# Energy Efficient Multicast Communication in Cognitive Radio Wireless Mesh Network
## 3 Network Model and Problem Formulation  
Consider a CR-WMN with N nodes. First, each node employs a spectrum sensing technique to identify the channels unused by the PU. In this work, any specific spectrum sensing technique was not considered as it is beyond the scope of this work. Once each node \(i\) performs spectrum sensing, it comes up with a set of available channels \(C_{i}\) unused by the PUs. The available channels for two nodes may be different from each other depending on their geographical location. Furthermore, it is also assumed that each node shares its spectrum sensing results with its neighboring nodes via a control channel. The control channel setup is also beyond the scope of this work. It is assumed that each node transmits with its maximum transmission power P and has a transmission range \(R_{T}\). Two nodes \(i\) and \(j\) are said to be neighbors if the distance \(\text{d}_{ij}\) between them is less than \(R_{T}\) and \(C_{i}\cap C_{j}\
eq\O\). There is a set \(K\) of multicast sessions. Each multicast session \(k\in K\) consists of a source node and multiple destination nodes. For each session, a multicast routing tree is constructed rooted at the source node. The multicast tree consists of source, forwarding/relay, and destination nodes. The multicasting on a multicast tree can be broken down into a number of local forwarding operations. For each forwarding operation, a hyperlink \(H(i,\,h,\,I)\) is established over channel \(h\), where \(i\) is the forwarding node and \(I\) is the set of receiving \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Ref** & **Year** & **Objective** & **CR** & **WMN** & **Multicast** & **Approach** & **Remarks** \\ \hline
[11] & 2013 & Channel allocation and multicast routing in CRN & & & Optimization problem which jointly defines multicast routes and channel assignments & Increased multicast throughput in multi-hop CRNs \\ \hline
[12] & 2017, & Design of cooperative non-orthogonal multicast cognitive & & & Implementation of multicast non-orthogonal multiple access (NOMA) in CRNs & Significant performance gains were achieved \\ \hline
[13] & 2018, & 2017 & & & A multicast tree construction method based on a minimal spanning tree & Reduced bandwidth usage \\ \hline
[15] & 2012 & & Minimum spanning tree-based multicast routing protocol for dynamic spectrum access networks & & & Increased total throughput and increased the routing protocol is proposed & Increased total throughput and increased the delivery rate of packets \\ \hline
[17] & 2013 & & Joint power and rate allocation for spectrum sharing cognitive radio multicast networks under service outage constraint & & & Maximized the average multicast rate in CRNs \\ \hline
[18] & 2018 & & An efficient channel assignment algorithm for multicast wireless mesh networks & & & Considered both partially channel assignment algorithm & Considered both partially overlapping as well as orthogonal channels \\ \hline
[19] & 2018 & & Interference optimization for multicast and broadcast traffic in multi-radio multi-channel multi-channel networks with & & Considered multi-channel multicast problem for a multi-radio network of wireless mesh nodes with directional antennas \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._nodes. The energy consumed by any node \(i\) involved in a hyperlink for a duration of bit \(\tau\) can be modelled as  
\[E_{i}= \begin{cases}E_{i}^{t}+E_{i}^{c}&\text{if $i$ is a source node;}\\ E_{i}^{t}+E_{i}^{t}+E_{i}^{r}&\text{if $i$ is a relay node;}\\ E_{i}^{r}&\text{if $i$ is a destination node;}\end{cases}  \tag{1}\]  
where \(E_{i}^{t}=\text{P}\tau\) is the transmission energy consumed per bit, \(E_{i}^{c}\) is the energy consumed per bit to activate the electronic circuitry and perform digital processing, and \(E_{i}^{r}\) is the energy consumed per bit at the receiver.