**4. Classification of POCA Schemes in Wireless Mesh Networks**

Partially overlapping channel assignment (POCA) schemes can be classified based on different criteria and approaches. The criteria that we have used for classification is the *interference model*, which is defined as the technique for capturing interference of radios belonging to nodes operating on partially overlapping channels in a WMN. Figure 10 presents the classification on which the rest of the section is based. Note that our classification based on interference model may not create disjoint categories and thus, a particular scheme may have significant overlaps with another scheme belonging to a different category.

Partially Overlapping Channel Assignments in Wireless Mesh Networks 115

of intersection between a transmitter's signal spectrum and receiver's band-pass filter, we can calculate how much overlap there is between these signals; this is defined as the interference factor (I-factor). Since, IEEE 802.11 standards operate on a set of discrete channels,

The authors of [5] have also revised two existing channel assignment algorithms in the context of WLANs and WMNs and have applied the I-factor model to these algorithms. First, an existing algorithm [22] was modified which is a centralized greedy-style approach for CA in WLANs using only orthogonal channels with the objective of increasing overall spectrum utilization. The algorithm employs an indicator variable to model the interference in WLANs and the authors have modified this indicator variable to capture not only the orthogonal channels (which was previously the case) but also channels with partial overlap (using their I-factor model). The actual channel assignment problem is formulated as a conflict set coloring problem where a conflict is present when clients belonging to a particular AP experience interference from neighboring clients (which are attached to their respective APs). The objective function is a min-max formulation to capture the total interference experienced by each client. The algorithm starts with a random permutation on how channels are assigned to APs; this is followed by the computation of the objective function. The best channel with minimum interference among the available channels is chosen and the process repeats for each AP. The modification lies in the interference calculation function to incorporate POCs into the algorithm. Interferences among channels with partial overlaps are calculated based on the I-factor interference model either empirically or analytically; this enables the possibility of assigning

Still in [5], another CA algorithm which was designed for wireless mesh networks using only orthogonal channels [21] was modified to include POCs. It is a joint channel assignment, routing and link scheduling approach and a mathematical formulation in the form of a linear program (LP) is presented. The formulation also includes an indicator variable to model interference in the network. The authors have modified the link scheduling part of the joint mathematical formulation to change the conflict links' constraints to include the Ifactor model (partial interference). They have evaluated the performance of this modified LP to show improved throughput in WMNs. The revised algorithms demonstrate that careful use of POCs can lead to significant improvements in spectrum utilization and application performance. They have performed extensive simulations to show that the use of POCs can improve network throughput (the extent of which depends on the nodal density of the net-

*4.1.2. Channel Assignment Exploiting Partially Overlapping Channels (CAEPO)* 

The authors in [12] have proposed a POC channel assignment scheme called CAEPO. The main contribution of their work is the design of a traffic-aware metric that captures the degree of overlap among the channels when measuring interference. It is a hybrid distributed channel assignment protocol, where each node collects information locally and hence performs the channel assignment locally. The proposed I-factor based metric captures

the continuous variable *δ* can be discretized as follows: *δ = 5|i-j|* (in MHz).

all available channels to the WLAN.

work).

**Figure 10.** Classification of partially overlapping channel assignment algorithms based on the interference model employed.

#### **4.1. Interference factor model (I-Factor)**

#### *4.1.1. Revised Channel Assignment Schemes for Wireless Networks*

One of the first models to capture partial interference in wireless networks was presented by A. Mishra, et al. in [5]. They have extensively studied the practicality of using POCs in WLANs and WMNs. Through analytical formulation they have shown the benefits of POCs in terms of how they increase network capacity and improve channel-reuse. In order to model the interference generated by nodes operating on channels with partial overlaps, they have proposed a novel concept called interference factor (I-factor) capturing the extent of overlap between two communicating nodes. They define I-factor as:

$$IF\_{\left(t,r\right)}\left(\delta\right) = \int\_{-\infty}^{+\infty} \mathcal{S}\_t\left(f\right)B\_r\left(f-\delta\right)df$$

where *t* and *r* are indices of the transmitting and receiving nodes, and *δ* denotes the difference of the frequencies of the transmitting and receiving nodes. In other words, parameter *δ* represents the amount of overlap between the two frequencies and is defined as a continuous variable*. St(f)* is the transmitter's signal's power distribution and *Br(f)* denotes the frequency response of the receiver's band pass filter. In lay man terms: if we measure the area of intersection between a transmitter's signal spectrum and receiver's band-pass filter, we can calculate how much overlap there is between these signals; this is defined as the interference factor (I-factor). Since, IEEE 802.11 standards operate on a set of discrete channels, the continuous variable *δ* can be discretized as follows: *δ = 5|i-j|* (in MHz).

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

Partially overlapping channel assignment (POCA) schemes can be classified based on different criteria and approaches. The criteria that we have used for classification is the *interference model*, which is defined as the technique for capturing interference of radios belonging to nodes operating on partially overlapping channels in a WMN. Figure 10 presents the classification on which the rest of the section is based. Note that our classification based on interference model may not create disjoint categories and thus, a particular scheme may have

**Figure 10.** Classification of partially overlapping channel assignment algorithms based on the interfer-

One of the first models to capture partial interference in wireless networks was presented by A. Mishra, et al. in [5]. They have extensively studied the practicality of using POCs in WLANs and WMNs. Through analytical formulation they have shown the benefits of POCs in terms of how they increase network capacity and improve channel-reuse. In order to model the interference generated by nodes operating on channels with partial overlaps, they have proposed a novel concept called interference factor (I-factor) capturing the extent of

> ��(���)(�) ��� ��(�)��(� � �)�� ��

�� where *t* and *r* are indices of the transmitting and receiving nodes, and *δ* denotes the difference of the frequencies of the transmitting and receiving nodes. In other words, parameter *δ* represents the amount of overlap between the two frequencies and is defined as a continuous variable*. St(f)* is the transmitter's signal's power distribution and *Br(f)* denotes the frequency response of the receiver's band pass filter. In lay man terms: if we measure the area

ence model employed.

**4.1. Interference factor model (I-Factor)** 

*4.1.1. Revised Channel Assignment Schemes for Wireless Networks* 

overlap between two communicating nodes. They define I-factor as:

**4. Classification of POCA Schemes in Wireless Mesh Networks** 

significant overlaps with another scheme belonging to a different category.

The authors of [5] have also revised two existing channel assignment algorithms in the context of WLANs and WMNs and have applied the I-factor model to these algorithms. First, an existing algorithm [22] was modified which is a centralized greedy-style approach for CA in WLANs using only orthogonal channels with the objective of increasing overall spectrum utilization. The algorithm employs an indicator variable to model the interference in WLANs and the authors have modified this indicator variable to capture not only the orthogonal channels (which was previously the case) but also channels with partial overlap (using their I-factor model). The actual channel assignment problem is formulated as a conflict set coloring problem where a conflict is present when clients belonging to a particular AP experience interference from neighboring clients (which are attached to their respective APs). The objective function is a min-max formulation to capture the total interference experienced by each client. The algorithm starts with a random permutation on how channels are assigned to APs; this is followed by the computation of the objective function. The best channel with minimum interference among the available channels is chosen and the process repeats for each AP. The modification lies in the interference calculation function to incorporate POCs into the algorithm. Interferences among channels with partial overlaps are calculated based on the I-factor interference model either empirically or analytically; this enables the possibility of assigning all available channels to the WLAN.

Still in [5], another CA algorithm which was designed for wireless mesh networks using only orthogonal channels [21] was modified to include POCs. It is a joint channel assignment, routing and link scheduling approach and a mathematical formulation in the form of a linear program (LP) is presented. The formulation also includes an indicator variable to model interference in the network. The authors have modified the link scheduling part of the joint mathematical formulation to change the conflict links' constraints to include the Ifactor model (partial interference). They have evaluated the performance of this modified LP to show improved throughput in WMNs. The revised algorithms demonstrate that careful use of POCs can lead to significant improvements in spectrum utilization and application performance. They have performed extensive simulations to show that the use of POCs can improve network throughput (the extent of which depends on the nodal density of the network).

#### *4.1.2. Channel Assignment Exploiting Partially Overlapping Channels (CAEPO)*

The authors in [12] have proposed a POC channel assignment scheme called CAEPO. The main contribution of their work is the design of a traffic-aware metric that captures the degree of overlap among the channels when measuring interference. It is a hybrid distributed channel assignment protocol, where each node collects information locally and hence performs the channel assignment locally. The proposed I-factor based metric captures

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

Partially Overlapping Channel Assignments in Wireless Mesh Networks 117

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,

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

��(�� �) =1− ���������� ��(��� ��)}

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

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

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

��(��� ��)

load-aware CAEPO-G achieves much better performance than the original CAEPO.

configured on POCs. The proposed interference factor *Ic(i,j)* is defined as follows:

two nodes are orthogonal if and only if their interference factor value is equal to 0.

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

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

same.

nearest integer).

$$Interference[i] = \sum\_{j \in N(l)} f[i][j] \* B(j)$$

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 [23]).

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