Referencebased fair MAC algorithm in WiFi WLANs with capture effect
 Jiwoong Jeong^{1},
 Sunwoong Choi^{2}Email author and
 Joon Yoo^{3}
https://doi.org/10.1186/16871499201350
© Jeong et al.; licensee Springer. 2013
Received: 30 May 2012
Accepted: 29 January 2013
Published: 26 February 2013
Abstract
The widespread deployment of infrastructure WLANs has made WiFi an integral part of today’s Internet access technology. Due to the inherent characteristics of the wireless medium in WLAN systems, the capture effect significantly affects the system performance; a receiver can successfully decode a collided frame given that its signaltointerference and noise ratio is sufficiently high enough, but results in an unfair channel access share among the wireless nodes. In this article, we propose fair capture effect aware MAC (FCMAC) algorithm, which achieves channel access fairness using a feedback control mechanism. We determine the average waiting time as a common control reference, which provides fair channel access even when the capture effect is present. In result, the algorithm enables each node to converge to a fair channel access share. Among multiple points that yields fair channel access, we determine the optimal target reference that maximizes the aggregate throughput. Through both dynamic system modeling and extensive simulation studies, we show that the FCMAC algorithm is stable and achieves fairness while improving the aggregate throughput.
Keywords
1. Introduction
The last decade has witnessed a rapid technology development in wireless networks. The IEEE 802.11 [1] WLAN standard has widely been deployed as a means for lowcost and easy wireless network access. IEEE 802.11 Medium Access Control (MAC) commonly uses the mandatory distributed coordination function (DCF) for channel access, due to its simplicity and efficiency in the operation of data transmission. In the mean time, the capture effect frequently takes place in such WLAN environment [2, 3]. The capture effect takes place when two or more nodes transmit simultaneously, i.e., a collision occurs at the common receiver. Even though the data frames may collide at the receiver, the data frame with the strongest received signal strength can still be successfully decoded, given that the signaltointerference and noise ratio (SINR) is sufficiently high enough. This capture effect significantly increases the system throughput since it mitigates the performance reduction due to collisions [4]. Moreover, in wireless multihop networks, the capture effect also improves the spatial reuse, thus increases the overall network performance [5, 6].
The channel access fairness can offer either throughput or temporal fairness by using diverse methods. If the conventional DCF is deployed, then the fair channel access gives throughput fairness. In the mean time, if methods such as transmission opportunity (TXOP) [1] are employed, where nodes may transmit multiple data frames in a predefined time duration, then temporal fairness can be achieved. In this article, we use the DCF so that throughput fairness can be provided. Several approaches have been proposed to offer channel access fairness in WLANs [8–10]. In these approaches, each node employs a common target CW size for fair channel access. However, despite the common CW settings, the strong signal nodes will still gain more channel access with capture effect in place. Therefore, we need a new common control reference that provides channel access fairness while not being affected by the capture effect.
In this article, we develop a referencebased fair capture effect aware MAC algorithm (FCMAC). We first determine the average waiting time as the common control reference, by which each node adjusts its own CW size. Second, we design the FCMAC algorithm based on feedback control, and also model a dynamic system to validate its stability. We determine the target reference value so that the aggregate throughput is improved while gaining channel access fairness. Finally, we give extensive ns2 simulations to show that FCMAC achieves channel access fairness and improves the aggregate throughput when the capture effect is present.
The remainder of the article is organized as follows. Section 2 discusses the related work. In Section 3, we give the motivation and Section 4 shows the design of our proposed algorithm, FCMAC. Section 5 presents the target reference to improve the system throughput. Section 6 shows a method to estimate the number of nodes. We provide simulation studies in Section 7, and finally, we draw our conclusions in Section 8.
2. Related work
Many MACrelated studies have been studied in 802.11 WLANs [6, 8–18]. Bianchi [8] proposes a simple and accurate Markov chain model for the DCF under the saturation condition after the BEB behavior of a node is observed. The optimal CW is presented using the analytic model when the number of nodes is given. Cali et al. [9] propose a MAC protocol based on ppersistent CSMA after observing the system behavior. They resolve the transmission probability p to maximize the system throughput. Heusse et al. [10] have presented a MAC algorithm called the Idle sense, which adjusts its CW using the additive increase multiplicative decrease (AIMD) method so as to make the length of the measured idle period become a target CW, in result, maximizes the system throughput. Nevertheless, they do not consider the misbehavior due to capture effect or channel error.
The results given in [3] demonstrate that the capture effect phenomenon occurs frequently in the practical 802.11based WLANs. Furthermore, the throughput for each sender becomes unfair depending on the spatial difference from a sender to a receiver on the assumption that all the senders use the same sending power level [2]. Boer et al. [19] propose a scheme that a data frame can be decoded by delivering the indication which notifies the occurrence of capture effect or the arrival of a new signal in PHY to the PHY layer management entity (PLME). In [20], the SINR threshold values are provided according to different transmission rates for 802.11a/b. The SINR value plays an important criterion in determining whether the capture effect occurs or not. Ganu et al. [21] have presented that AIFS+TxOP control may improve the throughput fairness under capture effect, but they do not propose any algorithms or protocols that can actually realize it. The main reason is that it requires a central coordinator to find the weaksignal receivers that are suffering from throughput unfairness. Furthermore, it also requires a control system to adjust these parameters. Meanwhile, this study proposes a feedback system that can be used as an algorithm that controls the parameters to converge to a fair state, in a distributed manner. Bejeranoa et al. [22] consider the capture effect unfairness. They view this problem in a multicell environment, where the interference from neighboring cells aggravates this phenomenon. They propose a frequency planning algorithm to solve this problem.
In summary, although there have been some considerations on the unfairness due to capture effect, the previous work either do not propose a protocol to solve this or focus on a different system. To the best of the authors’ knowledge, this is the first study to propose a feedbackbased control system that focuses on this problem.
3. Motivation
In this article, we consider an infrastructurebased 802.11 WLANs with a single AP and multiple wireless nodes which are associated with the AP. Since the focus of this article is on the unfairness stemming from the capture effect, only the upstream (from node to AP) traffic is considered. Again, the main objective of this article is to solve the unfairness resulting from the capture effect.
4. Referencebased fair MAC
This section describes a referencebased fair MAC algorithm with the physically unfair environment due to the capture effect. We first determine a control reference that is not affected by the capture effect. Then, we present the FCMAC algorithm via modeling the system dynamics. Finally, we analyze the system stability of the algorithm, and provide the range of the parameters that maintains the system to be stable.
4.1. Control reference
In computing the waiting time, we discriminate between the successful capture and failed reception due to collisions. Therefore, the average waiting time of each node is in inverse proportion to its own channel access opportunity [2, 23]. In other words, if the waiting time of node B is made to be equal to that of node A, both nodes would gain the same channel access opportunities. In result, the average waiting time is employed as the control reference for FCMAC.
4.2. Feedback control system and its modeling
The FCMAC algorithm can be presented by modeling the system dynamics. We assume that nodes are classified into M capture classes. Let N and N_{ i } denote the total number of nodes and the number of nodes in the class i (1 ≤ i ≤ M), respectively. Then, it is clear that N = N_{1}+· · · +N_{ M }.
Nodes in the same class have the same capture priority. Suppose a classi node and a classj node simultaneously transmit data frame. If i < j, then the data frame of classi node is captured (i.e., successfully transmitted) but that of classj node is dropped due to collision. We assume that data frame with higher capture priority can be decoded regardless of any data frames with lower priority. If i = j, then both data frames are dropped.
A summary of key notations
State variables  

τ_{ i }(t)  Transmission probability of the node in the classi at the time t 
p_{ i }^{ s }(t)  Success probability of the transmission of a node in the classi at the time t 
p_{ i }(t)  Probability that a node in the classi transmits simultaneously with other node at the time t 
p_{ i }^{capture}(t)  Probability that the transmission of the node in classi is successfully received when its transmissions simultaneously occurs with other node 
T_{ i }(t)  Waiting time of the node in classi, i.e., number of virtual slots between two consecutive successful transmissions 
W_{ i }(t)  CW size of the node in class i at the time t 
System parameters  
M  Number of classes in the system 
N _{ i }  Number of nodes in the class i 
N  Total number of nodes, i.e., N = N_{1} + N_{2} + · · · + N_{ M } 
Control parameters  
α and β  Control parameters 
T _{ref}  Desired waiting time, i.e., target waiting time 
5. Target reference to improve the system throughput
In this section, we present the target reference T_{ref} to give satisfactory results for a wide range of the network topologies. To resolve this issue, we establish the upper and lower bounds of maximizing the system throughput. Then, through simulation studies, we determine a value within the bound that can enhance the throughput to be commonly exploited irrespective of the network topology.
5.1. Two extreme cases
We consider two extreme topologies: the nocapture topology and the alwayscapture topology. When M = 1, the capture effect does not occur, i.e., a collision always results in a frame reception error. On the other hand, when N_{ i } = 1 for all 1 ≤ i ≤ M (>1), the capture effect always occurs whenever multiple nodes transmit simultaneously.
5.1.1. The no capture case
5.1.2.The always capture case
5.1.3. Bounds of reference
Note that the optimal K which maximizes the system throughput varies according to the topologies. In the next section, we will explain the effect of K and try to find a common K for an arbitrary topology.
5.2. Finding the target waiting time
where P^{simul} and P^{cap} denote the probability of one or more simultaneous transmissions occurring in a time slot and the probability that successful transmission occurs due to the capture effect, respectively.
When the simultaneous transmissions always yield in capture effect, ψ becomes 0. Conversely, ψ becomes 1 when the simultaneous transmissions always result in collision.
6. Estimating number of nodes
In this section, we present the method to compute the number of active nodes. To achieve improved aggregate throughput, the FCMAC acquires the number of active nodes or the traffic amount in a distributed manner by employing the method used in [16].
where ${T}_{\text{ref}}^{\text{current}}$ is the reference in use which is obtained from the preceding estimation.
We also employ the invention in [19] enabling the marking technique to be utilized. In [19], when the capture effect occurs, the information is transferred between the layer management entities. Namely, if the medium interface senses the capture effect, it sends PHY_CAPTURE.ind message to PLME. The MAC layer management entity requests the information to PLME, and to notify the capture effect occurrence to the MAC sublayer. Finally, the MAC sublayer decides whether it should send the marked ACK or a normal ACK according to the notification.
7. Simulations
In this section, we validate the channel access fairness and aggregate throughput of FCMAC algorithm using the ns2 simulator. The BSS data rate for data frames and basic rate for control frame (e.g., ACK) are set to 11 and 2 Mbps, respectively. The physical frame headers, e.g., preamble and PLCP header, are transmitted at 1 Mbps. We generated CBR over UDP traffic and the MSDU is set to 1500 bytes. The other system parameters are set by using the default values of the 802.11 specifications [1].
We compare the performance of FCMAC with the conventional DCF, Optimal CW, and Idle sense. In Optimal CW, the nodes set their CW size to an optimal value according to [8], so that the system throughput is maximized under the saturated traffic load. Note that, since this scheme does not consider the capture effect, it results in channel access unfairness. Furthermore, it overestimates the optimal CW, resulting in less than maximum throughput. In Idle sense[10], each node observes its idle time, i.e., E[idle], and adjusts its CW size using an AIMD control algorithm. The AIMD algorithm is controlled based on a theoretically derived value, n^{target}, which is calculated by E[idle] when N → ∞. Thus, Idle sense does not employ the runtime adaptive estimation reflecting the number of active nodes. Furthermore, since all the nodes within a system observe the same E[idle], and they regulate their CW size based on the E[idle], thus do not achieve fairness when the capture effect occurs. The Idle sense uses ε = 0.001 and 1/α = 1.2 for the control parameters and selects 5.68 for the n^{target}. The FCMAC uses α = 0.5 and β = 1 for control parameters and selects 0.86 for K. The CW control interval and the target reference adjustment interval are set to 50 and 100 ms, respectively.

Aggregate throughput: total throughput obtained by all the nodes in the system

Min/Max throughput ratio: the ratio of lowest node throughput over highest node throughput in a system$\mathrm{Min}/\mathrm{Max}\phantom{\rule{0.25em}{0ex}}\mathrm{ratio}=\frac{min\left\{{r}_{i}\right\}}{max\left\{{r}_{i}\right\}}.$

Normalized standard deviation (Std.): the dispersion of pernode throughputs from the average node throughput$\text{Normalized}\phantom{\rule{0.25em}{0ex}}\text{Std}.=\frac{\sqrt{{\displaystyle \sum _{i=1}^{n}{\left({r}_{i}\stackrel{\xc2\xaf}{r}\right)}^{2}}/n}}{\stackrel{\xc2\xaf}{r}}.$
7.1. Offered load
7.2. Number of nodes
Next, we compare the performance of FCMAC with other schemes when the number of nodes is varied (from 2 to 32). An equal number of nodes are assigned to each strong and weak signal class, and offered load is set to 10 Mbps. Figure 9a shows the aggregate throughput of each scheme. The FCMAC shows similar throughput compared to Optimal CW while outperforming the other two algorithms, by up to 13%. Meanwhile, the fairness of FCMAC shows major performance enhancement. Figure 9b plots the Min/Max throughput ratio as a function of the number of nodes. The Min/Max ratio of FCMAC always maintains a level above 0.9 while those of Optimal CW, Idle sense, and DCF decrease significantly as the number of nodes increases. Figure 9c illustrates the normalized standard deviation of pernode throughput. The normalized standard deviation of FCMAC is smaller compared to those of the other three algorithms. From Figures 9b,c, we see that the FCMAC achieves better channel access fairness regardless of the number of nodes.
7.3. Ratio between weak and strong signal nodes
7.4. Errorprone environment
As depicted in Figure 11a,d, with the increasing number of nodes, the fairness of DCF decreases dramatically and those of Optimal CW and Idle sense decline moderately. In Figure 11d, Min/Max ratio of FCMAC is approximately 0.827 even when the channel error is severe and the number of nodes is 32. As shown in Figure 11b,e, the FCMAC is better than the other algorithms in terms of fairness. Figure 11c,f plot the aggregate throughputs of DCF, Idle sense, Optimal CW, and FCMAC for different BER values. As shown in Figure 11c,f, the FCMAC also achieves higher throughput than those of the DCF and Idle sense. In summary, the FCMAC is still efficient and robust even in the errorprone environment.
7.5. Random topology
Since FCMAC is designed based on the assumption that all nodes are categorized into separate capture classes, we need to show that FCMAC performs well in various randomized environments. Therefore, we conduct simulations in random topologies. We set up eight topologies where all nodes are randomly located within a 20 × 20 m^{2} space and AP is at the center of the space.
8. Conclusions
The 802.11 DCF uses random channel access, thus resulting in frequent simultaneous transmissions, i.e., collisions. Even when a collision takes place, the receiver may capture the data frame of a significantly stronger received signal, so that it is decoded successfully. There is a strict tradeoff when this capture effect occurs; the system throughput increases since the errors due to collisions may be salvaged by the capture effect, but the nodes may experience unfair channel access.
In this article, we proposed a MAC algorithm based on a feedback control approach, called FCMAC, where each node uses the waiting time as a target reference to gain channel access fairness. By computing the optimal target reference, the nodes improve the aggregate throughput as well as achieve fairness even when capture effect is present. Then, FCMAC is compared with other MAC algorithms via ns2 simulations. The simulation results show that FCMAC consistently yields the best fairness irrespective of the number of nodes, errorprone channels or topologies, while improving the aggregate throughput. Last but not least, we envision that FCMAC can relatively easily be deployed into the common WiFi devices, and leave the real implementation of FCMAC as a part of our future research.
Endnote
^{a}The interval is within [$\stackrel{\xc2\xaf}{\psi}1.96\cdot \sigma /\sqrt{100},\phantom{\rule{1em}{0ex}}\stackrel{\xc2\xaf}{\psi}+1.96\cdot \sigma /\sqrt{100}$].
Appendix
where τ_{ i }^{*} is equilibrium point and 1 ≤ i ≤ M.
Corollary
Equation (24) means that the system is stable if the maximum eigenvalue among M eigenvalues is negative.
Declarations
Acknowledgments
This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011–0023856) and by the research program of Kookmin University in Korea.
Authors’ Affiliations
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