancellation (SIC). Consequently, the NOMA protocol can achieve high cell capacity. On the other hand, conventional orthogonal multiple access (OMA) protocols allocate resources to each user either in time or in frequency or in code, which limits the cell capacity. In underwater environments, acoustic waves are used for communications instead of radio frequency (RF) waves due to the absorption and diffusion of RF waves. Additionally, underwater ambient noise is not white noise, i.e., it has frequency-dependent characteristics. Thus, underwater acoustic channels suffer from low propagation speed, narrow frequency bandwidth, and low data rate. These unique channel conditions necessitate the modification of conventional terrestrial MAC protocols before they are applied to underwater acoustic sensor networks (UWASNs). The paper examines the feasibility of the NOMA protocol in an underwater channel that has distance/frequency-dependent attenuation and frequency-dependent ambient noise. Additionally, the performance degradation issues found in existing sum-rate maximization (SRM) power allocation schemes for downlink underwater NOMA are addressed. Wasteful resources caused by unequal transmission times between NOMA-paired channels may have an adverse effect on the data rate of multiplexed channels. Hence, this paper proposes a new scheme named equal transmission times (ETT) power allocation to eliminate wasteful resources. To guarantee equal transmission times, ETT

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first calculates the data rate required for each path, based on the number of packets waiting in the sender’s buffer. Subsequently, ETT calculates the transmission power required to achieve the calculated data rate. Equal transmission times are guaranteed, and the proposed ETT can prevent generation of wasteful resources. In terms of the overall sum-rate, which is defined as the mean of the sum of the data rates for two paired channels during a total transmission time, we observe that ETT outperforms existing SRM scheme irrespective of the number of packets for each path in the sender’s buffer. This paper is organized as follows. First, we provide an overview on the characteristics of the underwater channel and on the clustered UWASNs in Section 2. Section 3 gives a brief overview of problems with the existing SRM in underwater environments. The details of the proposed ETT are described in Section 4. Numerical results are presented in Section 5. Finally, conclusions are drawn in Section 6. 2. An Overview of the Characteristics of the Underwater Channel and the Clustered UWASNs 2.1. The Characteristics of the Underwater Channel In this paper, we consider Thorp’s underwater channel model [1], which is based on empirical data. Thorp’s model provides the attenuation and the ambient noise for the underwater channel. The attenuation of an acoustic wave is influenced by the frequency and the communication distance between the sender node and the receiver node. Hence, the overall attenuation can be expressed as a function of the distance (l) and the frequency ( f ), which is given by Equation (1), l

A(l, f ) = A0 l k a( f ) 103

(1)

where l is a distance (m) between the sender and the receiver node, f is signal frequency (kHz), A0 is the normalizing constant, and k is the spreading factor. The spreading factor has a value between 1 and 2 depending on the depth. k = 1 means a cylindrical spreading which characterizes shallow water communications. k = 2 means a spherical spreading which characterizes deep water communications. Generally, k = 1.5 is often considered as practical spreading. We therefore assume the spreading factor as 1.5 and the normalizing constant as 30 dB. a( f ) is the absorption coefficient and is expressed in decibels per kilometer, 10 log a( f ) = 0.11

f2 f2 + 44 + 2.75 × 10−4 f 2 + 0.003. 1 + f2 4100 + f 2

(2)

For lower than a few hundred Hz, the following formula may be used: 10 log a( f ) = 0.002 + 0.11

f2 + 0.011 f 2 . 1 + f2

(3)

Figure 1 illustrates the ambient noise sources. There are four ambient noise sources in the ocean: turbulence, shipping, waves, and thermal noise of the molecules. Equation (4) gives the power spectrum density (PSD) of these noise sources in dB re µ Pa2 /Hz [2],  10 log Nt ( f ) = 17 − 30 log f     10 log N ( f ) = 40 + 20(s − 0.5) + 26 log f − 60 log( f + 0.03) s . 1  10 log Nw ( f ) = 50 + 7.5w 2 + 20 log f − 40 log( f + 0.4)    10 log Nth ( f ) = −15 + 20 log f

(4)

where Nt ( f ), Ns ( f ), Nw ( f ), and Nth ( f ) denote the noise components of turbulence, shipping, waves, and thermal noise, respectively. The PSD of total ambient noise Ntotal ( f ), which is sum of the PSDs of four sources, can be described by

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N total  f   N t  f   N s  f   N w  f   N th  f  . Ntotal ( f ) f= NNt ( f )f + N ( f ) + N ( f ) + N f(f.). N Ns  f   N w f   N th total

t

s

w

(5) (5) (5)

th

Figure 1. The ambient noise sources: turbulence, shipping, wave, and thermal. Figure 1. The ambient noise sources: turbulence, shipping, wave, and thermal.

The ambient noise decays with a frequency that is limiting the system bandwidth. By The ambient ambient noise decays a frequency that Nistotalthe limiting the system bandwidth. considering the attenuation and the ambient noise , the signal to noise (SNR)By  f system Al ,with f  with The noise decays a frequency that is limiting bandwidth. Byratio considering considering the attenuation and the ambient noise , the signal to noise ratio (SNR)     A l , f N f can calculated by thebeattenuation A(l, f ) and the ambient noise Ntotal ( f ), thetotalsignal to noise ratio (SNR) can be can be calculated by calculated by Psender Psender SNR l , f   (6) (6) SNR(l, f ) =Al , f P  f ( f ) SNR l , f   A(l, Nfsender Ntotal )total (6) Al , f N total  f  where wherePPsender the transmitted transmitted signal signalby bythe thesender sendernode. node.The Thefrequency frequencydependent dependentpart part sender is a PSD of the where is a PSD of the transmitted signal by the sender node. The frequency dependent part P of the signal to noise ratio (SNR), A l, f N f , is called the AN product. Figure 2 shows the AN ( ) ( ) sender of the signal to noise ratio (SNR), Al , f N total  f  , is called the AN product. Figure 2 shows the AN total of the signal to noise ratio (SNR), Adistance , frequency. is called the AN product. Figure 2 shows the AN ldistance and , f N totaland f  frequency. product according communication product according totocommunication product according to communication distance and frequency. -80 5 km 7.07 km 5 km 8.66 km 7.07 km 10 km 8.66 km 10 km

-80 -85 -85 -90 -90

1/AN [dB] 1/AN [dB]

-95 -95

-100 -100

-105 -105 -110 -110 -115 -115 -120 5 -120 5

10 10

15 20 frequency [kHz] 15 20 frequency [kHz]

25

30 25

30

Figure AN product according distance and frequency. Figure 2. 2. AN product according toto distance and frequency. Figure 2. AN product according to distance and frequency.

2.2.Clustered Clustered UnderwaterAcoustic AcousticSensor SensorNetworks Networks(UWASNs) (UWASNs) 2.2. Underwater 2.2. Clustered Underwater Acoustic Sensor Networks (UWASNs) UWASNs, energy efficiency is widely considered as most the most important challenge. InInUWASNs, thethe energy efficiency is widely considered as the important challenge. To To prolong the network lifetime, various approaches have been proposed to solve this issue in clustered Inthe UWASNs, energy efficiency is widely considered as thetomost To prolong network the lifetime, various approaches have been proposed solveimportant this issue challenge. in clustered networks [3–5]. Figurelifetime, 33 shows the UWASN considered in this paper. The UWASN prolong the network various approaches have been proposed solve thisclustered issue clustered networks [3–5]. Figure shows theclustered clustered UWASN considered into this paper. The in clustered comprises a surface sink3node theand underwater sensorsensor nodes.nodes. Every sensor nodenode has the networks [3–5]. Figure shows the clustered UWASN considered inEvery this paper. The clustered UWASN comprises a surface sinkand node the underwater sensor hassame the capabilities such as storage, processing power, communication range, and battery life. Each sensor UWASN comprises sinkprocessing node and the underwater sensor nodes. Every the same capabilities sucha surface as storage, power, communication range, and sensor batterynode life. has Each node can become a cluster header (CH) node or a cluster member (CM) node, depending on the same capabilities such as storage, processing power, communication range, and battery life. Each sensor node can become a cluster header (CH) node or a cluster member (CM) node, depending on sensor node can become a cluster header (CH) node or a cluster member (CM) node, depending on

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the situation. The CM nodes gather event or environmental information and forward this data to its CH node. i.e., as a coordinator node of the cluster, the CH node aggregates data from the CM nodes situation. The CM nodes gather event or environmental information and forward this data to its CH in their cluster or sometimes transmits data to its CM nodes for controlling the cluster. Periodically, node. i.e., as a coordinator node of the cluster, the CH node aggregates data from the CM nodes in their each CH node transmits aggregated data to the surface sink node through single-hop or multi-hop cluster or sometimes transmits data to its CM nodes for controlling the cluster. Periodically, each CH transmission. Finally, the surface sink node transfers aggregated data to the control center using node transmits aggregated data to the surface sink node through single-hop or multi-hop transmission. RF waves. Finally, the surface sink node transfers aggregated data to the control center using RF waves.

Figure 3. The clustered underwater acoustic sensor network (UWASN) considered in this paper. Figure 3. The clustered underwater acoustic sensor network (UWASN) considered in this paper.

The and inter-cluster communications are different from thefrom communication between Theintra-cluster intra-cluster and inter-cluster communications are different the communication the surface sink node and the control center. Because of the half-duplex property and space-time between the surface sink node and the control center. Because of the half-duplex property and uncertainty [6] of the underwater channel, a variety ofaMAC protocols proposed UWASNs space-time uncertainty [6] of the underwater channel, variety of MACare protocols arefor proposed for to prevent collisions. The underwater MAC protocols can be classified into three broad types [7]: UWASNs to prevent collisions. The underwater MAC protocols can be classified into three broad contention-free MAC protocol, MAC protocol, hybridand MAC protocol. types [7]: contention-free MACcontention-based protocol, contention-based MACand protocol, hybrid MACHowever, protocol. most of these OMA protocols are operated in a manner that the resource is temporarily unavailable However, most of these OMA protocols are operated in a manner that the resource is temporarily to other nodes communicating nodes. Thus, nodes. if a NOMA is applied to UWASNs unavailable to except other nodes except communicating Thus,protocol if a NOMA protocol is appliedby to exploiting attenuation noise characteristics of the underwater which is mentioned UWASNs the by exploiting theand attenuation and noise characteristics of the channel underwater channel which is above, multiple nodes can share the same two-dimensional time-frequency resource according to the mentioned above, multiple nodes can share the same two-dimensional time-frequency resource channel gain difference. according to the channel gain difference. The of resources resources can canenhance enhancethethe performance of underwater communications. The sharing sharing of performance of underwater communications. The The performance of NOMA highly depends on node pairing and power allocation schemes [8]. performance of NOMA highly depends on node pairing and power allocation schemes [8]. Thus, Thus, when we find the power allocation ratio for paired nodes, calculating the received power and when we find the power allocation ratio for paired nodes, calculating the received power and the the expected at each paired is essential. However, conventional power allocation expected datadata rate rate at each paired node node is essential. However, conventional power allocation schemes schemes for the terrestrial NOMA are not suitable for the underwater channel which has lowtraffic. data for the terrestrial NOMA are not suitable for the underwater channel which has low data traffic. Therefore, in this we paper, we propose novelallocation power allocation scheme that canfor be downlink used for Therefore, in this paper, propose a novel apower scheme that can be used downlink NOMA for clustered UWASNs. This scheme assumes that the cluster header has already NOMA for clustered UWASNs. This scheme assumes that the cluster header has already chosen the chosen the paired cluster member nodes. In other words, the node pairing scheme does not fall paired cluster member nodes. In other words, the node pairing scheme does not fall within thewithin scope the scope of this paper. of this paper. 3. SRM Power Allocation Scheme in Underwater Channels and Their Issues 3. SRM Power Allocation Scheme in Underwater Channels and Their Issues The conventional OMA protocols have some weakness when they are applied in the underwater The conventional OMA protocols have some weakness when they are applied in the underwater channel. Time division multiple access (TDMA) needs accurate timing synchronization and a guard channel. Time division multiple access (TDMA) needs accurate timing synchronization and a guard time to avoid collisions. These degrade the performance of the TDMA because of low channel time to avoid collisions. These degrade the performance of the TDMA because of low channel utilization. Frequency division multiple access (FDMA), which use frequency bands exclusively at the utilization. Frequency division multiple access (FDMA), which use frequency bands exclusively at same time, is not suitable for the narrow bandwidth underwater channel. In the case of code division the same time, is not suitable for the narrow bandwidth underwater channel. In the case of code

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division multiple access (CDMA), the problem near-far is problem is one of the major In theproblem, near-far multiple access (CDMA), the near-far one of the major issues. In issues. the near-far problem, thecannot receiver cannot the weak signal in theof presence a strong signal. To this overcome the receiver detect the detect weak signal in the presence a strongofsignal. To overcome issue, this issue, the sender node requires an extra overhead for the power control technique to ensure equal the sender node requires an extra overhead for the power control technique to ensure equal received received contrast, NOMA the gainbetween difference the receiver nodes. This power. In power. contrast,InNOMA exploits theexploits gain difference the between receiver nodes. This characteristic characteristic is suitable for the underwater channel that has a severe attenuation. is suitable for the underwater channel that has a severe attenuation. Regarding resource resource allocation, allocation, there is is aa significant significant difference difference between between the the OMA OMA and and NOMA NOMA Regarding protocol as as shown shown in Figure 4 where the resource allocated to different user is colored protocol colored differently. differently. OMA protocols in Figure4a exclusively allocate resources such as time, frequency, and code to each each OMA protocols in Figure 4a and code to user. Theoretically, Theoretically, there there is is no nointerference interference among among users users so so aa receiver receiver can cansimply simply detect detect each each user’s user’s user. packet. Hence Hencebecause because of exclusive resource allocation, the maximum number of users being packet. of exclusive resource allocation, the maximum number of users being supported supported is limited. In contrast, as illustrated in Figure 4b, the NOMA protocol allocates same twois limited. In contrast, as illustrated in Figure 4b, the NOMA protocol allocates same two-dimensional dimensional time-frequency resourceusers to multiple users in the power domain.protocol The NOMA protocol time-frequency resource to multiple in the power domain. The NOMA allocates the allocates the same resource exploiting the characteristics of channelwhich difference, which allows multiple same resource exploiting the characteristics of channel difference, allows multiple users who usersawho have achannel significant gain difference to share the Therefore same resource. Therefore the have significant gain channel difference to share the same resource. the number of users number of users isbeing supported is not strictly Unlike the protocol, theneeds NOMA being supported not strictly limited. Unlike thelimited. OMA protocol, theOMA NOMA protocol an protocol needs an elaborate user signal detection process named SIC at the receiver node side. elaborate user signal detection process named SIC at the receiver node side. Through the SIC, each Through the SIC, user can decode from thepower superposed in the user can decode an each individual packet froman theindividual superposedpacket packets in the domainpackets and therefore domain and is therefore a high cell capacity is achieved. apower high cell capacity achieved.

Figure 4. 4. The The difference difference between between orthogonal orthogonal multiple multiple access access (OMA) (OMA) and and non-orthogonal non-orthogonal multiple multiple Figure access (NOMA), (NOMA), the the resource resource allocated allocated to to different different user user is is colored colored differently: differently: (a) (a) Orthogonal Orthogonal Multiple Multiple access Access; Access; (b) (b) Non-Orthogonal Non-OrthogonalMultiple MultipleAccess. Access.

Figure 55 provides provides an an example example of of the the downlink downlink NOMA NOMA transmission transmission via via power power domain domain Figure multiplexing between between aa sender sender node node SS and and two two receiver receiver nodes nodes G G and and B. B. Among Among the the two two receiver receiver multiplexing nodes, G has good channel quality as it is located near to S, and B has bad channel quality because of nodes, G has good channel quality as it is located near to S, and B has bad channel quality because of severe attenuation commensurate with its distance from S. In general, node S pairs two receiver nodes severe attenuation commensurate with its distance from S. In general, node S pairs two receiver nodes that have have large large differences differences in in their their channel channel gains gains and and then then transmits transmits data data packets packets to to the the paired paired nodes nodes that concurrently at the same frequency. To achieve collision-free concurrent transmissions, the paired concurrently at the same frequency. To achieve collision-free concurrent transmissions, the paired nodes’ packets packets are are superposed superposed in in the the power power domain, domain, wherein wherein SS allocates allocates aa larger larger transmission transmission power power nodes’ ( Pb) to ) to bad quality channel transmission a smaller transmission to the good Pg )good (P thethe bad quality channel transmission and and a smaller transmission powerpower (Pg ) to( the quality b quality channel transmission exceeding the transmission constraint channel transmission withoutwithout exceeding the transmission power power constraint (Ptx ), as( Pshown in the tx ), as shown upper-left part of Figure There is5.aThere direct is association between thebetween power allocation ratio (γ = Pg /P tx ) in the upper-left part of5.Figure a direct association the power allocation ratio and sum-rate, which is defined by R + R , where R and R are the data transmission rates of g g (  the ) and the sum-rate, which is defined by , where and are the data R b b P g Ptx R g  Rb Rg b the good and bad quality channels, respectively. Therefore, finding the optimized γ in terms of the transmission rates of the good and bad quality channels, respectively. Therefore, finding the sum-rate is critical for NOMA performance. Superposed packets are decoded in the following manner. optimized  in terms of the sum-rate is critical for NOMA performance. Superposed packets are Node B decodes its packet by considering G’s packet as interference. On the other hand, node G has to decoded in the following manner. Node B decodes its packet by considering G’s packet as decode B’s packet first. Subtracting the decoded packet from the superposed packets, node G can then interference. On the other hand, node G has to decode B’s packet first. Subtracting the decoded packet decode its packet from the subtracted packet, which is the summation of its packet and the ambient from the superposed packets, node G can then decode its packet from the subtracted packet, which noise. This procedure is called SIC [9]. is the summation of its packet and the ambient noise. This procedure is called SIC [9].

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Figure Figure5. 5. Two Tworeceiver receivernodes nodesdownlink downlinkNOMA. NOMA.

Moststudies studieson onpower powerallocation allocationfor forNOMA NOMAhave havefocused focusedon onmaximizing maximizingthe thesum-rate. sum-rate.In In[10] [10] Most theauthors authorsproposed proposedtwo twosub-optimal sub-optimalpower powerallocation allocationschemes schemesbased basedon onthe theusers’ users’instantaneous instantaneous the channel state information (CSI) in a sub-carrier based NOMA system. In [11] the authors firststudied studied channel state information (CSI) in a sub-carrier based NOMA system. In [11] the authors first theergodic ergodiccapacity capacitymaximization maximizationproblem problemfor forthe theRayleigh Rayleighfading fadingmultiple-input multiple-inputmultiple-output multiple-output the (MIMO)NOMA NOMAsystems. systems. In In this this literature, literature, the theauthors authors proposed proposed both bothoptimal optimaland andlow lowcomplexity complexity (MIMO) sub-optimal power allocation schemes to maximize the ergodic capacity under the conditions sub-optimal power allocation maximize the ergodic capacity under the conditionswith witha weak user. user. The sum sum rate rate atotal totaltransmit transmitpower powerconstraint constraint and and minimum minimum rate rate constraint constraint of the weak maximization of ofaamultiple-input multiple-inputsingle-output single-output (MISO) (MISO) downlink downlink NOMA NOMA system system has hasbeen beenstudied studied maximization in [12]. [12]. The The authors authors used used aaminorization-maximization minorization-maximization algorithm algorithm to to solve solve the the downlink downlink sum-rate sum-rate in maximizationproblem. problem. the authors proposed a sub-optimal water filling based power maximization In In [13][13] the authors proposed a sub-optimal water filling based power allocation allocation scheme to improve the total achieved system throughput. This scheme is operated in two scheme to improve the total achieved system throughput. This scheme is operated in two stages: the stages: the water filling–based inter sub-band power allocation and the adaptive intra sub-band water filling–based inter sub-band power allocation and the adaptive intra sub-band power allocation. power allocation. formulation problem of an optimization problem for maximizing sum capacity has The formulation of The an optimization for maximizing the sum capacity hasthe been studied in [14] been studied in [14] for the single-input single-output (SISO) method. This paper considered for the single-input single-output (SISO) method. This paper considered maximizing the sum capacity maximizing sumconstraint capacity under a total power constraint and a quality of service under a total the power and a quality of service (QoS) condition of each user. (QoS) condition of each user. since SRM is based on the assumption that paired transmissions last until the end However, However, since is based on the assumption that paired transmissions last until the end of of transmissions, the SRM maximum sum-rate cannot be sustained in the case of unequal transmission transmissions, thepaired maximum sum-rate be sustained in the completes case of unequal transmissionbefore times times between the channels whencannot one of the paired channel the transmission between the paired channels when one of the paired channel completes the transmission before the the other. Hence, resource waste occurs while only one channel is in transmission. Resource waste other. Hence, resource waste occurs while only one channel is in transmission. Resource waste means means the resource is available but cannot be used by any other nodes (including the sender node). the resource is available but cannot used by any other the nodes (includingdue thetosender Especially in UWASNs, resource waste be may severely degrade performance the lownode). data Especially in UWASNs, resource waste may severely degrade the performance due to the low data rate and long propagation delay. rate Figure and long propagation delay. 6 shows an example where resource waste is generated due to unequal transmission times. Figure 6 the shows an example whereofresource is generated due to unequal transmission For simplicity, packet size in number bits, L p , waste is considered to be constant. Packet transmission times. For simplicity, the packet size in number of bits, , is considered to be constant. Packet Lp times of nodes G and B, which are denoted by τg and τb , respectively, are obtained by transmission times of nodes G and B, which are denoted by  g and  b , respectively, are L τg = Rpg obtained by (7) L . τb = Rp b Lp g  Rg Thus, the total transmission times of G and B, which are denoted by Tg and Tb , respectively, are . (7) obtained by Lp  b τg × Mg Tg = R , (8) Tb = τb × bMb and respectively, the M total transmission times of G and B, which are denoted T b ,transmission, g whereThus, Mg and G andby B inT the current b are the number of packets transmitted to nodes
are obtained by respectively. The discrepancy in transmission times, δT = Tg − Tb , causes the aforementioned

where M where M

g g

and Mb are the number of packets transmitted to nodes G and B in the current and Mb are the number of packets transmitted to nodes G and B in the current





transmission, respectively. The discrepancy in transmission times, T  Tg  Tb , causes the transmission, respectively. The discrepancy in transmission times, T  Tg  Tb , causes the aforementioned resource waste. In this case, even though one of the transmissions is complete, to aforementioned resource waste. In this case, even though one of the transmissions is complete, to Sensors 2017, 17, 2465 the other nodes cannot use resources for transmitting until the sender nodes’ 7total of 13 avoid a collision avoid a collision the other nodes cannot use resources for transmitting until the sender nodes’ total transmission time ( max T g , T b  ) elapse. In general, the sum-rate is maximized when R g is much transmission time ( max T g , T b  ) elapse. In general, the sum-rate is maximized when R g is much greater than (i.e., ) [15]. Even one under suchtransmissions conditions, if is the number of Rb In  even resource waste. thiscase, though of the complete, to packets avoid a destined collision greater than Rb (i.e.,  gg   bb ) [15]. Even under such conditions, if the number of packets destined the other nodes cannot use resources for transmitting until the sender nodes’ total transmission time for G and B in buffer of node S is very large, we can easily make  small enough to be negligible
the for G and B in the buffer of node S is very large, we can easily make  TT small enough to be negligible (max Tg , Tb ) elapse. In general, the sum-rate is maximized when R is much greater than Rb (i.e., by adjusting the M g and Mb . However, in UWASNs where the trafficg generation is infrequent, by adjusting and . However, in UWASNs where the traffic generation is infrequent, the Mbsuch g τg