Performance analysis of an enhanced cooperative MAC protocol in mobile ad hoc networks
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Abstract
In this paper, we evaluate the performance of an enhanced cooperative MAC with busy tone (eBTCOMAC) protocol in mobile ad hoc networks via a combination of theoretical analysis and numerical simulation. Our previously proposed BTCOMAC protocol was enhanced by (1) redesigning the minislots used in the helper node selection procedure; (2) specifying complete frame formats for newly defined and modified control frames; and (3) using a new metric (the received SNR rather than the received power) in the helper node competition. In this eBTCOMAC protocol, cooperation probability is calculated based on a geometric analysis, and a Markov chainbased model is used to derive steadystate probabilities for backoffrelated parameters. These results are used to analytically characterize two performance measures: system throughput and channel access delay. Numerical simulation of a mobile wireless network where all communication nodes are assumed to be uniformly distributed in space and move independently based on a random waypoint model is used to validate the analytical results and demonstrate the performance gains achieved by the proposed eBTCOMAC protocol.
Keywords
Cooperative communication eBTCOMAC protocol Helper node selection Received SNRAbbreviations
 ACK
Acknowledgement
 BTCOMAC
Cooperative MAC with busy tone
 CCTS
Cooperative clear to send
 CRTS
Cooperative request to send
 CTH
Clear to help
 CTS
Clear to send
 eBTCOMAC
Enhanced BTCOMAC
 EC
Exact contention
 GI
Group indication
 HA
Helper node address
 HC
Harsh contention
 HCTS
Helper clear to send
 MAC
Medium access control
 MI
Member indication
 MIMO
Multiple input multiple output
 PLCP
Physical layer convergence procedure
 RC
Random contention
 RRTS
Relay ready to send
 RTH
Request to help
 RTS
Request to send
 SIFS
Short interframe space
 SNR
Signaltonoise ratio
 WLAN
Wireless local area network
1 Introduction
1.1 Related work
Most studies on cooperative MAC protocols follow the IEEE 802.11 WLAN design principle [11] and thus, only IEEE 802.11based cooperative MAC protocols with link adaptation [12] are surveyed in this paper. There are three typical studies on reactive helper node selection schemes. In [13], three busy signals are used to find an optimal helper node, which is not energy efficient. A threestep helper node selection scheme was adopted in two previous studies [14, 15] consisting of GI (group indication), MI (member indication), and K minislot contention. The optimal cooperation region and system parameters were determined in [14] while an additional energy metric was used to select the best helper node in order to increase network lifetime in [15]. However, all three of these schemes use data transmission ratesrelated metrics for their helper node selection procedures, which has its drawbacks, as will be discussed in Section 1.2
There have also been several recent studies on cooperative MAC protocol design [16, 17, 18, 19]. In [16], three transmisson modes are suggested where relay nodes were chosen based on proactive mechanisms: direct transmission, cooperative relay transmission, and twohop relay transmission. Cooperative relay transmission mode is used for increasing system throughput while the twohop relay transmission mode helps extend the service range. However, there is no suggested algorithm for choosing an appropriate mode. In [17], a new cooperative MAC protocol based on a threeway handshake with request to send (RTS), clear to send (CTS), and relay ready to send (RRTS) is proposed. Its reactive relay node selection scheme is based on the fact that the fastest relay candidate will reply to an RRTS frame earlier. However, [17] does not consider the possibility of relay node competition and approaches to deal with collisions. In [18], a helper node initiated cooperative MAC protocol is proposed. Helper nodes are decided in advance with the help of a relay table, and they initiate cooperative communication by sending a helper clear to send (HCTS) frame when the transmission rate between sender and receiver nodes falls below a threshold. In [19], three data transmission modes similar to those suggested in [16] are discussed. In contrast to [16], an algorithm to find a suitable transmission mode is suggested in [19]. It is described that the optimal helper node is chosen via the shortest path algorithm. However, there is no detailed discussion on how to select the optimal helper node. Therefore, issues such as helper node competition and whether the shortest path can be decided without additional control frame exchanges remain unanswered. In this paper, we aim to address these issues via the design and analysis of a new cooperative MAC protocol.
1.2 Contributions

The use of a new reactive helper node selection scheme with received SNR as the selection metric;

Clear design of the packet formats for the required control frames for eBTCOMAC protocol in order to support the helper node selection scheme;

Presentation and validation (via computer simulation) of a comprehensive mathematical analysis of the throughput and delay associated with eBTCOMAC;

The provision of increased system throughput performance with the eBTCOMAC protocol that is 58% higher than IEEE 802.11 WLAN [11] and 6% higher than prior work [14];

Easy extension of the entire approach to current standards, although IEEE 802.11b WLAN is the standard considered in this work.
This paper consists of five sections. A detailed explanation of the eBTCOMAC protocol is presented in Section 2; the system model and performance analysis are discussed in Section 3. The numerical results from the analysis and simulation are described in Section 4, and Section 5 presents the conclusions.
2 eBTCOMAC protocol
Here, L_{ d } is the DATA length in bits; N_{HC(EC)} is the number of HC (EC) minislots; N_{ R C } is the number of RC slots; T_{ACK,RTH,CTH} are the transmission times of control frames ACK, RTH, and cleartohelp (CTH), respectively, and R_{SH(HR)} corresponds to the DATA frame transmission rates between a sender and a helper (a helper and a receiver) node; SIFS is a MAC parameter representing short interframe space.
2.1 Helper Node Selection
3 Performance evaluation
Definition of system parameters
r  The maximum value of the backoff stage 
m  The maximum value of the contention window 
size  
N_{ s }(N_{ h })  The number of sender (helper) nodes 
τ  CRTS frame transmission probability on a 
wireless channel  
p_{ m }(p_{ d })  Control (DATA) frame transmission error 
probability due to a bad wireless channel  
p _{ c }  CRTS frame transmission failure probability due 
to collision  
p _{ sr }  Helper node selection success probability 
p _{ fr }  Helper node selection failure probability 
R _{ i }  Data transmission rate in Mbps 
for i=1,2,5.5,11  
r _{ i }  Maximum distance (m) for each R_{ i } 
p _{ i }  Probability for transmitting DATA at R_{ i } 
p _{ h }  Cooperation probability that at least one 
candidate helper node is in cooperation  
p _{ r }  Probability that a receiver node is located within 
its sender node’s transmission range 
We begin the analysis of the proposed protocol with the derivation of the cooperation probability. Let us consider an example in Fig. 1 where the sender and receiver nodes are far apart and thus can communicate with each other only at a rate of 1 Mbps. In this case, a helper node, located in the shaded area, can help increase the system throughput for communication between the sender and the receiver nodes.
Lemma 1
where, r_{ i },p_{ i }, and p_{ r } are defined in Table 1, and S_{1}(·) represents the size of overlapping area in Fig. 1.
Proof
Minimum participation criteria for cooperative communication
Direct transmission  Minimum criteria for R_{ S H },R_{ H R } 

1 Mbps  One over 2 and the other over 5.5 Mbps 
2 Mbps  All over 5.5 Mbps 
5.5 Mbps  All over 11 Mbps 
Transmission rates and ranges
Data rate(R_{ i })  11  5.5  2  1 

Distance(r_{ i })  ≤ 48.2  ≤ 67.1  ≤ 74.7  ≤ 100 
Probability(p_{ i })  0.23  0.22  0.11  0.44 
System parameters
Parameter  Value  Parameter  Value 

CRTS length  176 b  SIFS  10 μs 
CCTS length  112 b  DIFS  50 μs 
RTH length  176 b  CWmin  32 slots 
DATA length  1024 B  CWmax  1024 slots 
MAC header  272 b  PLCP header  192 bits 
CTH size (L/S)  136/72 b  Basic rate  1 Mbps 
Slot size (σ)  20 μs  p_{ m }(p_{ d })  Variable 
N_{ H C },N_{ E C },N_{ R C }  3  m  5 
V _{ m a x }  30 m/s  T _{ p a u s e }  5 s 
Sim. time  1500 s  r  6 
As described in Section 2, the helper node selection scheme consists of three steps: HC, EC, and RC competitions. The probability of successful helper node selection in each step is provided in Lemma 2.
Lemma 2
Proof
Finally, the probability that the optimal helper node is selected successfully is the weighted sum of the successful selection of helper nodes at each step, which is provided in Eq. (3). □

b(t): backoff stage of the sender node, b(t)=0,1,⋯,r

c(t): value of the backoff counter, c(t)=0,1,⋯,W_{b(t)}−1

o(t): frame transmission phase, o(t)=0,1,⋯,7.
Here, the variable o(t) represents the sending phase for each frame, which is shown in Fig. 7: 0 represents the sending phase of a CRTS frame; 1 refers to a CCTS frame, 2,3,4, and 5 are for RTH, CTH, DATA1, and DATA2, repectively; 6 represents an ACK frame; and 7 is for DATA frame at direct transmission. We attempt to derive steadystate probabilities for this system state vector. Our mathematical analysis approach is carried out based on previous research in [21, 22, 23]. It is assumed that every sender node always has data frames to transmit in its buffer, which is known as a saturated traffic model.
Here, A(i)≡(1−p_{ r }+p_{ m }p_{ r })α_{i01}+p_{ m }α_{i03}+p_{ d }(α_{i04}+α_{i05}+α_{i07}) and \(p_{r} = \pi r_{1}^{2} / A_{c}\) where A_{ c } refers to the size of the communication area.
Two performance measures were considered for the performance analysis. One is the system throughput in bps, and the other performance measure is the average channel access delay in seconds. In order to derive the system throughput, two types of average delays should be calculated in advance. The first one is D_{ S }, the average time delay from the transmission of the CCTS frame to the successful reception of the ACK frame, and the second one is D_{ E }, the average time delay from the transmission of the CCTS frame to transmission failure with the CCTS, RTH, CTS, DATA, or ACK frame.
Lemma 3
where, \(D_{S}^{k}\) is the average time delay spent at phase k for successful frame transmission. \(D_{E}^{2}\) is the average time delay spent at phase 2 because of frame transmission error; it will be derived in the Lemma 4.
Proof
Then, the average time delays from the CCTS transmission to successful reception of the ACK frame for direct transmission and twohop transmission are as given in Eqs. (17) and (18). □
Lemma 4
Here, \(D_{E}^{k},~k=1,2, \cdots, 7\) are the average time delays spent at phase k because of frame transmission failure.
Proof
For example, the phase k=2 represents the transmission of RTH frames and it means helper node selection competition. Thus, \(D_{E}^{2}\) refers to the required time delay for complete failure of the helper node selection procedure. This delay consists of a busy tone signal, HC and EC contention periods, RC slots, and two short CTH frame transmissions in the HC and EC contentions, respectively. Then, the average time delay from the CCTS frame to complete transmission failure can be expressed as a weighted sum of consumed time delays until complete transmission failure in each phase. If complete failure occurs at the phase k=4, then, frame transmissions at phases 1, 2, and 3 should be successful. Thus, the time delay from the CCTS frame to DATA frame transmission failure is \(D_{S}^{1} + D_{S}^{2} + D_{S}^{3} + D_{E}^{4}\). Therefore, the average time delay from the CCTS frame to any frame transmission failure corresponds to Eq. (21). □
The following two theorems provide the expression for evaluating two performance measures of interest: system throughput and channel access delay.
Theorem 1
where, L_{ h } is the sum of the MAC header and PLCP header, E[S] is the average slot time, P_{ tr } is the probability that there is at least one CRTS frame transmission by N_{ s } mobile users in the considered time duration, and P_{ s } is the probability that the transmitted CRTS frame is successfully received by the helper node without collision and transmission error. P_{a1} and P_{a2} are the probabilities that no transmission errors occur during the period from the CCTS frame to ACK frame transmission for direct and twohop transmissions, respectively.
Proof
The probability that the given DATA frame is transmitted successfully is the product of three probabilities derived in Eqs. (23)–(26): P_{ t r }, P_{ s }, and P_{a1}+P_{a2}. Because the system throughput can be expressed as the ratio of the total length of the DATA frame successfully transmitted in bits to the average time slot, it corresponds to Eq. (22). □
Theorem 2
Here, W represents the minimum contention window size, CW_{ m i n } and T_{ A }=T_{ C R T S }+SIFS+{D_{S1}p_{ f r }+D_{S2}(1−p_{ f r })}, and P_{ S }(i) represents the probability that one sender node receives the ACK frame successfully at the ith backoff stage.
Proof
It is assumed that when the current system state of the sender node is {b(t)=i,c(t)=0,o(t)=k} as in Fig. 6, the next system state is determined based on uniform distribution. That is, the next possible system state will be (0,j,0) or (i+1,j,0) depending on whether the current frame transmission is successful or not. Here, the value j is uniformly distributed between 0 and W_{0}−1 or W_{i+1}−1. Because the sender node stays in any state until the upcoming idle slot, the average time to stay in any state in Fig. 6 equals the average slot size E[ S]. Thus, the channel access delay corresponds to the weighted sum of the products of E[ S], and the number of states where the sender node stayed from the beginning of channel sensing to any state of (i,0,6),0≤i≤r when the ACK transmission is successful. Therefore, the expression of the channel access delay is given as Eq. (28). □
4 Network model and numerical results
4.1 Network model and environment
where d_{0} is the reference distance and n is the path loss exponent (in this paper, we use n = 3).
The simulation code was programmed with a gnu C++ compiler using the SMPL library [25]. Computer simulation was conducted 10 times with a different seed each time, and we used the averaged data as simulation results. For simplicity, it was also assumed that transmission error probabilities for the control and DATA frames caused by a bad wireless channel were the same (p_{ m }=p_{ d }). Mathematical analysis and computer simulations were conducted and compared in order to prove the correctness of the mathematical equations. The system parameters used in the performance evaluation are described in Table 4.
4.2 Numerical results
Figure 10 shows a comparison of delay performances by analysis and simulation when there are forty helper nodes in the communication area. This figure shows that the eBTCOMAC protocol has an obvious advantage over direct communication. The analytical and simulation results are consistent; although there is a discrepancy between the simulation and analysis of about 22% when N_{ s } = 100, the difference is negligible.
Figure 11 shows a comparison of throughput performances as a function of the number of helper nodes when N_{ s } = 10. According to the approximation that we used in deriving the probability p_{ s r } in Eq. (3), analytical results are sensitive to the number of helper nodes. According to Eqs. (4)–(6), when M_{1} = 1, M_{2} = 1, and M_{3} = 1, helper node competition becomes completely successful with p_{ s r } = 1. In addition, when M_{1},M_{2}, and M_{3} is less than one, the probability that the best helper node is successfully decided becomes zero in Eqs. (4)–(6). Significant jumps in this figure occur when N_{ h } is about 15, 35, and 95. These values of N_{ h } corresponds to cases when M_{1},M_{2}, and M_{3} are slightly greater than one, respectively, and this is why there are significant jumps in this figure.
Figure 12 shows a comparison of delay performances as a function of the number of helper nodes when N_{ s } = 10. The discrepancy between the simulation and analysis results may be due to our approximation when deriving Eqs. (2) and (3). However, Fig. 12 shows that the simulation results show a slight increase, although it is a little, in the section where the analysis results show a consistent increase.
5 Conclusions
In this paper, we presented for the first time, a comprehensive theoretical performance analysis of an enhanced BTCOMAC protocol and validated the analytical results via numerical simulations. The new helper node selection scheme in the eBTCOMAC protocol is based on received SNR values at each candidate node. This results in a dynamic characteristic that presents challenges in analytical modeling. In this paper, two probabilities, the cooperation probability and the probability that a helper node is successfully selected, were derived based on a geometric analysis. These probabilities, along with steadystate probabilities of backofrelated parameters (derived based on a Markov analysis), are used to derive theoretical expressions for the system throughput and channel access delay of the eBTCOMAC protocol. Although the analytical results are not exact and are based on approximations that provide theoretical tractability, they are for the most part consistent with the numerical simulations. Future work will involve the design of an energyaware eBTCOMAC protocol that can provide throughput gains while improving network lifetime.
6 \thelikesection Appendix 1: calculation of cooperative area
Notes
Acknowledgements
The authors would like to thank the reviewers for their thorough reviews and helpful suggestions.
Funding
This research work was funded by a grant from Inje University for the research in 2016 (20160432).
Availability of data and materials
Not applicable.
Authors’ contributions
JJ proposed the system model, derived the mathematical equations, and performed the simulation and manuscript writing. BN contributed in manuscript revision and correction. Both authors read and approved the final manuscript.
Author’s information
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Competing interests
The authors declare that they have no competing interests.
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