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Improving throughput and fairness by improved channel assignment using topology control based on power control for multiradio multichannel wireless mesh networks
EURASIP Journal on Wireless Communications and Networking volume 2012, Article number: 155 (2012)
Abstract
Multiradio multichannel (MRMC) wireless mesh networks (WMNs) achieve higher throughput using multiple simultaneous transmissions and receptions. However, due to limited number of nonoverlapping channels, such networks suffer from cochannel interference, which degrades their performance. To mitigate cochannel interference, effective channel assignment algorithms (CAAs) are desired. In this article, we propose a novel CAA, Topologycontrolled Interferenceaware Channelassignment Algorithm (TICA), for MRMC WMNs. This algorithm uses topology control based on power control to assign channels to multiradio mesh routers such that cochannel interference is minimized, network throughput is maximized, and network connectivity is guaranteed. We further propose to use twoway interferencerange edge coloring, and call the improved algorithm Enhanced TICA (eTICA), which improves the fairness among flows in the network. However, the presence of relatively long links in some topologies leads to conflicting channel assignments due to their high interference range. To address this issue, we propose to utilize minimum spanning tree rooted at the gateway to reduce conflicting channels, and in turn, improve medium access fairness among the mesh nodes. We call the improved algorithm eTICA version 2 (eTICA2). We evaluate the performance of the proposed CAAs using simulations in NS2. We show that TICA significantly outperforms the Common Channel Assignment scheme in terms of network throughput, and eTICA and eTICA2 achieve better fairness among traffic flows as compared to TICA. It is also shown that eTICA2 leads to improved network throughput, as compared to TICA and eTICA.
1. Introduction
In multiradio multichannel (MRMC) wireless mesh networks (WMNs), a key issue is the cochannel interference from simultaneous transmissions of mesh nodes located within the interference range of each other, which degrades the capacity of the network. Mitigating such interference in the MRMC WMN architecture requires effective Channel Assignment (CA). This involves assigning a channel to each radio in a way that minimizes interference on any given channel as well as ensures network connectivity [1].
Topology control using transmit power control is a useful technique for reducing the cochannel interference in a WMN and increasing the network capacity. This is done by adjusting the transmission range (TR) of a mesh node by controlling its transmit power. The main goal of a Topology Control Algorithm (TCA) is to minimize the cochannel interference, enhance spatial channel reuse, and maintain network connectivity through the selection of minimum transmission power for each radio interface. Hence, mesh nodes transmit at the minimum power required to maintain connectivity with their immediate neighbors. This leads to multihop communication instead of long direct links and results in lower interference in the network.
In this article, we propose centralized Channel Assignment Algorithms (CAAs), which build a controlled topology using power control with the goal of minimizing interference between Mesh Routers (MRs) and ensuring network connectivity at the same time. The advantage of topology control based on power control lies in the fact that it improves network spatial reuse and hence, the traffic carrying capacity. To the best of the authors' knowledge, the proposed CAAs are the first of their kind to use topology control based on power control for CA in MRMC WMNs. The main contributions of this study are as follows:

A new TCA, Select x for less than x, that builds the network connectivity graph by selecting the nearest neighbors for each mesh node in the network with the objective of minimizing interference among MRs and enhancing frequency reuse as well as simultaneously ensuring a connected network.

A new CAA, Topologycontrolled Interferenceaware Channelassignment Algorithm (TICA), which uses the Select x for less than x TCA to intelligently assign the available channels to the MRs with the objective of minimizing interference and hence, improving network throughput. A preliminary work on TICA has been presented in [2].

An extension of TICA, Enhanced TICA (eTICA), which, instead of using the oneway interferencerange edge coloring approach of TICA, uses twoway interferencerange edge coloring. eTICA results in a more accurate CA, which leads to an enhancement in the fairness among traffic flows without compromising the network throughput. A preliminary work on eTICA has been presented in [3].

An enhancement of eTICA, eTICA version 2 (eTICA2), which employs a Minimum Spanning Tree (MST) rooted at the gateway instead of a Shortest Path Tree (SPT) employed in TICA and eTICA, to reduce conflicting channels. This approach improves medium access fairness among the mesh nodes, which leads to an improvement in the network throughput.

A centralized Failure Recovery Mechanism (FRM) for our proposed CAAs, which provides automatic and fast failure recovery by reorganizing the network to bypass the failed node and to restore connectivity. A preliminary work on the proposed FRM has been presented in [4].
The rest of the article is organized as follows. In Section 2, we present existing literature related to CA schemes and schemes using topology control for CA. The network architecture for the proposed model is presented in Section 3. In Section 4, we present the TCA, Select x for less than x, and the details of its phases. In Section 5, we explain the CA problem and present TICA along with the details of its phases. In Section 6, we discuss the problem of oneway interferencerange edge coloring and present eTICA. In Section 7, we discuss the problem of long links, and present eTICA2 along with the details of its MST approach to counter this problem. In Section 8, we present the FRM for our proposed CAAs. In Section 9, we provide simulation results to evaluate the performance of the proposed CAAs. The article concludes in Section 10.
2. Related study
A number of CAAs have been proposed with the objective of addressing the capacity problem in multihop WMNs. In centralized CA schemes such as Traffic and Meshbased Interference Aware Channel Assignment (MesTiC) [1] and Centralized Hyacinth (CHYA) [5], the traffic load is required to be known before assigning channels, whereas our proposed CAAs require no such knowledge. The Hybrid Multiple Channel Protocol (HMCP) proposed in [6] requires radios to switch between channels on a perpacket basis. In such cases, time synchronization and coordination between mesh nodes is required, which is not needed in our proposed CAAs. The Breadth First SearchChannel Assignment (BFSCA) scheme proposed in [7] requires certain number of MRs with certain number of radio interfaces to be placed at certain hops from the gateway, whereas our proposed CAAs simply require all MRs to have four data radios, do not require any careful router placement strategy and work with any placement of MRs as verified by the performance evaluation. Unlike our proposed CAAs and Distributed Hyacinth (DHYA) [8], the abovementioned CA schemes do not possess fault tolerance capability and have not provided any mechanism of recovery after a node failure. In [9], the Joint Resource and Channel Assignment (JRCA) algorithm was introduced. This algorithm determines the number of radios required at each node based on the traffic demand and produces the CA for each radio, such that the interference among the links operating on the same channel is minimized. The Maxflowbased Channel Assignment and Routing (MCAR) algorithm presented in [10] splits the CA into two stages. In the first stage, links are sorted into groups based on the flows they carry, while in the second stage, a channel is selected for each group and is assigned to all links of this group. If it is possible to do so, different channels are assigned to groups containing interfering links. In [11], a centralized tabu searchbased algorithm is proposed, the objective of which is to minimize the total network interference. Though all of the CAAs presented in [1, 5–11] are interferenceaware and aim to minimize the cochannel interference, but unlike our proposed CAAs, they do not use topology control based on power control for CA. Also unlike eTICA, they do not employ the technique of twoway interferencerange edge coloring to achieve a more accurate CA.
Topology control in WMNs is typically targeted toward reducing interference and improving spectral efficiency while maintaining network connectivity. Interference is confined by lowering the transmit power. Since transmit power is directly proportional to the distance between the nodes, a reasonable strategy is to replace the long links with shorter ones. Local Minimum Spanning Tree (LMST) is a TCA presented in [12], which uses MST to achieve short link lengths resulting in the medium being shared efficiently. In CAAs proposed in [13–15], the network topology has been built using MST. The motivation for using MST in these CA schemes is that shorter links resulting from MST imply more capacity in WMN by reducing interference with nearby links which use the same channel. Our proposed CAA, eTICA2, minimizes conflicting channels by employing an MST rooted at the gateway in combination with topology control based on power control and twoway interferencerange edge coloring.
Since the main network resource, namely the frequency spectrum is limited, it must be shared fairly among the contending nodes. Achieving fairness in WMNs can broadly be categorized in terms of pernode and perflow fairness. Perflow fairness refers to equal share of the data among traffic flows arriving at the gateway. Unfairness among flows arises due to multiple flows sharing the same link. This causes congestion at such links which leads to unfairness among flows reaching the gateway. Pernode fairness refers to equal access for each node to the wireless medium. Unfairness in medium access arises in MRMC WMNs due to some nodes operating on a conflicting channel and contending with each other for medium access on that channel. The authors have proposed an algorithm in [16] to improve the fairness by differentiating the traffic among the connections in a wireless multihop network. In [17], the authors propose a receiving node assistance feature in addition to the existing CSMA/CA protocol to remove exposed terminal problem and enhance fairness in multihop wireless networks. The authors have proposed a graphbased algorithm in [18] for improving fairness in WMNs that is based on employing multiple queues per node, using different backoff parameters and EIFS values. In [19], the authors have proposed a fair binary exponential backoff algorithm by adapting the contention window to reduce the effect of flow starvation, thereby improving fairness in a WMN. All of these schemes have used Jain's fairness index [20] as a measure of the network fairness. Unlike [16–19], our proposed CAAs, eTICA and eTICA2, improve fairness among flows through a more accurate CA and improve medium access fairness by reducing the conflicting channels, respectively.
3. Network architecture
In our proposed model, each MR is equipped with five radios which operate on IEEE 802.11a [21] channels (5 GHz band). One of these radios is used for control traffic, while the other four radios are used for data traffic. Each radio interface of the multiradio MR is equipped with an omnidirectional antenna.
The IEEE 802.11a standard uses Orthogonal Frequency Division Multiplexing (OFDM) as the physical layer transmission technology. Out of the 12 available nonoverlapping 802.11a channels, channel 12 is used for control radio on each MR and the remaining 11 channels are used for data radios. Since each MR is equipped with four data radios, it can communicate with a maximum of four neighbors for data communication simultaneously, which implies that the Maximum Node Degree (MND) per node is four. The MND of four is selected in order to fully utilize the 11 available nonoverlapping channels. Results have shown that with 12 available channels, network throughput increases up to an MND of four per node and saturates after that [5].
Roofnet [22] is an experimental WMN built by Massachusetts Institute of Technology (MIT). Similar to Roofnet, we assume that each mesh node has omnidirectional antennas installed on the roof of a building and the propagation environment is characterized by a strong lineofsight component. So, the channel propagation model used is either freespace propagation model or tworay propagation model, depending on the crossover distance.
4. Select x for less than x TCA
4.1. Gateway advertisement
Initially, the gateway broadcasts a "Hello" message on the control channel, announcing itself as the gateway. Each MR that receives this Hello message on the control channel over its control radio broadcasts it again and it is flooded throughout the network. The Hello message contains a hopcount field that is incremented at each hop during its broadcast. An MR may receive multiple copies of this message. However, the distance of an MR from the gateway is the shortest path length (shortest hop count) of the Hello message received by the MR through its control radio over different paths. In this way, each MR knows the next hop to reach the gateway using its control radio.
4.2. Topology control problem
The problem of topology control in multiradio WMNs involves the selection of transmission power for each radio interface of each mesh node in the network, so as to maintain the network connectivity with the use of minimum power [23]. The objective of the proposed Select x for less than x TCA is to build a connectivity graph with a small node degree to mitigate the cochannel interference and enhance spatial channel reuse as well as preserve network connectivity with the use of minimal power, as less transmit power translates to less interference.
4.3. Assumptions
Our proposed TCA controls the network topology by selecting the nearest neighbors for each mesh node in the network with the objective of minimizing interference among MRs. The proposed TCA, which is shown in Figure 1, is based on the following assumptions:

All mesh nodes start with the maximum transmission power.

Each mesh node has its location information.

Each mesh node uses an omnidirectional antenna for both transmission and reception.

Each mesh node is able to adjust its own transmission power.

The maximum transmission power is the same for all mesh nodes.

The maximum TR for any two mesh nodes to communicate directly is also the same.

The initial topology graph created, when every mesh node transmits with maximum power, is strongly connected.
4.4. Phases of Select x for less than x TCA
4.4.1. Exchange of information between nodes
In the first exchange, each node broadcasts a Hello message at maximum power containing its node ID and position.
4.4.2. Building the maximum power neighbor table
From the information in the received Hello messages, each node arranges its neighboring nodes in ascending order of their distance. The result is the maximum power neighbor table (MPNT). Then, each node sends its MPNT along with its position and node ID to the gateway using its control radio.
4.4.3. Building the direct neighbor table
For each node in the network, the gateway builds a direct neighbor table (DNT). Based on the information in the MPNT of node v and the MPNTs of its neighbors, if (a) node w is in the MPNT of node v and (b) node w is closer to any other node y in the MPNT of node w than to node v, then the gateway eliminates node w from the MPNT of node v. If after removing nodes from the MPNT of node v, the remaining number of nodes in the MPNT of node v is equal to "x  1," then the gateway selects "x" nearest nodes as neighbors of node v, which results in the DNT. However, after removing nodes from the MPNT of node v, if the remaining number of nodes is greater than or equal to "x," the result is the DNT. We call the above algorithm as Select x for less than x TCA, where x is a positive integer.
4.4.4. Converting into bidirectional links
For each node in the network, the gateway converts the unidirectional links in the DNT of a node into bidirectional links. For each unidirectional link, this is done by adding a reverse link in the DNT of the neighboring node. This converts the DNT into bidirectional DNT, which results in the Final Neighbor Table (FNT).
4.4.5. Calculating the minimum power required
For each node in the network, the gateway calculates the minimum power required to reach each of the nodes in the FNT of a node, using appropriate propagation model formulas. If the distance between two nodes u and v is less than the crossover distance, i.e., d(u, v) < Cross_over_dist, Free Space propagation model is used, whereas if d(u, v) > Cross_over_dist, tworay propagation model is used. Crossover distance is given by [24]
where h_{ t } and h_{ r } are the antenna heights of the transmitter and receiver, respectively. The minimum power for the freespace propagation model is calculated as [24]
The minimum power for the tworay propagation model is given by [24]
where G_{ t } and G_{ r } are the transmitter and receiver antenna gains, respectively. RxThresh is the power required by the radio interface of the receiving node to correctly receive the message.
5. TICA
5.1. CA problem
The CA problem in MRMC WMNs involves assigning a channel to each radio of an MR in a way that minimizes interference on any given channel and ensures connectivity between the mesh nodes.
5.1.1. Objectives
The CAA should satisfy the following two main goals:

Minimize cochannel interference between MRs

Ensure network connectivity
5.1.2. Constraints
In order to achieve these goals, the CAA should satisfy the following requirements:

In order to communicate, a pair of mesh nodes within transmission range of each other needs to have a common channel assigned to their endpoint radios.

Links in direct interference range of each other should be assigned nonoverlapping channels.

The number of distinct channels that can be assigned to an MR is bounded by the number of radios it has.

The total number of nonoverlapping channels is fixed.

Since the traffic in a WMN is directed to and from the gateway, the traffic flows aggregate at routers close to the gateway. Links that are expected to support heavy traffic should be given more bandwidth than others. In other words, these links should use a radio channel that is shared by fewer nodes. Therefore, priority in CA should be given to links starting from the gateway based on the number of nodes that use a link to reach the gateway.
5.2. Interferencerange edge coloring
If K be the number of available colors (channels), then for K ≥ 4, the distance2 edge coloring problem, also known as strong edge coloring problem, is NPcomplete [25]. A distance2 edge coloring of a graph G is an assignment of colors to edges so that any two edges within distance2 of each other have distinct colors. Two edges of G are within distance2 of each other if either they are adjacent or there is some other edge that is adjacent to both of them. The distance2 edge coloring has been used in [26] for CA, where the authors have described the interference model as twohop interference model. In this model, two edges interfere with each other if they are within twohop distance. In other words, two edges cannot transmit simultaneously on the same channel if they are sharing a node or are adjacent to a common edge.
To minimize cochannel interference in a WMN, it is necessary to assign channels to links such that links within interference range of each other are assigned different channels (colors). This problem can be termed as interferencerange edge coloring, and the corresponding interference model can be called interferencerange interference model. In a grid topology where links are of equal length, the interferencerange edge coloring is similar to distance2 edge coloring, as shown in Figure 2a. The channel assigned to link l_{1} cannot be assigned to links l_{2} and l_{3} as they are within the interference range of Node 2, which is an end node of link l_{1}. Note that l_{2} and l_{3} are also within twohop distance of l_{1}. However, in a random topology where links are of different lengths due to the random nature of the topology, the interferencerange edge coloring can be harder than distance2 edge coloring, as shown in Figure 2b. In this case, the channel assigned to link l_{1} cannot be assigned to links l_{2}, l_{3}, and l_{4} as they are within the interference range of Node 2, which is an end node of link l_{1}. Note that l_{2}, l_{3}, and l_{4} are within threehop distance of l_{1}.
In our proposed network model, the number of available channels (colors) is 11 which means that K = 11. Based on its similarity to distance2 edge coloring problem which is NPcomplete for K ≥ 4, the interferencerange edge coloring problem is, therefore, also NPcomplete. Hence, we propose TICA, which is an approximate algorithm for CA in MRMC WMNs. TICA has an overall computational complexity of O(N^{3}), where N is the number of nodes in the network.
5.3. Phases of TICA
TICA, as shown in Figure 3, has the following phases.
5.3.1. Topology control
In order to create the network connectivity graph with the aim of reducing the interference between MRs, network topology is controlled using power control at each MR. All nodes send their MPNTs to the gateway using their control radio. Note that in order to send its MPNT to the gateway, each MR knows the next hop to reach the gateway using its control radio via gateway advertisement process. Gateway starts with the Select 1 for less than 1 TCA and builds FNTs for all nodes. The computational complexity of this phase is O(L_{ M } + N^{3}+ L_{ D }^{2}) ≈ O(N^{3}), since L_{ M } < N^{2} and L_{ D }^{2} < N^{3}, where L_{ M } is the number of links in the MPNTs of all nodes, L_{ D } is the number of links in the DNTs of all nodes, and N is the number of nodes in the network.
5.3.2. Connectivity graph
Based on the FNTs of all nodes, the gateway builds the connectivity graph. It checks the resulting network for connectivity to ensure that it can reach any node in the network directly or through intermediate hops. If the resulting network is not connected, the gateway moves to a higher TCA by incrementing x in the Select x for less than x TCA. The computational complexity of this phase is O(L_{ F } + N), where L_{ F } < N^{2} and is the number of links in the FNTs of all nodes in the network.
5.3.3. Minimum powerbased SPT with an MND of 4
After ensuring that the connectivity graph is connected, the gateway builds the SPT based on the connectivity graph. The computational complexity of this phase is O(L_{ F } + N^{3}) ≈ O(N^{3}). The metric for path selection is minimum power. While building the SPT, the gateway ensures that each node can have only four TR neighbors and builds an SPT with an MND of four per node. If any node in the SPT has more than four links, gateway selects those four links for that node that have the minimum weight and sets the weights of all other links to infinity. It then checks the resulting Minimum Powerbased SPT (MPSPT) graph for connectivity. If the resulting MPSPT is not connected, the gateway moves to a higher TCA.
5.3.4. Link ranking
The gateway calculates the rank of each link in the SPT based on the number of nodes that use a link to reach the gateway. If l is a link and n is a node using link l to reach the gateway, then the rank of link l, i.e., r_{ l } , is given by
where N is the total number of nodes in the network. I_{ n, l } is 1 if node n is using link l, and 0 otherwise. In case of links with the same rank, link whose power of farthest node to the gateway is smallest is given a higher rank. If there are still links with the same rank, link with smallest node IDs is given a higher rank. The computational complexity of this phase is O(N^{2}).
5.3.5. CA
The algorithm then assigns a channel to each link of the MPSPT according to its rank. The computational complexity of this phase is O(N^{3}). It begins with assigning the 11 available channels to the 11 highestranked links such that channel 1 is assigned to firstranked link. For the 12thranked link and onwards, the gateway checks the CA of all links within the interference range of both nodes that constitute that link. Out of the 11 available channels, those channels that are not assigned to any link within the interference range (IR) of both nodes that constitute that link are termed as nonconflicting channels. If the gateway finds one or more nonconflicting channels, it assigns that channel to the link which has the highest channel number.
5.3.5.1. Least interfering channel
If the gateway cannot find any nonconflicting channel, it selects a channel that causes minimum interference to the link. Such a channel is called a Least Interfering Channel (LIC).
5.3.5.2. Interference level
To find out the LIC, the gateway builds the interference level (IL) for all 11 channels. LIC is the channel with minimum IL, which means that assigning this channel to the 12thranked link results in minimum interference in the network. For example, in order to build IL for channel 1, the gateway finds all links within IR of each of the two nodes that constitute the 12thranked link that use channel 1 and calculates IL of each link based on its rank and distance from a node of the 12thranked link. It sums up individual ILs of all links that use channel 1 within IR of each of the two nodes that constitute 12thranked link, to find out the total IL for channel 1. This is done by using
where i is the channel that has value between 1 and 11, (IL) _{ i } is IL of channel i, r is rank of link using channel i, R is maximum rank assigned to a link in MPSPT, m is a link using channel i that is within IR of a node of the 12thranked link, d is distance from a node of link m to a node of the 12thranked link, and α is 2 or 4 depending on crossover distance.
If a link is emanating from either of the two nodes that constitute the 12thranked link and a channel has been assigned to that link, then IL for this channel is set to infinity. LIC is selected as
Similarly, the gateway assigns channels to all the links in the MPSPT. Using its control radio, it then sends each mesh node the channel assignment and routing message (CARM). For each channel assigned to an MR, the CARM message contains the channel number and the neighbor node to communicate with using this channel. The CARM also contains the next hop to reach the gateway for data traffic. Based on the channel assigned to an MR to communicate with a neighbor and its distance to that neighbor, the MR applies power control and adjusts its transmission power accordingly, using (2) or (3), depending on the crossover distance.
6. eTICA
TICA uses interferencerange edge coloring for assigning a channel to a link, whereby it inspects the channelassigned links within the interference range of both mesh nodes that constitute that link before assigning it a channel. However, this approach of oneway interferencerange edge coloring does not find all the LICs in most cases. This leads to undetected hidden links which results in the CAA allocating the same channel to two links within the interference range of each others' end nodes. This leads to decreased network throughput and fairness. This drawback of TICA has been addressed by employing twoway interferencerange edge coloring in eTICA. eTICA results in an accurate CA thus reducing interference and improving fairness among flows without sacrificing the network throughput. Its computational complexity is the same as that of TICA.
We investigate a scenario, as shown in Figure 4, where TICA, which is based on oneway interferencerange edge coloring, has been used for CA. This scenario consists of a random topology comprised of 36 MRs where Node 15 is the gateway. The interference range is indicated by the circular disks in Figure 4. Link 2319 is ranked nine and hence, it is allocated channel 9, which has not been allocated to any other link yet. Link 117 has a lower rank as it is used by four nodes to reach the gateway. Since the algorithm has already allocated the 11 channels, it searches the interference range of nodes 1 and 17 for an available channel. Link 117 is assigned channel 9 as the algorithm cannot find any other link using channel 9, as shown in Figure 4. From Figure 4, it can be observed that nodes 1 and 17 are in the interference range of nodes 23 and 19 of link 2319, which is not identified by TICA because it is based on oneway interferencerange edge coloring. In other words, link 2319 becomes a hidden link during the CA phase of link 117. Eventually, links 117 and 2319 share the same channel even though the nodes which constitute these links are within the interference range of each other. Therefore, the hidden link problem may lead to degradation in the network throughput and fairness.
The proposed algorithm, eTICA, resolves the above problem by using twoway interferencerange edge coloring. When channels are being assigned to links, eTICA inspects the links in the interference range of both nodes associated with both links. For example, in order to assign a channel to link 117, eTICA checks the channels being used in the interference range of nodes 1 and 17, as well as the channel assigned to link 2319. We term the new model as twoway interferencerange edge coloring, which implies that links formed by nodes that are within the interference range of each other will not be allocated the same channel, provided that there is a channel available for allocation. Table 1 summarizes the CA with TICA as well as eTICA for the scenario described above. As is evident from this table, eTICA allocates channel 7 to link 117 instead of channel 9. TICA also allocates the same channel to links 1936 and 131 in this scenario even though the nodes that constitute these links are within the interference range of each other, whereas eTICA allocates channel 8 to link 131 instead of channel 11, thereby eliminating the hidden link problem.
Tables 2 and 3 show a comparison of the number of LICs resulting from TICA and eTICA for 25 different random topologies (RTs) of a 36node network and a 100node network, respectively. As can be seen from these tables, TICA does not find all the LICs in most cases, whereas eTICA is able to do so and thus results in a more accurate CA.
7. eTICA2
The twoway interferencerange edgecoloring introduced in eTICA leads to an improved CA scheme and eliminates the problem of hidden links. However, in some topologies, owing to the long links, LICs result in increasing the interference. Hence, reuse of a channel within the interference range causes significant decrease in network throughput. Since the long links contribute to interference, they should be replaced with shorter links wherever possible. So, a modified CAA, eTICA2, is presented in this section which employs an MST rooted at the gateway instead of a SPT to reduce the occurrence of conflicting channels, thereby, improving fairness in medium access and network throughput. Its computational complexity is also same as that of TICA.
7.1. Improving fairness in medium access using MST
A scenario as shown in Figure 5 is investigated, where a topology encounters LICs while utilizing the eTICA algorithm. Due to LICs, the network throughput decreases as a result of interference caused by links using the same channel within the interference range. In this scenario, link 1828 has been assigned channel 5 by eTICA and link 1224 has also been allocated channel 5. The circular disk in Figure 5 indicates the interference range of node 18. Since the link 1224 is in the interference range of node 18, both nodes 28 and 24 will compete for access to the medium on this channel. Specifically, when node 24 needs to communicate with node 12 on channel 5 and node 28 needs to communicate with node 18 on the same channel simultaneously, contention for medium access based on CSMA/CA will occur on channel 5. The presence of LICs affects the fairness in medium access and hence the network throughput, since some nodes, such as nodes 28 and 24, compete for access to the medium.
A new approach is proposed for maximizing spatial channel reuse and reducing LICs by utilizing an MST rooted at the GW instead of the SPT. The motivation behind using MST is to achieve short link lengths which will result in the medium being shared efficiently by reducing LICs. Since transmit power is proportional to the distance between the nodes, the shorter the distance, the lower the transmit power. Less transmit power translates to less interference which leads to better spatial channel reuse. The modified CAA, eTICA2, replaces the SPT approach of eTICA with the MST approach. In both approaches, the link weight is the minimum transmit power required by a node to reach its neighbor for building the minimum power based tree. Figure 6 shows that utilizing MST results in shorter hops between nodes and hence, the interference range of node 18 is shrunk. Table 2 also shows the number of LICs resulting from eTICA2 for 25 different RTs of a 36node network. In the investigated scenario, the SPT approach results in 6 LICs, whereas the MST approach, indicated by RT 17 in Table 2, reduces the number of LICs to 4. eTICA2 results in a reduction of LICs, as indicated in Tables 2 and 3, which implies that nodes have better access to the medium whenever they have data to transmit. Thus, competition with other nodes for access to the medium on the assigned channel is lower. So, utilizing minimum powerbased MST (MPMST) will improve the fairness in medium access and hence, the network throughput.
7.2. Improving throughput using four radios of the gateway
The maximum achievable throughput of a topology is limited by the performance bottleneck at the links which originate from the GW, as well as the number of traffic sources using those links. The maximum data rates achievable at a link with one, two, and three sources are 8.192, 16.384, and 24.576 Mbps, respectively. IEEE 802.11a supports a maximum data rate of 54 Mbps. However, the effective data rate is 24.748 Mbps, while the rest is consumed by overhead. Hence, if there are more than three sources sharing a link, there is a traffic bottleneck at that link with the achievable data rate being limited to 24.748 Mbps. The maximum achievable throughput and in turn the throughput performance of eTICA2 can be improved by utilizing all four radios of the gateway. In order to utilize all four radios of the gateway, eTICA2 builds an MPMST from the gateway utilizing its four nearest neighbors.
A scenario is investigated using eTICA and eTICA2 as shown in Figures 7 and 8, respectively. From Figure 7, it can be seen that eTICA results in the GW utilizing only one of its four radios. This limits the maximum achievable throughput to 24.748 Mbps. As shown in this figure, all sources are using the same link to reach the GW which causes a bottleneck at link 1525. This traffic bottleneck limits the throughput performance of the network by confining the maximum achievable throughput. Applying eTICA2 to the same topology increases the maximum achievable throughput to 49.3 Mbps. As shown in Figure 8, eTICA2 ensures that the GW utilizes all four of its radios. The traffic load is now distributed among the four links of the GW where the maximum traffic load on the links 158, 1516, 1525, and 152 is 24.748, 8.192, 8.192, and 8.192 Mbps, respectively. Thus, the traffic load is distributed among the four radios in eTICA2 as compared to one radio in eTICA. This reduces traffic congestion on the links which are close to the GW and results in an improvement in the throughput and fairness of the network. The throughput of this scenario with TICA and eTICA is 24.6 Mbps, whereas with eTICA2 is 49.3 Mbps.
8. FRM
The proposed CAAs are faulttolerant and support automatic and fast failure recovery. In case of node failure, the FRM is initiated by the gateway.
All nodes send periodic "keepalive" messages to the gateway on the control channel using their control radios. The keepalive message tells the gateway that the node is active. If the gateway does not receive three consecutive keepalive messages from a node z, then it concludes that node z has failed and is no longer active. The gateway then deletes the MPNT for this node and deletes node z from MPNTs of all its neighboring nodes. Note that the gateway received MPNTs of all nodes during the setup phase. During the setup phase, nodes exchanged Hello messages, which were transmitted at maximum power on the control channel and contained the node ID and node position. From the received Hello messages, each node built an MPNT by arranging its neighboring nodes in ascending order of their distance. Each node then sent its MPNT to the gateway over the control channel using its control radio.
After detecting the failed node, deleting its corresponding MPNT and deleting it from the MPNTs of its neighbors, the gateway builds the DNT for each node using the Select x for less than x TCA. The gateway converts the unidirectional links in the DNT of a node into bidirectional links, which results in the FNT of that node. Similarly, the gateway builds the FNTs for all active nodes. Based on the FNTs of all active nodes in the network, the gateway builds the connectivity graph and checks the resulting network for connectivity. After ensuring that the connectivity graph is connected, the gateway builds the MPSPT (as in TICA and eTICA) or MPMST (as in eTICA2), with an MND of four. After ensuring that the minimum powerbased tree is connected, the gateway builds the link ranking. Based on the link ranking, the gateway assigns the channels to links.
The gateway then sends the new CARM to all nodes in the network on the control channel. Each MR receives the CARM on the control channel over its control radio and compares the existing CA with the updated CA. It switches its radios to new channels in case the new CA is different from the old one. Based on the channel assigned to an MR to communicate with a neighbor and its distance to that neighbor, the MR applies power control and adjusts its transmission power accordingly, using (2) or (3) depending on the crossover distance. Each MR also updates its next hop required to reach the gateway for data traffic. Figures 9, 10, and 11 highlight the FRM, which reorganizes the network to bypass the failed Node 9 and restores connectivity.
9. Performance evaluation
The performance of our proposed CAA, TICA, for MRMC WMNs is compared against the Common Channel Assignment (CCA) scheme [27] as well as its variant, CCA with topology control (CCATC), in terms of network throughput. CCA is a well known and commonly used benchmark scheme, which has also been used before by other firstoftheirkind schemes, such as [5, 7], for performance comparison. Then, we have compared the performance of eTICA and eTICA2 with TICA in terms of throughput ratio and fairness ratio. If x_{ i } be the throughput of a flow i and N is the total number of flows (sources) in the network, then the Jain's fairness index, F_{J}, is given by
Absolute fairness is achieved when F_{J} = 1 and absolute unfairness is achieved when F_{J} = 1/N.
For the purpose of comparison between the fairness of CAAs, we define the 'Fairness Ratio', F_{ X,Y } , as
where X and Y could be TICA, eTICA, or eTICA2. Therefore, F_{ X,Y } > 1 indicates that fairness of CAA X is better than that of CAA Y.
The 'Throughput Ratio', T_{ R } , is defined as the ratio of the throughput achieved by eTICA2, eTICA, and TICA over their maximum achievable throughputs, respectively. T_{ R } = 1 indicates that the algorithm has achieved the maximum achievable throughput for that particular topology.
In the CCA scheme, all MRs have four radio interfaces. The first radio on each MR is tuned to the first nonoverlapping channel; the second radio is tuned to the second nonoverlapping channel, and so on. In this scheme, MRs do not control their power, transmit with the same maximum power, and use AODV (Adhoc OnDemand Distance Vector) routing protocol [28]. In the CCATC scheme, the MRs follow the same network model as that proposed in Section 3. In this scheme, the network topology is controlled using the Select x for less than x TCA. However, the channels are assigned to the links of the MPSPT similar to the CCA scheme. From the CARM, each MR applies power control based on the channel assigned to an MR to communicate with a neighbor and its distance to that neighbor as well as updates its next hop.
9.1. Simulation environment
The performance of the proposed CAAs has been evaluated using simulations which have been carried out in NS2 (version 2.30) [29]. The original model in NS2 was modified using the procedure given in [30] to create multiinterface mesh nodes. All radios are IEEE 802.11a radios that support 12 channels. The packet reception threshold is set to 65 dBm in order to achieve a maximum data rate of 54 Mbps supported by IEEE 802.11a. In order to achieve a strongly connected topology, the maximum transmission power for all radios is set to 27 dBm. RTS/CTS is disabled.
9.2. Network topology
A random topology has been used for the evaluation, in which MRs are distributed randomly according to a uniform distribution in a 500 × 500 m^{2} area. Twentyfive different random topologies of a 36node network and a 100node network are considered. Irrespective of its location, Node 15 is set to be the gateway for all random topologies.
9.3. Simulation parameters
The physical (PHY) and medium access control (MAC) layer settings used for the simulations are shown in Tables 4 and 5, respectively. The MRs at the periphery of the network are the traffic sources and send traffic to the gateway simultaneously, thus representing a scenario in which multiple flows within the WMN interfere with each other. Each of these nodes generates an 8 Mbps Constant Bit Rate UDP traffic stream consisting of 1024 bytes packets for 100 s. The propagation model is chosen to be tworay propagation model if the distance between two nodes is greater than the cross over distance and the free space propagation model otherwise.
9.4. Simulation results
9.4.1. TICA versus CCA
9.4.1.1. Network throughput
Tables 6 and 7 and Figures 12 and 13 show the results for the average network throughput of all three CAA schemes for 25 different random topologies of the 36node network and the 100node network, respectively. These results clearly indicate that TICA significantly outperforms the other two schemes.
9.4.2. eTICA versus TICA
9.4.2.1. Throughput ratio
As stated earlier, the maximum achievable throughput of a topology is limited by the performance bottleneck at the links that originate from the gateway, as well as the number of traffic sources using these links. For the scenario in Figure 4, there are four links emanating from the GW. The maximum achievable throughput for links 152 and 155 is 8.192 Mbps each since there is only one source using each link. The maximum achievable throughput for link 1531 is 24.576 Mbps since there are three sources using this link. The maximum achievable throughput for link 158 is limited to 24.748 Mbps since there are more than three sources using this link. Hence, the total maximum achievable throughput for this scenario is 65.7 Mbps.
In Tables 8 and 9 and Figures 14 and 15, the throughput ratios of eTICA and TICA over the maximum achievable throughput for 25 different realizations of the random topology for the 36node network and the 100node network are shown, respectively. The difference in T_{ R } achieved by eTICA and TICA is apparent from these results. For the 100node network, the average T_{ R } achieved by eTICA is 9% more than that achieved by TICA.
9.4.2.2. Fairness ratio
In Tables 10 and 11 and Figures 16 and 17, the F_{ R } among traffic flows in the network using eTICA is compared with that achieved using TICA for 25 different realizations of the random topology for the 36node network and the 100node network, respectively, using (8). F_{ R } > 1 indicates better fairness by eTICA than by TICA. It is apparent from these results that eTICA outperforms TICA in terms of fairness. For the 100node network, the average F_{ R } over the 25 random topologies is 1.20. This improvement is due to the twoway interferencerange edge coloring during CA, which results in the elimination of hidden links leading to a more accurate CA with eTICA. As a result, fairness among traffic flows in the network is improved with eTICA without sacrificing the average network throughput.
9.4.3. eTICA2 versus eTICA and TICA
TICA and eTICA use the SPT approach to build a minimum powerbased tree from the gateway to each node whereas eTICA2 employs the MST approach for the same. For a fair comparison, we have ensured that the number of traffic sources is the same for all three CAAs in the following way. If A = {end nodes for SPT} and B = {end nodes of MST}, then for comparing all three CAAs, we have made a super set 'C' which is defined as C = A U B. Hence, C = {end nodes of SPT and MST}. Thus, the traffic sources in each realization of the random topology for each CAA are the end nodes of the SPT and the end nodes of the MST.
9.4.3.1. Throughput ratio
Tables 12 and 13 and Figures 18 and 19, which show a comparison of the T_{ R } for the three CAAs for the 36node network and the 100node network, respectively, indicate that eTICA2 outperforms TICA and eTICA in most random topologies. For the 100node network, the average T_{ R } achieved by eTICA2 is 14% more than that achieved by eTICA and 23% more than that achieved by TICA. This improvement is due to the MST approach and the use of maximum possible radios out of the four available radios of the GW to build the MST. MST rooted at the gateway replaces long links with shorter ones. Shorter hops lead to shrinking the interference range which in turn leads to better spatial reuse. Hence, LICs are reduced, thereby improving fairness of medium access for the mesh nodes. Also, utilizing the maximum possible radios of the GW to build the MST results in the distribution of the traffic load among the links of the GW, thereby, reducing the traffic bottleneck at the GW.
9.4.3.2. Fairness ratio
Tables 14 and 15 and Figures 20 and 21 show that fairness ratio of eTICA2 is better than that of TICA but less than that of eTICA. For the 100node network, the average fairness ratio of eTICA2 over TICA is 1.07 whereas the average fairness ratio of eTICA2 over eTICA is 0.97.
These results clearly show that eTICA2 leads to improved network throughput, as compared to eTICA and TICA. Also, eTICA2 is fairer than TICA but less fair as compared to eTICA. In eTICA2, MST leads to shorter links/hops having shorter interference range, which leads to reduced LICs, improved fairness in medium access and hence, improved network throughput. Although MST leads to shorter hops but it also leads to more hops from the source to the gateway and the average number of hops from the sources to gateway increases. Due to these more hops from the sources to the gateway, more flows pass through the same link and have to share that link, which negatively impacts the fairness among the flows in the network.
10. Conclusion
In this article, we have introduced Select x for less than x TCA, which minimizes the cochannel interference by selecting the nearest neighbors for each mesh node in the network. We have introduced TICA, which is a fixed and centralized CAA for MRMC WMNs. It employs topology control based on power control by using Select x for less than x TCA for building the connectivity graph. It assigns channels to the multiradio mesh nodes with the objective of improving the network throughput by minimizing the cochannel interference as well as ensures network connectivity. As verified by simulation results, TICA significantly outperforms the CCA scheme and its variant, CCATC scheme, in terms of network throughput. We proposed a new FRM for our proposed CAAs, which supports automatic and fast failure recovery. The GW runs the FRM in case of node failure.
We have shown that enhancements made to TICA lead to an improved CAA, eTICA, which is verified by the simulation results presented herein. The key objective during the CA phase in an MRMC WMN is to eliminate the presence of conflicting channels within the interference range of nodes. However, due to the availability of a limited number of orthogonal channels, this is not always possible. Hence, a CAA that reduces interference among nodes and provides maximum spatial reuse is needed. The twoway interferencerange edge coloring model, introduced in eTICA, implies that links formed by nodes that are within the interference range of each other will not be allocated the same channel, provided that there is a channel available for allocation. This leads to a better CA strategy yielding an improved CAA, eTICA, which improves the fairness among traffic flows without compromising the network throughput.
We have shown that enhancements made to eTICA lead to a more efficient CAA, eTICA2, which has been verified by the simulation results. To overcome the cochannel interference problem caused by long links in a random topology, eTICA2 utilizes an MST rooted at the GW. The shorter links resulting from MST lead to a small interference range. Replacing SPT with MST in eTICA2 leads to the reduction of LICs, which reduces the interference and improves medium access fairness, thereby, increasing the network throughput. The simulation results indicate that the average throughput ratio over 25 random topologies for the 100node network, using eTICA2, is 14% more than that achieved by eTICA and 23% more than that achieved by TICA. The fairness among traffic flows with eTICA2 is better than that with TICA but less than that with eTICA. The two enhancements of utilizing an MST and maximum possible out of the four radios of the GW, when coupled together, yield an improved CAA, eTICA2, which is successful in improving the medium access fairness by reducing the conflicting channels, thereby increasing network throughput, while also improving the fairness among traffic flows.
The propagation model used is freespace model or tworay model depending upon the crossover distance. As part of future work, the performance of the proposed CAAs may be tested under more realistic propagation models, such as Shadowing and Rayleighfading.
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Chaudhry, A.U., Ahmad, N. & Hafez, R.H.M. Improving throughput and fairness by improved channel assignment using topology control based on power control for multiradio multichannel wireless mesh networks. J Wireless Com Network 2012, 155 (2012). https://doi.org/10.1186/168714992012155
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Keywords
 channel assignment
 fairness
 interferencerange edge coloring
 topology control
 wireless mesh networks