*4.1.3. Load-Aware Channel Assignment Exploiting Partially Overlapping Channels (Load-Aware CAEPO-G)*

The authors of [13] present an extension to the previously discussed CAEPO [12] to make it traffic load-aware in addition to being interference-aware. A grouping algorithm is also proposed with the goal of achieving better aggregate network throughput. In the grouping algorithm, each node sends periodic hello messages; based on a node's weight (which is determined by how many hello messages it has received so far from its one-hop neighbors) the node may become a group leader. There can only be one group leader in the one-hop vicinity of any particular node. New nodes can join the group by sending a *join message* and similarly existing nodes can leave the group by sending a *quit message* to the group leader. Once the group leaders have been assigned (grouping is done), channels are assigned to links similarly to that in [12], with only one major difference: any update of the channel (i.e., channel switching) has to be initiated by the group leader. If a node "feels a need" to switch to a new, less contentious channel, it will send a "channel switch" request to its corresponding group leader who if agrees relays the information onwards to the other members in the group. Because of the addition of a new grouping algorithm and the load-aware feature, load-aware CAEPO-G achieves much better performance than the original CAEPO.

#### *4.1.4. Minimum Interference for Channel Allocation (MICA)*

116 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

Thus, the interference metric at node *i* is calculated as:

formance when all 11 channels of IEEE 802.11b are used.

[23]).

*Aware CAEPO-G)* 

the interference experienced by nodes operating on channels with partial interference. Each node measures the interference according to the degree of overlap between channels and scales it to the traffic load experienced by its neighboring node (this information is maintained by each node). Each node does this for all of its neighbors and combines the results to determine the total interference it is "suffering" due to its neighboring nodes.

ܫ݊ݐ݁ݎ݂݁ݎ݁݊ܿ݁ሾ݅ሿ ൌ݂ሾ݅ሿሾ݆ሿ כ ܤሺ݆ሻ אேሺሻ where *B(j)* is the proportion of the busy time of a neighboring node *j*, and *N(i)* is the set of neighbors of node *i*; *f[i][j]* captures the extent of overlap a node operating on a particular channel has from its neighboring nodes configured on another channel. This is based on the extent of the channel separation between the channels used by the two nodes (taken from

More precisely, CAEPO works as follows: each node in the network is equipped with two interfaces; the first interface is configured to a fixed channel while the other interface can be dynamically switched between channels. The algorithm starts with each node assigning a fixed channel to its fixed interface and a default channel to its switchable interface using the interference estimation metric with the initial value of *B(j)*=1. Then, this channel assignment information, together with the interference measurements are relayed to all neighbors. After this initial channel assignment, each node periodically calculates the interference using the interference metric described above and if the fixed interface channel needs to be changed, then that information is relayed on the default channel of the switchable interface. Similarly, when a node has data to send, it switches its dynamic interface to the fixed channel of the receiver node's interface. Performance evaluations of CAEPO show improved network per-

*4.1.3. Load-Aware Channel Assignment Exploiting Partially Overlapping Channels (Load-*

The authors of [13] present an extension to the previously discussed CAEPO [12] to make it traffic load-aware in addition to being interference-aware. A grouping algorithm is also proposed with the goal of achieving better aggregate network throughput. In the grouping algorithm, each node sends periodic hello messages; based on a node's weight (which is determined by how many hello messages it has received so far from its one-hop neighbors) the node may become a group leader. There can only be one group leader in the one-hop vicinity of any particular node. New nodes can join the group by sending a *join message* and similarly existing nodes can leave the group by sending a *quit message* to the group leader. Once the group leaders have been assigned (grouping is done), channels are assigned to links similarly to that in [12], with only one major difference: any update of the channel (i.e., channel switching) has to be initiated by the group leader. If a node "feels a need" to switch to a new, less contentious channel, it will send a "channel switch" request to its corresponding In [10], the authors have introduced the concept of *node orthogonality:* two nodes, operating over adjacent and partially overlapping channels, are considered orthogonal if they are sufficiently physically apart. A novel interference model is proposed that captures the adjacent channel interference and also takes into account the physical distance of the two nodes configured on POCs. The proposed interference factor *Ic(i,j)* is defined as follows:

$$I\_c(i,j) = 1 - \frac{\min\{d\_{l,j}, D\_l(c\_l, c\_j)\}}{D\_l(c\_l, c\_j)}$$

where *Di(ci,cj)* is the adjacent channel interference range between channels *i* and *j,* extracted from the physical model of the I-factor described in [3-6]. *Di(ci,cj)* captures both the channel separation and physical distance among the nodes to model the interference due to POCs. The proposed interference factor *Ic(i,j)* can be used to define *node orthogonality* by stating that two nodes are orthogonal if and only if their interference factor value is equal to 0.

Given a particular channel assignment, a weighted interference graph can be constructed with weights on the edges measured by the interference factor *Ic(i,j)*; Figure 11 shows an example. Here, it is assumed that the data rate and the transmit power for all the APs are the same.

**Figure 11.** Construction of a weighted interference graph

Using the weighted interference graph model, a minimum weighted interference optimization problem is formulated with the objective of minimizing the sum of weights in the interference graph. A centralized heuristic is proposed called minimum interference for channel allocation (MICA) to obtain a near-optimal solution which relaxes the formulated minimum interference problem in order to find fractional interference in polynomial time and eventually to assign POCs to APs (after rounding off the fractional solution to the nearest integer).

In addition to the above approaches, there have been other research efforts in designing MAC protocols that exploit POCs in wireless networks. One such scheme is presented in [11] in which some of the challenges that may be faced when using overlapping channels in the design of a MAC protocol are discussed. Analytical models are designed to capture partial interference at the MAC layer in order to improve channel utilization and to enhance network capacity. Based on the model, an efficient medium access scheme with collision avoidance mechanism is developed which increases network throughput (exploiting multiple channel transmissions).

Partially Overlapping Channel Assignments in Wireless Mesh Networks 119

Complexity; ignoring switching overhead; SI not considered

Offline solution; only designed for single radio networks; SI not considered

Simplistic

Simplistic

interference model; SI not considered; scalability issues

interference model

...

**Technique Objective Methodology Limitations** 

found

Approximate

algorithm for channel allocation using integer linear programming (ILP) formulation.

Heuristic distributed load-aware algorithm. Channel assignment based on traffic-aware

estimation and packet loss ratio metrics

Extension of [12] with the addition of selfinterference factor and a grouping algorithm to make CA scalable.

interference

**Interference Factor experienced at channels** 1 2 3 4 5 6 7 8 9 10 11

**Interference Factor experienced at channels** 1 2 3 4 5 6 7 8 9 10 11

6 d6 0 f6,2 f6,3 f6,4 f6,5 ∞ f6,7 f6,8 f6,9 f6,10 0

1 d1 ∞ f1,2 f1,3 f1,4 f1,5 0 0 0 0 0 0 2 d2 f2,1 ∞ f2,3 f2,4 f2,5 f2,6 0 0 0 0 0 ... ... ... ... ... ... ... ... ... ... ... ...

11 d11 0 0 0 0 0 0 f11,7 f11,8 f11,9 f11,10 ∞

Routing, channel assignment, and link flow scheduling; performed stepwise until optimal CA and routing solution is

Maximization of the total throughput (maximizes simultaneous link activations)

Minimization of the sum of the weighted interference in an interference graph

network interference

Minimization of the network interference

**Table 2.** Comparison of POCA schemes based on the I-factor model.

CAEPO [12] Minimization of the

A. Mishra [5]

MICA [10]

Load-Aware CAEPO-G [13]

CH di

CH di

**Table 4.** I-Matrix

**Table 3.** Interference vector for channel 6.

The authors of [14] study the use of POCs for data aggregation in sensor networks. In a typical sensor network, the job of each sensor node is to collect the data, aggregate it and send it back to the sink for further processing. Arguably, reducing latency of data aggregation is therefore one of the fundamental issues in sensor networks. This is also called the minimum latency scheduling (MLS) problem in which a conflict free transmission schedule is designed with the objective of minimizing the overall data transmission latency. The concept of POCs is used in order to reduce the data aggregation latency; a joint tree construction, channel assignment and scheduling algorithm is proposed to solve the MLS problem. The basic idea is to compute a partially overlapping channel assignment algorithm for the sensor network, and then construct a data aggregation tree for the whole network followed by finally designing a link schedule so that the data aggregation latency is minimized.

Table II provides a side-by-side comparison for the above four POCA schemes based on their objectives, the procedures that are used in obtaining a partially overlapping channel assignment algorithm and their limitations.

#### **4.2. Interference matrix model (I-Matrix)**

The second type of interference model we consider for POCA schemes was originally presented in [19]. The model is called I-Matrix, and is designed to measure the adjacent channel interference (ACI) among different POCs on adjacent nodes as well as selfinterference (SI) among different radios on a single node. I-Matrix captures the interference that a channel belonging to a particular radio experiences due to all other possible channels (10 channels in the case of 802.11b). The proposed interference model (I-Matrix) is made up of three components, namely the interference factor, the interference vector, and the I-Matrix itself. The interference factor is derived from the I-factor of [5] and is the ratio of the interference range and the physical distance between two radios configured on adjacent channels (݂ǡ ൌ ܫܴሺߜሻȀ݀). In other words, the interference factor captures both the physical distance and the channel separation between nodes. This means that even if the respective channels of two nodes are overlapping, but their physical distance is greater than the interference range (demonstrated by *IR(δ)* and taken from [8, 24]), the value of *fi,j* will be zero. The interference factor is computed for all the channels with respect to a particular channel and put in a vector called the interference vector as shown in Table III. Similarly, each node combines all the interference vectors it has calculated for each channel and constructs the I-Matrix as outlined in Table IV.


**Table 2.** Comparison of POCA schemes based on the I-factor model.


**Table 3.** Interference vector for channel 6.


**Table 4.** I-Matrix

118 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

multiple channel transmissions).

In addition to the above approaches, there have been other research efforts in designing MAC protocols that exploit POCs in wireless networks. One such scheme is presented in [11] in which some of the challenges that may be faced when using overlapping channels in the design of a MAC protocol are discussed. Analytical models are designed to capture partial interference at the MAC layer in order to improve channel utilization and to enhance network capacity. Based on the model, an efficient medium access scheme with collision avoidance mechanism is developed which increases network throughput (exploiting

The authors of [14] study the use of POCs for data aggregation in sensor networks. In a typical sensor network, the job of each sensor node is to collect the data, aggregate it and send it back to the sink for further processing. Arguably, reducing latency of data aggregation is therefore one of the fundamental issues in sensor networks. This is also called the minimum latency scheduling (MLS) problem in which a conflict free transmission schedule is designed with the objective of minimizing the overall data transmission latency. The concept of POCs is used in order to reduce the data aggregation latency; a joint tree construction, channel assignment and scheduling algorithm is proposed to solve the MLS problem. The basic idea is to compute a partially overlapping channel assignment algorithm for the sensor network, and then construct a data aggregation tree for the whole network followed by finally design-

Table II provides a side-by-side comparison for the above four POCA schemes based on their objectives, the procedures that are used in obtaining a partially overlapping channel

The second type of interference model we consider for POCA schemes was originally presented in [19]. The model is called I-Matrix, and is designed to measure the adjacent channel interference (ACI) among different POCs on adjacent nodes as well as selfinterference (SI) among different radios on a single node. I-Matrix captures the interference that a channel belonging to a particular radio experiences due to all other possible channels (10 channels in the case of 802.11b). The proposed interference model (I-Matrix) is made up of three components, namely the interference factor, the interference vector, and the I-Matrix itself. The interference factor is derived from the I-factor of [5] and is the ratio of the interference range and the physical distance between two radios configured on adjacent channels (݂ǡ ൌ ܫܴሺߜሻȀ݀). In other words, the interference factor captures both the physical distance and the channel separation between nodes. This means that even if the respective channels of two nodes are overlapping, but their physical distance is greater than the interference range (demonstrated by *IR(δ)* and taken from [8, 24]), the value of *fi,j* will be zero. The interference factor is computed for all the channels with respect to a particular channel and put in a vector called the interference vector as shown in Table III. Similarly, each node combines all the interference vectors it has calculated for each channel and

ing a link schedule so that the data aggregation latency is minimized.

assignment algorithm and their limitations.

**4.2. Interference matrix model (I-Matrix)** 

constructs the I-Matrix as outlined in Table IV.

Partially Overlapping Channel Assignments in Wireless Mesh Networks 121

Simplistic

Simplistic

interference model

interference model, network can be disconnected, CCI is not considered, topology is not preserved

**Technique Objective Methodology Limitations** 

Greedy heuristic channel assignment algorithm based on I-Matrix interference model, links are visited in descending order of the node

degrees

load

In order to model orthogonal and non-orthogonal channels, a novel interference model called *channel overlapping matrix* is proposed in [18]. Consider a MRMC-WMN consisting of *N* routers, each equipped with *I* radios and *C* available frequency channels. For any two routers *a,b* ∈ *N*, a channel assignment vector *xab* of size *C x 1* can be defined which defines the channel on which the two routers are communicating (that particular element in the matrix becomes 1). Similarly, a vector of size *I x1* defines an interface assignment vector yab, which tells which radio belonging to a particular router *a* is used to communicate with router *b* (by changing the value of that element in the vector to 1). To model the partial overlap among channels, a *C x C* channel overlapping matrix *W* was proposed whose mth row, rth

> ��� <sup>=</sup> � F�(w)F�(w)dw �� ��

� F� � (w)dw ��

�� where *Fm(w)* denotes the power spectral density (PSD) function of the band-pass filter for channel *m* and consequently the same for channel *n*. Based on this channel overlap matrix, the authors have formulated a linear mixed-integer program consisting of few integer variables in order to solve a joint channel assignment, interface assignment and scheduling prob-

lem when the whole spectrum of the IEEE 802.11 frequencies is to be used.

Extended [19] to incorporate traffic load into I-Matrix for channel assignment, ensures network connectivity, links are visited in descending order of the traffic

M. Hoque [19] Maximization of

P. Duarte [20] Minimization of

column entry can be calculated as:

**Table 5.** Summary of the two I-Matrix based approaches.

**4.3. Channel Overlapping Matrix Model (CO-Matrix)** 

network capacity

network interference

[19] also proposes a heuristic channel assignment algorithm exploiting POCs based on the I-Matrix model. The algorithm assigns channels to the maximum number of links with the objective of minimizing network interference. The algorithm starts with an input describing the number of links that need to have channel assignments. The links are then assigned to their respective nodes and those nodes are sorted in descending order of their degrees. For each node, its incident link is assigned a channel which has the minimum interference calculated from the I-Matrix; accordingly after the channel assignment, the interference vectors of the corresponding channel are updated. This in turn forces the node to update the I-Matrix with the new channel's interference measurements against all other channels. [19] shows that using POCs can improve network capacity by as much as 15% compared to when only non-overlapping channels are used.

## *4.2.1. Channel assignment based on I-Matrix model*

In [20], the authors have extended the work of [19] by trying to remove some of the limitations in the proposed I-Matrix interference model and the channel assignment algorithm. More precisely, the CA algorithm in [19] sorts the links in descending order based on nodal degrees; however, this is not practical in multi hop WMNs as most of the traffic is targeted to gateway nodes. Therefore, the descending order should be based on the traffic load, implying that the busiest link should be assigned the channel first, i.e., gateway links should be first (thus being in accordance with typical WMN traffic characteristics). Another, shortcoming of [19] pointed out is that it suffers from the network partitioning problem, in the sense that some of the links may remain unassigned because the CA algorithm only assigns POCs and never assigns the same channel (as it tries to completely avoid the co-channel interference). To overcome this limitation, the I-Matrix model is modified to consider co-channel interference by adding a co-channel column to the matrix. This ensures network connectivity (because now the links can be assigned the same channels).

The algorithm of [20] consists of two phases. In the first phase, instead of the number of links as the input, links with traffic load information are provided as input and they are sorted in descending order of the traffic they carry. Then a suitable channel with the minimum interference is extracted from the I-Matrix. The second phase guarantees network connectivity in which the algorithm looks for those nodes that do not have a path to the gateway and if such nodes are found, their radios can be configured to the same channel on which one of their neighbor node's radio is already configured on. This ensures full network connectivity at the cost of co-channel interference. They have shown through experiments that the existence of such co-channel interference does not strongly influence the network performance (as such formerly disconnected nodes are likely to be at the peripheral of the network).

Table V summarizes the I-Matrix POCA schemes. It states the objective of each algorithm, the procedures used in obtaining a partially overlapping channel assignment algorithm, and the limitations of each scheme.


**Table 5.** Summary of the two I-Matrix based approaches.

120 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

non-overlapping channels are used.

network).

the limitations of each scheme.

*4.2.1. Channel assignment based on I-Matrix model*

ty (because now the links can be assigned the same channels).

[19] also proposes a heuristic channel assignment algorithm exploiting POCs based on the I-Matrix model. The algorithm assigns channels to the maximum number of links with the objective of minimizing network interference. The algorithm starts with an input describing the number of links that need to have channel assignments. The links are then assigned to their respective nodes and those nodes are sorted in descending order of their degrees. For each node, its incident link is assigned a channel which has the minimum interference calculated from the I-Matrix; accordingly after the channel assignment, the interference vectors of the corresponding channel are updated. This in turn forces the node to update the I-Matrix with the new channel's interference measurements against all other channels. [19] shows that using POCs can improve network capacity by as much as 15% compared to when only

In [20], the authors have extended the work of [19] by trying to remove some of the limitations in the proposed I-Matrix interference model and the channel assignment algorithm. More precisely, the CA algorithm in [19] sorts the links in descending order based on nodal degrees; however, this is not practical in multi hop WMNs as most of the traffic is targeted to gateway nodes. Therefore, the descending order should be based on the traffic load, implying that the busiest link should be assigned the channel first, i.e., gateway links should be first (thus being in accordance with typical WMN traffic characteristics). Another, shortcoming of [19] pointed out is that it suffers from the network partitioning problem, in the sense that some of the links may remain unassigned because the CA algorithm only assigns POCs and never assigns the same channel (as it tries to completely avoid the co-channel interference). To overcome this limitation, the I-Matrix model is modified to consider co-channel interference by adding a co-channel column to the matrix. This ensures network connectivi-

The algorithm of [20] consists of two phases. In the first phase, instead of the number of links as the input, links with traffic load information are provided as input and they are sorted in descending order of the traffic they carry. Then a suitable channel with the minimum interference is extracted from the I-Matrix. The second phase guarantees network connectivity in which the algorithm looks for those nodes that do not have a path to the gateway and if such nodes are found, their radios can be configured to the same channel on which one of their neighbor node's radio is already configured on. This ensures full network connectivity at the cost of co-channel interference. They have shown through experiments that the existence of such co-channel interference does not strongly influence the network performance (as such formerly disconnected nodes are likely to be at the peripheral of the

Table V summarizes the I-Matrix POCA schemes. It states the objective of each algorithm, the procedures used in obtaining a partially overlapping channel assignment algorithm, and

#### **4.3. Channel Overlapping Matrix Model (CO-Matrix)**

In order to model orthogonal and non-orthogonal channels, a novel interference model called *channel overlapping matrix* is proposed in [18]. Consider a MRMC-WMN consisting of *N* routers, each equipped with *I* radios and *C* available frequency channels. For any two routers *a,b* ∈ *N*, a channel assignment vector *xab* of size *C x 1* can be defined which defines the channel on which the two routers are communicating (that particular element in the matrix becomes 1). Similarly, a vector of size *I x1* defines an interface assignment vector yab, which tells which radio belonging to a particular router *a* is used to communicate with router *b* (by changing the value of that element in the vector to 1). To model the partial overlap among channels, a *C x C* channel overlapping matrix *W* was proposed whose mth row, rth column entry can be calculated as:

$$\mathcal{W}\_{mn} = \frac{\int\_{-\infty}^{+\infty} \mathcal{F}\_{\rm m}(\mathbf{w}) \mathcal{F}\_{\rm n}(\mathbf{w}) d\mathbf{w}}{\int\_{-\infty}^{+\infty} \mathcal{F}\_{\rm m}^2(\mathbf{w}) d\mathbf{w}}$$

where *Fm(w)* denotes the power spectral density (PSD) function of the band-pass filter for channel *m* and consequently the same for channel *n*. Based on this channel overlap matrix, the authors have formulated a linear mixed-integer program consisting of few integer variables in order to solve a joint channel assignment, interface assignment and scheduling problem when the whole spectrum of the IEEE 802.11 frequencies is to be used.

Partially Overlapping Channel Assignments in Wireless Mesh Networks 123

where *t1* and *t2* are the throughputs of two links (link-1 and link-2) each belonging to a pair of nodes which are placed at various locations to measure interference when the other link is idle. Similarly, *t'1* and *t'2* are the corresponding link throughputs when both links are active. As it can be seen from the formula, a higher *IF* value indicates lower interference. Experimental studies of [7] measured link interference (*IF*) and found out that for a particular channel separation, the interference between two links degrades quickly (higher IF factor) even with a slight increase in distance. From this *IF* metric, the interference range of two links separated by a fixed number of channels can be extracted. Multiple interference ranges are calculated for all five possible channel separations under different IEEE 802.11b

The concept of interference range is then applied to formulate the channel assignment problem into a weighted conflict graph model where the edges in the conflict graph are labeled by the minimum channel separation that two interfering links must have in order to have a conflict free communication. This weighted graph serves as an input to select the edges having minimum weights, eventually minimizing the overall network interference. A greedy partially overlapping channel assignment algorithm is proposed to solve the weighted conflict graph problem. The algorithm consists of two parts, namely *select* and *assign*. During *select*, the link with the minimum expected interference among all available links is selected. In the *assign* phase, a channel is assigned to this link with the minimum interference to all previously assigned channels. These steps are repeated until all links are covered, i.e., all links are assigned channels. In addition, the authors in [7] have also designed a novel genetic algorithm for channel assignment which produces slightly better results compared to the greedy algorithm for solving the assignment using the conflict graph. In order to map the partially overlapping channel assignment algorithm, a channel assigned to a single link is considered as a DNA sequence and the channel assignments of the all the links are mapped to an individual. In a typical genetic algorithm, a generation consists of a set of individuals; therefore, in this case, it will be a series of channel assignment solutions. An example of this mapping of the channel assignment problem to a genetic

The procedure for encoding the channel assignment scheme into an individual in a genetic algorithm requires first to sort the links, convert them to fixed length binary strings (a DNA sequence), and then to concatenate the binary strings together to form a single individual. The fitness function is defined as the inverse of the total interference in the network. The algorithm starts with randomly generating *N* channel assignment schemes (individuals).

bitrates (i.e., 2Mbps, 5.5Mbps, and 11Mbps).

algorithm is shown in Figure 12 [7].

**Figure 12.** Example of POCA using a genetic algorithm [7]

## *4.3.1. Channel Assignment based on Channel Overlapping Matrix Model*

Another channel assignment algorithm based on the channel overlapping matrix was proposed in [15]. Here, a joint channel assignment and flow allocation problem in MRMC WMNs is considered. [15] formulates this joint problem into a mixed integer linear program with the objectives of maximizing aggregate end-to-end throughput while minimizing queuing delays in the network (given that the traffic characteristics are known). In order to model the partially overlapping channels, the I-factor of [5] is used, capturing the overlap between two different nodes configured on two different channels. Based on the I-factor a *C x C* symmetric channel overlapping matrix *O* is proposed:

$$o\_{lj} = \begin{cases} 1 & l = f \\ \frac{I(5|l-j|)}{I(0)} & l \neq j \end{cases}$$

where *oij* represents an entry in the *ith* row and *jth* column of the matrix *O*. To model the impact of interference, a physical model is employed [25].

Table VI provide a side-by-side comparison of the two algorithms surveyed above based on their objectives, the methodology used to assign POCs, and their limitations.


**Table 6.** Comparison of the two CO-Matrix based POCA schemes.

#### **4.4. Conflict Graph based Model (CGM)**

#### *4.4.1. Channel Assignment with Partially Overlapped Channels*

A weighted conflict graph model is proposed in [7] to more accurately model interference among nodes operating on overlapping channels. In order to measure the partial interference, a metric called interference factor (IF) is defined:

$$IF = \frac{t\_1' + t\_2'}{t\_1 + t\_2}$$

where *t1* and *t2* are the throughputs of two links (link-1 and link-2) each belonging to a pair of nodes which are placed at various locations to measure interference when the other link is idle. Similarly, *t'1* and *t'2* are the corresponding link throughputs when both links are active. As it can be seen from the formula, a higher *IF* value indicates lower interference. Experimental studies of [7] measured link interference (*IF*) and found out that for a particular channel separation, the interference between two links degrades quickly (higher IF factor) even with a slight increase in distance. From this *IF* metric, the interference range of two links separated by a fixed number of channels can be extracted. Multiple interference ranges are calculated for all five possible channel separations under different IEEE 802.11b bitrates (i.e., 2Mbps, 5.5Mbps, and 11Mbps).

The concept of interference range is then applied to formulate the channel assignment problem into a weighted conflict graph model where the edges in the conflict graph are labeled by the minimum channel separation that two interfering links must have in order to have a conflict free communication. This weighted graph serves as an input to select the edges having minimum weights, eventually minimizing the overall network interference. A greedy partially overlapping channel assignment algorithm is proposed to solve the weighted conflict graph problem. The algorithm consists of two parts, namely *select* and *assign*. During *select*, the link with the minimum expected interference among all available links is selected. In the *assign* phase, a channel is assigned to this link with the minimum interference to all previously assigned channels. These steps are repeated until all links are covered, i.e., all links are assigned channels. In addition, the authors in [7] have also designed a novel genetic algorithm for channel assignment which produces slightly better results compared to the greedy algorithm for solving the assignment using the conflict graph. In order to map the partially overlapping channel assignment algorithm, a channel assigned to a single link is considered as a DNA sequence and the channel assignments of the all the links are mapped to an individual. In a typical genetic algorithm, a generation consists of a set of individuals; therefore, in this case, it will be a series of channel assignment solutions. An example of this mapping of the channel assignment problem to a genetic algorithm is shown in Figure 12 [7].

**Figure 12.** Example of POCA using a genetic algorithm [7]

122 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

Another channel assignment algorithm based on the channel overlapping matrix was proposed in [15]. Here, a joint channel assignment and flow allocation problem in MRMC WMNs is considered. [15] formulates this joint problem into a mixed integer linear program with the objectives of maximizing aggregate end-to-end throughput while minimizing queuing delays in the network (given that the traffic characteristics are known). In order to model the partially overlapping channels, the I-factor of [5] is used, capturing the overlap between two different nodes configured on two different channels. Based on the I-factor a *C* 

> ������������������� � � ���|���|) ���) �������������

where *oij* represents an entry in the *ith* row and *jth* column of the matrix *O*. To model the

Table VI provide a side-by-side comparison of the two algorithms surveyed above based on

**Technique Objective Methodology Limitations** 

Joint CA, interface assignment and flow scheduling algorithm based on channel overlapping matrix to model POCs / linear mixed-integer program formulation

Joint CA and flow allocation algorithm based on CO matrix / mixed integer linear

program formulation

A weighted conflict graph model is proposed in [7] to more accurately model interference among nodes operating on overlapping channels. In order to measure the partial interfer-

> �� � �� ���� � �����

SI is not considered, extensive computational complexity

extensive computational complexity, offline solution; no bounds on completion

*4.3.1. Channel Assignment based on Channel Overlapping Matrix Model*

��� � �

their objectives, the methodology used to assign POCs, and their limitations.

*x C* symmetric channel overlapping matrix *O* is proposed:

impact of interference, a physical model is employed [25].

Minimization of the maximum link utilization

Maximization of the aggregate endto-end flow allocations

**Table 6.** Comparison of the two CO-Matrix based POCA schemes.

ence, a metric called interference factor (IF) is defined:

*4.4.1. Channel Assignment with Partially Overlapped Channels* 

**4.4. Conflict Graph based Model (CGM)** 

A. Rad [18]

V. Bukkapatanam

[15]

The procedure for encoding the channel assignment scheme into an individual in a genetic algorithm requires first to sort the links, convert them to fixed length binary strings (a DNA sequence), and then to concatenate the binary strings together to form a single individual. The fitness function is defined as the inverse of the total interference in the network. The algorithm starts with randomly generating *N* channel assignment schemes (individuals).

The selection strategy selects two individuals (from the *N* sized population) by using the roulette wheel selection method and then choosing the better one of them according to the tournament selection strategy. These two strategies are commonly referred to as the stochastic selection strategy. After the selection stage, a reproduction step is performed in which one-point crossover and two-point crossover and mutation is applied to the selected two individuals. Both the greedy and genetic channel assignment algorithms are evaluated on various sets of topologies. The greedy algorithm is faster but the genetic algorithm provides better results and thus can generate better channel assignment schemes which eventually result in improved network capacity.

Partially Overlapping Channel Assignments in Wireless Mesh Networks 125

assigning colors to vertices such that the conflicts is minimized. In each iteration, a tabu list of the colors (channels) that have already been assigned is maintained to avoid their assignment a second time and to achieve fast convergence. This phase terminates after a certain number of iterations (solutions). In the second phase, the interface constraints are satisfied by a merge operation in which, those nodes who have been assigned more distinct colors (channels) to links than how many radios they have, have their colors merged to bring them to be equal to their number of radios. To ensure network connectivity by this merge operation, the just changed color is propagated to all the other links that were assigned the old color to repeat the merge operation on them (those links must be part of the

A distributed greedy heuristic channel assignment algorithm based on Max K-cut is also proposed by the authors [17]. Given a conflict graph, the max K-cut problem deals with dividing vertices into K partitions to maximize the number of edges that lie in different partitions. Two formulations of their proposed channel assignment problem are provided, one is a semi-definite programming (SDP) formulation and the other is a linear programming formulation in order to obtain tighter lower bounds on optimal network interference. The linear programming formulation is modified to capture partial interference that exist when overlapping channels are being used and in order to make the formulation compatible to POCs. The SDP formulation however turns out to be too complex and therefore, it is not

Mishra et al., in [4] formulate the channel assignment problem as a weighted variant of the graph coloring problem incorporating realistic channel interference based on the I-factor model. The channel assignment problem is formulated as a weighted graph coloring problem with APs representing vertices in the graph and potential interference among them is represented by an edge between the vertices in the weighted graph. The weight on each edge depicts the significance of using different colors for the vertices that are connected by that edge. The weights are defined as the number of clients attached to an AP, scaled by the degree of interference between the chosen channels (I-factor). Therefore, the goal of the weighted graph coloring solution is to minimize the objective function. A higher weight translates to higher amounts of partial overlap between the channels; the algorithm attempts to assign different channels or channels with higher spatial difference to the edges in the graph. An edge weight of zero means that there is no interference among the clients of the corresponding APs. It is proved that the proposed weighted graph coloring problem is NPhard, therefore, two distributed channel assignment techniques are proposed with the objective of minimizing the overall network interference. The first technique tries to minimize each individual AP's interference and does not require any inter-AP communication. It consists of two steps; i.e. an initialization and an optimization step. The initialization step starts with assigning the same channel to all the APs. In the optimization step (which is incremental in nature), each AP performs the greedy optimization trying to minimize its local maximum interference by taking the maximum weight edge (which eventually minimizes the objective function). The algorithm stops when the network achieves an acceptable "coloring" configuration. The second channel assignment algorithm

common node).

been evaluated.

#### *4.4.2. Partially Overlapped Channel Assignment (POCAM)*

In [16], a new partially overlapped channel assignment for multi-radio multi-channel wireless mesh networks called POCAM is proposed, where the interference model stems from measurements of commercial radios using real testbeds. An extensive set of testbed experiments were performed to analyze the effect of partial interference and self-interference in WMNs. Through these tests it is shown that the self-interference issue is worse than it is usually assumed as it still needs to be considered even if the two radios on the same node are configured on non-overlapping channels. The proposed POCAM algorithm consists of two steps and incorporates the traffic load distribution. First, a transformation of the partially overlapped channel assignment problem into a weighted conflict graph (WCG) is performed followed by calculation on that weighted conflict graph. The WCG is a graph *G = (V,E)* where *V* represents the number of nodes in a WMN. For each edge in *E*, edge weights are assigned based on a table in [7] capturing interference ranges against each channel separation. The WCG is constructed with links represented as vertices in the conflict graph and there is a weighted edge between two vertices in the conflict graph if those two links interfere. The WCG formulation becomes a constraint satisfaction problem (CSP) which is an NP hard problem. CSPs are usually solved by applying backtracking search algorithms [27], thus [7] shows a design of three heuristics specially tailored for WMN characteristics.

#### *4.4.3. Minimum Interference Channel Assignment*

The authors in [17] propose a centralized channel assignment algorithm based on the tabusearch heuristic [26] which is used to find quasi-optimal solution for a graph coloring problem. The objective of the channel assignment algorithm is to minimize the overall network interference by assigning channels to links in a WMN. Network interference is captured as a graph coloring problem by assigning colors (channels) to the vertices of a conflict graph using K colors while maintaining interface constraints. The interface constraints limit the number of different channels assigned to interfaces belonging to a single node by the number of interfaces on that node. The proposed tabu-search based channel assignment algorithm consists of two phases. In the first phase, the algorithm starts with a random solution by assigning random colors to each vertex in the conflict graph, followed by a series of solutions which are created with the objective of minimizing overall network interference by assigning colors to vertices such that the conflicts is minimized. In each iteration, a tabu list of the colors (channels) that have already been assigned is maintained to avoid their assignment a second time and to achieve fast convergence. This phase terminates after a certain number of iterations (solutions). In the second phase, the interface constraints are satisfied by a merge operation in which, those nodes who have been assigned more distinct colors (channels) to links than how many radios they have, have their colors merged to bring them to be equal to their number of radios. To ensure network connectivity by this merge operation, the just changed color is propagated to all the other links that were assigned the old color to repeat the merge operation on them (those links must be part of the common node).

124 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

result in improved network capacity.

*4.4.2. Partially Overlapped Channel Assignment (POCAM)* 

*4.4.3. Minimum Interference Channel Assignment* 

The selection strategy selects two individuals (from the *N* sized population) by using the roulette wheel selection method and then choosing the better one of them according to the tournament selection strategy. These two strategies are commonly referred to as the stochastic selection strategy. After the selection stage, a reproduction step is performed in which one-point crossover and two-point crossover and mutation is applied to the selected two individuals. Both the greedy and genetic channel assignment algorithms are evaluated on various sets of topologies. The greedy algorithm is faster but the genetic algorithm provides better results and thus can generate better channel assignment schemes which eventually

In [16], a new partially overlapped channel assignment for multi-radio multi-channel wireless mesh networks called POCAM is proposed, where the interference model stems from measurements of commercial radios using real testbeds. An extensive set of testbed experiments were performed to analyze the effect of partial interference and self-interference in WMNs. Through these tests it is shown that the self-interference issue is worse than it is usually assumed as it still needs to be considered even if the two radios on the same node are configured on non-overlapping channels. The proposed POCAM algorithm consists of two steps and incorporates the traffic load distribution. First, a transformation of the partially overlapped channel assignment problem into a weighted conflict graph (WCG) is performed followed by calculation on that weighted conflict graph. The WCG is a graph *G = (V,E)* where *V* represents the number of nodes in a WMN. For each edge in *E*, edge weights are assigned based on a table in [7] capturing interference ranges against each channel separation. The WCG is constructed with links represented as vertices in the conflict graph and there is a weighted edge between two vertices in the conflict graph if those two links interfere. The WCG formulation becomes a constraint satisfaction problem (CSP) which is an NP hard problem. CSPs are usually solved by applying backtracking search algorithms [27],

thus [7] shows a design of three heuristics specially tailored for WMN characteristics.

The authors in [17] propose a centralized channel assignment algorithm based on the tabusearch heuristic [26] which is used to find quasi-optimal solution for a graph coloring problem. The objective of the channel assignment algorithm is to minimize the overall network interference by assigning channels to links in a WMN. Network interference is captured as a graph coloring problem by assigning colors (channels) to the vertices of a conflict graph using K colors while maintaining interface constraints. The interface constraints limit the number of different channels assigned to interfaces belonging to a single node by the number of interfaces on that node. The proposed tabu-search based channel assignment algorithm consists of two phases. In the first phase, the algorithm starts with a random solution by assigning random colors to each vertex in the conflict graph, followed by a series of solutions which are created with the objective of minimizing overall network interference by A distributed greedy heuristic channel assignment algorithm based on Max K-cut is also proposed by the authors [17]. Given a conflict graph, the max K-cut problem deals with dividing vertices into K partitions to maximize the number of edges that lie in different partitions. Two formulations of their proposed channel assignment problem are provided, one is a semi-definite programming (SDP) formulation and the other is a linear programming formulation in order to obtain tighter lower bounds on optimal network interference. The linear programming formulation is modified to capture partial interference that exist when overlapping channels are being used and in order to make the formulation compatible to POCs. The SDP formulation however turns out to be too complex and therefore, it is not been evaluated.

Mishra et al., in [4] formulate the channel assignment problem as a weighted variant of the graph coloring problem incorporating realistic channel interference based on the I-factor model. The channel assignment problem is formulated as a weighted graph coloring problem with APs representing vertices in the graph and potential interference among them is represented by an edge between the vertices in the weighted graph. The weight on each edge depicts the significance of using different colors for the vertices that are connected by that edge. The weights are defined as the number of clients attached to an AP, scaled by the degree of interference between the chosen channels (I-factor). Therefore, the goal of the weighted graph coloring solution is to minimize the objective function. A higher weight translates to higher amounts of partial overlap between the channels; the algorithm attempts to assign different channels or channels with higher spatial difference to the edges in the graph. An edge weight of zero means that there is no interference among the clients of the corresponding APs. It is proved that the proposed weighted graph coloring problem is NPhard, therefore, two distributed channel assignment techniques are proposed with the objective of minimizing the overall network interference. The first technique tries to minimize each individual AP's interference and does not require any inter-AP communication. It consists of two steps; i.e. an initialization and an optimization step. The initialization step starts with assigning the same channel to all the APs. In the optimization step (which is incremental in nature), each AP performs the greedy optimization trying to minimize its local maximum interference by taking the maximum weight edge (which eventually minimizes the objective function). The algorithm stops when the network achieves an acceptable "coloring" configuration. The second channel assignment algorithm requires collaboration among APs and is intended to minimize interference by reducing the number of clients that are experiencing interference. Simulations and testbed experiments show that the proposed channel assignment algorithms achieve 45.5% reduction in interference when the network is sparse. The algorithms are scalable and provide better performance than existing channel assignment algorithms.

Partially Overlapping Channel Assignments in Wireless Mesh Networks 127

In this section, we provided a survey of existing POCA schemes in WMNs and summarized them based on their objectives, methodologies and limitations. Table VIII presents an overall summary of all the POCA approaches examined; the table shows the comparison of these

In spite of a reasonable amount of research in the late literature, there are still some challenges and open issues that need to be addressed in designing efficient channel assignment schemes exploiting POCs, particularly in WMNs. Below, we outline what we believe some

As explained in Section 2.2, self-interference restricts parallel communication originating from a node having more than one radio unless these radios operate on completely orthogonal channels (OCs). Since, there are only three OCs for IEEE 802.11b/g in the 2.4GHz band, there is a need to further investigate how the self-interference issue can be better addressed. Few CA schemes have addressed self-interference in multi radio MWNs and we believe that

More robust and efficient modeling schemes are required to intelligently capture the interference experienced by neighboring nodes operating on POCs in MRMC-WMNs. Although existing approaches do partially capture one or two types of interferences in a WMN, they are not complete solutions (they do not capture all the different types of interferences realistically). Furthermore issues arising from geographical positions of neighboring nodes and the availabil-

Most existing simulators [29-31] still do not support underlying physical models and easy POC evaluation scripting to capture partial interference between adjacent nodes in WMNs. However, we believe the reason for the lack of this feature is because the concept of POCs in

CA schemes is relatively new and is still progressing and evolving to its maturity.

ity of variable data rates still pose major challenges for POCA algorithms.

**4.5. Summary of all POCA approaches** 

schemes based on the following six questions:

**5. Open issues in POCA design** 

of these challenges and open issues are.

**5.1. Capturing self interference** 

there is room for improvement.

**5.3. Lack of simulation tools** 

**5.2. Modeling interference of POCs** 

*Implementation:* Is the proposed POCA centralized or distributed?

*Connectivity:* Does the algorithm ensure network connectivity?

 *Multi-radio support:* Is the POCA scheme designed for multi-radio WMNs? *Interference:* What type of interference does the proposed POCA capture? *Routing dependency:* Is the POCA dependent on a particular routing algorithm?

*Channel switching frequency:* How frequently are the channels switched?

A heuristic-based channel assignment and link scheduling algorithm is proposed in [9] to enhance network capacity by exploiting partially overlapping channels in WMNs. Since, finding optimal channel assignment and link scheduling together for a given network is NPhard, heuristic based policies are summoned to provide a sub-optimal solution. The problem is divided into two parts; first channel assignment is performed and then based on that an optimal link scheduling is explored. For the channel allocation, a genetic algorithm [28] is used. The authors have also studied some of the factors that influence the performance of POCs in channel assignment in a wireless mesh network (such as node density and node distribution).

All of the above three POCA schemes make use of graph-theory to model partial overlap among nodes in MRMC-WMNs except [7] which is designed for single radio WMNs. The approaches then apply a heuristic for channel assignment. Table VII provides a side-byside comparison of the three POCA schemes based on their objectives, methodology, limitations.


**Table 7.** Comparison on the objective, methodology and limitations of POCA schemes based on CGM.

## **4.5. Summary of all POCA approaches**

126 Wireless Mesh Networks – Efficient Link Scheduling, Channel Assignment and Network Planning Strategies

performance than existing channel assignment algorithms.

distribution).

tations.

POCAM [16] Minimization of

Y. Ding [7] Minimization of

A. Subramanian [17] Minimization of

network interference

network interference

network interference

requires collaboration among APs and is intended to minimize interference by reducing the number of clients that are experiencing interference. Simulations and testbed experiments show that the proposed channel assignment algorithms achieve 45.5% reduction in interference when the network is sparse. The algorithms are scalable and provide better

A heuristic-based channel assignment and link scheduling algorithm is proposed in [9] to enhance network capacity by exploiting partially overlapping channels in WMNs. Since, finding optimal channel assignment and link scheduling together for a given network is NPhard, heuristic based policies are summoned to provide a sub-optimal solution. The problem is divided into two parts; first channel assignment is performed and then based on that an optimal link scheduling is explored. For the channel allocation, a genetic algorithm [28] is used. The authors have also studied some of the factors that influence the performance of POCs in channel assignment in a wireless mesh network (such as node density and node

All of the above three POCA schemes make use of graph-theory to model partial overlap among nodes in MRMC-WMNs except [7] which is designed for single radio WMNs. The approaches then apply a heuristic for channel assignment. Table VII provides a side-byside comparison of the three POCA schemes based on their objectives, methodology, limi-

**Technique Objective Methodology Limitations** 

**Table 7.** Comparison on the objective, methodology and limitations of POCA schemes based on CGM.

Weighted conflict graph, constraint satisfaction problem, heuristic based backtracking search

Weighted conflict graph, graph

coloring, greedy CA algorithm, genetic algorithm based on partially overlapped channel assignment

Conflict graph, Max K-cut, SDP and ILP formulation, tabu based CA and heuristic based greedy CA algorithm Simplistic

extensive computational complexity, edge weight assignment is difficult, does not consider traffic load

Extensive computational complexity, SI is not considered, ignores switching overhead

interference model, no SI is considered

SI is not considered,

algorithm

In this section, we provided a survey of existing POCA schemes in WMNs and summarized them based on their objectives, methodologies and limitations. Table VIII presents an overall summary of all the POCA approaches examined; the table shows the comparison of these schemes based on the following six questions:

