Mitigating MAC Layer Performance Anomaly of Wi-Fi Networks through Adaptable Channelization

802.11 wireless local area networks (WLANs) can support multiple data rates at physical layer by using adaptive modulation and coding (AMC) scheme. However this differential data rate capability introduces a serious performance anomaly in WLANs. In a network comprising of several nodes with varying transmission rates, nodes with lower data rate (slow nodes) degrade the throughput of nodes with higher transmission rates (fast nodes). The primary source of this anomaly is the channel access mechanism of WLANs which ensures long term equal channel access probability to all nodes irrespective of their transmission rates. In this work, we investigate the use of adaptable width channelization to minimize the effect of this absurdity in perfor mance. It has been observed that surplus channel-width due to lower transmission rate of slow nodes can be assigned to fast nodes connected to other access points (APs) which can substantially increase the overall throughput of the whole network. We propose a medium access control (MAC) layer independent anomaly prevention (MIAP) algorithm that assigns channel-width to nodes connected with di_erent APs based on their transmission rate. We have modeled the effect of adaptable channelization and provide lower and upper bounds for throughput in various network scenarios. Our empirical results indicate a possible increase in network throughput by more than 20% on employing the proposed MIAP algorithm.


Introduction
The exponential increase in wireless enabled devices require maximum capitalization of available resources in WLANs.This imminent requirement has triggered the reevaluation of wireless protocols.Today's WLANs acclimatize several transmission parameters to achieve optimal network performance.However, some of the parameters like channel width and MAC layer functioning still remain static resulting in sub-optimal network performance.Authors in [8] provide a detailed analysis of a performance anomaly at MAC layer of WLANs.If a wireless cell contains nodes with varying data rates, the throughput performance of fast nodes decreases substantially due to longer channel capturing of slow nodes.In [8] authors analytically modeled this anomalous behavior which is applicable to any multi-rate 802.11 network that uses contention based channel access mechanism [1] at MAC layer.If Xs and Xf are the throughput of slow and fast nodes respectively, these can be measured as given in equation 1where Sd is frame size, N is the number of wireless nodes and Tf and Ts is the transmission time of fast and slow nodes respectively.Pc(N) is collision probability and tjam is the time elapsed in collision.
Equation 1 is applicable only to single cell networks.However, rapid improvements in wireless technologies have shifted the paradigm of few users, single AP networks to several APs and numerous users per AP environments.We found that substantial increase in network wide performance is achievable if we divert network resources from a cell with limited need to another resource hungry cell.Adaptable width channelization [9] has been used to achieve this intelligent diversion of resources.In this work, we propose MIAP algorithm, that uses adaptable channelization to minimize the effect of MAC layer performance anomaly.The elementary concept of MIAP is to assign channels with high level of granularity thus maximizing the spectrum utilization.A node with low SNR values and subsequent low transmission rate transmit at narrow channel width and vice versa.In addition to this, use of adaptable channelization is independent of MAC layer and do not require any modification in channel access mechanism.It ensures that long term channel access probability of all the nodes remains equal and slow nodes do not suffer starvation.The channel width is adjusted by adding different number of sub-carriers.The use of narrower channels at nodes with lower SNR values adds several benefits to communication.Since narrower channels have higher spectral efficiency, it increases SNR of nodes.The performance of MIAP algorithm is measured on essential network parameters like network throughput, fairness index and frame size.The contributions of this research work can be outlined as; 1) Implementation of MAC layer independent channel width adaptation algorithm for minimizing the effect of MAC layer performance anomaly.2) Analysis of proposed algorithm by measuring its effect on essential network parameters like throughput, fairness of channel access mechanism and frame size.3) Implementation of proposed algorithm on real test-bed of USRP devices for accurate performance measurements.The rest of this paper is organized as follows, Section 2 provides an overview of research work and proposed method for elimination of MAC layer performance anomaly.Section 3 presents the problem formulation and analytically models the solution.We have explained our proposed algorithm in Section 4. Section 5 explains the test-bed environment and experimentation methodology.Achieved results and discussion on these results is presented in section 6.Finally, we have concluded this work in Section 7.

Related Work
A substantive research on mitigating the effect of MAC layer performance anomaly in multi-rate WLANs has been presented in literature.The work proposed in [2] [13] [15][11] are of premier importance to this research study.In [13] authors have proposed an algorithm for performance anomaly reduction using open flow access points.The pro-posed model jointly reduces the effect of performance anomaly and number of hand offs, thus maximizing throughput by 26.7%.The research work given in [15] proposes a modification to control packets by embedding the data rate of two hops neighbors.In response to this control packet, the nodes adjust the initial value of contention window (CWmin) according to the data rate of neighboring nodes.In [11] authors claim that the performance anomaly model presented in [8] is only valid for networks having static channel characteristics.The nodes with better Signal-to-Noise (SNR) have higher channel access rate as compared to nodes having lower SNR.This assertion ensures that the effect of MAC layer performance anomaly can be substantially reduced by using time-varying and time-correlated channels with rayleigh fading effects.The work presented in [2] mitigates the effect of MAC anomaly by controlling the value of back-o_ contention window based on signal strength of a node.Authors have concluded that, lower values of contention window for nodes having higher SNR considerably reduces the effect of MAC anomaly.In [12] an anomaly mitigation scheme for TCP friendly rate control (TFRC) protocol is presented.We named this approach as channel occupancy time based anomaly mitigation (COTAM).In this approach nodes estimate their share of leftover channel occupancy time and only make their communication in that slot.Majority of the techniques for mitigation of MAC layer anomaly restricts the channel access of nodes having lower transmission rate.This methodology adds further disadvantage to already poor performance of these nodes.This below par performance of slower nodes, in turns negatively affects the overall performance of complete network.The use of adaptable channelization has gained significant importance in recent studies [9] [16].The concept of adaptable channelization involves the granular use of available frequency spectrum.Research in [9][5] [16] shows that a considerable increase in network capacity can be achieved if we use channels of adaptable widths.Since the advent of flexible channelization concept with the work presented on [5], the main focus of researchers remains on physical layer parameters, like transmission rate, interference, power consumption, delay spread and likewise.To best of our knowledge, to-date, no study for effect of flexible channelization on MAC layer is presented in literature.

Problem Formulation
802.11 networks use two spectrum blocks for their communication.These blocks consist of 2.4 GHz and 5 GHz frequency ranges.In this work, we are emphasizing only 2.4 GHz frequency spectrum used by 802.11 b/g/n networks for proof of concept purpose.The total available spectrum block in 802.11 b/g/n networks is divided into 14 channels of equal width of 22 MHz each [1].To minimize the effect of co-channels interference (CCI), a guard band of 5 MHz is incorporated between any two consecutive channels.Each 22 MHz Wi-Fi channel is constituted of 52 sub-carriers.Out of these 4 sub-carriers are used for control signals while rest of 48 sub-carriers are used for data symbols [1].The physical layer of Wi-Fi networks spread the data symbols on these 48 sub-carriers through orthogonal frequency division multiplexing (OFDM) or direct sequence spread spectrum (DSSS).The DSSS is only used to support legacy Wi-Fi devices like 802.11b.where nt  Ki denotes the total number of nodes (nt) associated to an access point Ki.Consider the probability of a slow and a fast node connected to an AP Ki is _ and (1p) respectively.Then the joint probability distribution of slower and faster nodes attached to any AP Ki is given by The probability that exactly s number of slow nodes are attached to any AP Ki at any given time ti can be given as, For s = 0; 1; 2;………..ns and ns = 0; 1; 2; ……….ntThe probability that maximum number of slow nodes at-tached to any AP Ki at any given time ti is less than s can be given as, In a similar way the probability that exactly f number of fast nodes are attached to any AP Ki at any given time ti will be, Similarly, the probability for slow and fast nodes operating in whole network at any given time ti can be calculated by using equation 8 and 9 respectively.

Similarity Extraction Throughput and Adaptable Channel
Let us assume that the network model given in section 3.1 uses L transmission channels (L1,L2,....,Lu) for communication with Li representing the ith channel.According to the throughput calculations given in [17], the channel capacity C (or maximum achievable throughput T) of a node operating on static width communication channel of bandwidth B in the presence of noise is T = B log2 (1 + SINR (dB)) and SINR (dB) = 10 log10 (SINR).The achievable throughput of any node Ni (slower or faster) can be written as follows.
Authors in [4] have calculated signal to interference plus noise ratio (SINR) for static width channels.We can extend the same approach to get SINR for varying channel widths as follows, is the ambient noise and ' (Li;Lj) is the partial overlapping degree between channel Li and Lj .This partial overlapping degree is given in [9].The expression Li !Ki shows that channel Li is associated to access point Ki.Equation 11 is true when the network operates in saturation mode, that is, all the APs have data to send or receive and not idle at any time.As this is not always true, it is generalized as shown in equation 12 below, where B(Li) is the probability of channel occupation of any channel Li.It is '1' when the network operates in saturation mode showing that all available channels have been occupied by the APs.by substituting the value of SINR (Ni) in equation 10 from equation 12 , T(Ni) = B log2(1+ Equation 13gives the throughput of a single node of network irrespective of its transmission rate.It is evident that throughput of any node is a function of available bandwidth (B).If a node is transmitting at a slower rate, it means that its bandwidth requirement is inherently less, which can be diverted to faster nodes.T = B NP i=1 log2 (1+

Mitigating the Effect ofMAC Performance Anomaly
The bandwidth (B) of a channel is a sum of individual bandwidths of its sub-carriers.Using adaptable channelization we can increase or decrease the width of channel by varying the number of sub-carriers in that channel accordingly.In this work, we have varied the number of sub-carriers from 12 (5 MHz channel width) to 72 (30 MHz channel width).Let us consider that Nt wireless nodes are distributed randomly across Kt APs.The transmission probability of a slower node is ts and transmission probability of faster node will then be (1-ts).The probability that at any given time, only slow nodes are transmitting in each cell will be (ts)Kt .Similarly, the probability that only faster nodes are transmitting in a cell will be (1-ts) K t .The joint probability distribution that only fast or slower nodes will be transmitting at any time ti will be given as This implies that both slower and faster nodes are transmitting in same or different cells will have the probability as given in equation 16.
Since contention base CSMA/CA protocol ensures equal long term probability of channel access to all nodes irrespective of their transmission rate, equation 14 implies that, the overall efficiency of a network is dependent on number of slower and faster nodes in that network.In this way, we have three possible scenarios.(1) Number of slower nodes is larger than number of faster nodes that result in ts > (1-ts).( 2

) Number of slower nodes is equal to the number of faster nodes that results in ts = (1 -ts). (3) Number of slower nodes is less than number of faster nodes that results in ts < (1 -ts).
If adaptable channelization is implemented and bandwidth assigned to one AP can be diverted to other AP(s) based on difference of transmission rates then, where T(ns) is the throughput of any slower node and (Bl) is the surplus bandwidth that is not required by slower node.Similarly the throughput of faster node will be, from equation 17 and 18, it is evident that use of adaptable channelization ensures that total throughput of the network remains same.The loss in throughput of one cell operating at slower transmission rate is rectified by the gain in throughput of another cell that is operating on higher transmission rate.

THE PROPOSED CHANNEL WIDTH ADAPTATION ALGORITHM
In 802.11 networks the transmission rate of any node is a function of received signal strength (RSS) values.MIAP calculates the RSS and subsequent transmission rate of any node through channel reciprocity [14].Based on these calculations, MIAP estimates the bandwidth requirement of a specific node and assigns channel of that width.At the initialization phase all the APs use standard non-overlapping channels.All APs are connected to a back-end management server through a wired link which controls all the activities like spectrum allocation, transmission rate determination etc. MIAP runs at this sever.The server calculates the optimal channel width and number of sub-carriers for the spectrum allocation to AP dynamically on the basis of transmission rate and RSS values.
If transmission rate changes at an AP, it is communicated to the management server.The AP releases or demands spectrum resource according to its current bandwidth status.If an AP needs more bandwidth, it notifies the server and the server check the status of available sub-carriers still not assigned to any AP.MIAP asks the server to check the demand considering the threshold values of RSS and transmission rate and decides if the increment in channel width is possible.Server then communicates the values of sub-carriers to the corresponding AP.After increasing the channel width AP starts spreading it signal by adding more frequencies to already in use sub-carriers.On the other hand, if an AP has less bandwidth requirement it releases spectrum resource which is added by the management server in its available pool of sub-carrier frequencies for its on demand dissemination to other APs on the network.If throughput requirement of an AP decreases at any given time it sends its new status to the management server.The management server checks the in-use sub-carriers and ask the AP to reduce its channel width by spreading its signal on lesser number of sub-carrier frequencies.Algorithm 1 explains the working of MIAP.

EXPERIMENTAL SETUP AND IMPLEMENTATION
For empirical evaluation of MIAP, we have deployed an indoor network of three USRP kits connected to laptops running GNU radio software on Linux operating system (OS).Figure \ref{spectrum} shows the layout of deployed network.As proof of concept, implementation of MIAP for 802.11g wireless networks has been made by significantly modifying transceiver implementation provided at CGRAN (Comprehensive GNU Radio Archive Network) website [3][10] and better explained in [6].This implementation is extendable to any $802.11$standard, by modifying its parameters at physical layer accordingly.A central management server constituted of Dell T-620 computer running MIAP on Linux OS has been placed for implementation of flexible channelization.Each USRP2 kit contained a 2400 RX/TX daughter card with omni-directional antennas.The specifications of USRP kit and daughter cards are available at website [7].We have customized the physical layer of each AP in such a way that an AP can switch to any of narrower or wider channel widths at the end of current frame transmission.The wireless nodes detect the width of channels based on the preamble being transmitted by APs before the transmission of each frame.

PERFORMANCE RESULTS AND DISCUSSIONS
We performed a series of experiments to evaluate the affect of deploying MIAP on essential network performance parameters by using varying number of network nodes.We have deployed a network of 5, 10, 15, 20, 25, and 30 nodes in each cell with varying number of slow and fast nodes.The obtained results are averaged out by collecting traces of all APs for accurate efficiency measurement of MIAP.We have evaluated our proposed algorithm for throughput gains for various ratio of slower and faster nodes.The slower nodes randomly choose their data rate from 6, 9, 12, 18. 24 and 36(Mbps), while the faster nodes operate on maximum data rate they can achieve.The physical layer of faster nodes is modified to achieve maximum transmission rate.In some cases it is noted that TR of faster nodes may reach to 128 Mbps.The achieved results are compared with standard 802.11gimplementation, COTAM [12] and signal to noise ratio based contention window (SNR based CW) [2].
The comparison given in Fig 2 demonstrate that presented algorithm outperforms all its counterparts and shows a significant improvement in achieved throughput when compared with standard implementation of 802.11g physical layer.This improvement in achieved throughput becomes almost equal to 30% at some points.The reason behind this high throughput is the fact that, at any given time if a slower node in one cell is transmitting, the TR of faster node in other cell automatically increases.This increase in TR of faster cell diminishes the effect of slower node thus keeping the network wide average throughput on higher side. In

Conclusion
In this work, we propose an efficient mechanism to mitigate the effect of MAC layer performance anomaly by using adaptable width channelization in WLANs.The proposed algorithm assigns the channel widths based on transmission rate of nodes and divert the surplus frequency spectrum to resource hungry cells operating at higher transmission rates.We first probabilistically modeled the lower and upper bounds on number of slower and faster nodes in the network.In addition to this, we also analytically modeled the throughput and SINR of adaptable width channels.The evaluation of proposed algorithms is made based on throughput gains for different network settlements with varying number of slow and fast nodes.The throughput measurements show a significant improvement of more than 20% in achieved network capacity, with different combinations of slow and fast nodes.Moreover a detailed analysis on channel access fairness has also been presented.Since proposed algorithm is independent of channel access mechanism and do not require any change at MAC layer, thus long term channel access probability remains same for each network node.Future work includes the implementation of adaptable channel widths in MIMO based wireless networks like 802.11n.In addition, development of a distributed channel adaptation algorithm that can assign spectrum resources locally on each AP is required.The effect of adaptable channelization on other essential network parameters like power consumption, transmission range etc is also needed to be explored.
Consider a network of Nt nodes operating at transmission rate R. The set of Nt nodes is divided in two subsets of Ns and Nf such that Ns;Nf 2 Nt and (Ns [ Nf ) = Nt, where Ns consists of all the nodes transmitting below a threshold transmission rate Rs and referred as slow nodes.The other subset of Nf nodes transmit above the threshold transmission rate (Rs) and referred as fast nodes.The Nt nodes of network are associated with Kt access points with Ki denoting any ith AP.The maximum number of nodes associated to any AP Ki is nt such that nt = ns + nf and nt 2 Nt; ns 2 Ns and nf 2 Nf , where ns and nf are the number of slower and faster nodes attached to any single AP Ki.The Kt access points of network form K identifical circles in which their transmission can be received and decoded correctly.The association of nodes with an AP is independent of each other and follows Poisson distribution with probability density function as given by equation 2.
for Li & Lj belongs L; Ki & Kj belongs K; Li !Ki & Lj belongs Kj ; i 6= j Where P is the transmission power, d(Ni; Ki) is the distance between node Ni and access point Ki, _ is the path loss which varies from 2 to 4 for a typical 802.11 network.
Fig 5 shows throughput of cell with faster node when TR of cell with slower nodes is fixed.The throughput comparison of MIAP for different MAC protocol data unit (MPDU) is given in Fig 6.The results show that longer the MAC fram higher will be the throughput.These results are self explanatory considering that longer frames reduce the per unit time overhead of communication thus maximizing the throughput.The adaptable nature of MIAP further increases the throughput by utilization of frequency spectrum.

Finally, Fig 7 and
Fig 8 show channel access fairness of MIAP for various sizes of MPDU and different number of nodes respectively.The achieved results depict that fairness of MIAP algorithm in granting channel access to various nodes is near to standard implementation.It is better than SNR based CW adaptation and below the performance of COTAM.Since MIAP is MAC layer independent mechanism and it does not change the channel access mechanism, therefore the fairness remains similar to standard implementation of 801.11MAC.On the other hand SNR based CW 3 due to different sizes of contention window at different nodes.
for Different Number of Nodes