# An Integrated Access and Backhaul Approach to Sustainable Dense Small Cell Network Planning
## 2 System Model
### Communication Model  
The foundation of our analysis revolves around understanding the received power, \(P_{r}\), of a particular node. Mathematically, this can be described by the following [15]:  
\[P_{r} =P_{node}+G_{all}-L_{all}-N_{0}, \tag{1}\] \[G_{all} =G_{t}+G_{r},\] (2) \[L_{all} =L_{r}+O_{tr}+L_{loss},\] (3) \[N_{0} =-174+10\log_{10}(W), \tag{4}\]  
Here, \(P_{r}\) represents the received power in dB, while \(G_{all}\) signifies the cumulative antenna gains from the transmitting side \(G_{t}\) and the receiving side \(G_{r}\). \(L_{all}\) embodies the total losses, which include the path loss \(L_{loss}\), atmospheric attenuation \(O_{tr}\), and rain-induced attenuation \(L_{r}\), with \(N_{0}\) denoting thermal noise.  
Delving deeper into the path loss, it emerges as a function of the distance between nodes and encapsulates the consequences of signal propagation. Given the pronounced attenuation characteristics of 60 GHz mmWave, our parameter selections are crucial. We use the parameters 12.6 dB/km from ITU-R P.838 for rain attenuation if we consider an average annual rainfall rate of 35 mm/h [16]. To further strengthen our analysis, we also considered oxygen absorption of about 16 dB/km [17]. We undertook a comprehensive link budget analysis to ascertain the viability and performance of our proposed communication system and Figure 4 shows the results of the analysis.  
Given the challenges posed by such pronounced path losses, the design aspiration for our system is heavily influenced by the advantages of antenna design. For the access  
Figure 4: Achievable data rate for access and backhaul with transmit power 30 dbm, antenna gain for access side 5 dBi, directional antenna gain for backhaul side 30 dBi, and pathloss exponent 2.  
side, the preference is towards omni-directional antennas. Their innate ability to ensure consistent radiation across all horizontal trajectories is encapsulated by the gain expression:  
\[G_{\text{omni}}=G_{0}, \tag{5}\]  
where \(G_{0}\) symbolizes the invariant gain regardless of direction.  
On the flip side, backhaul links demand a more directional approach, specifically utilizing sector antennas. These are strategically chosen to counteract the challenges posed by atmospheric and rain attenuations. Their spatial filtering capabilities stand as a bulwark against interference, with the gain between two nodes expressed as:  
\[G_{tr}=\begin{cases}G_{t}\cdot G_{r}&\text{if }\frac{-\theta_{t}pBW}{2}\leq \psi\leq\frac{\theta_{t}pBW}{2}\\ 0&\text{otherwise}\end{cases} \tag{6}\]  
We delineate our communication model with the distinct operational dynamics of access and backhaul links. The access link, characterized by connections between nodes/donors and user equipment, capitalizes on the ubiquitous coverage afforded by omni-directional antennas. In this domain, each node/donor produces a circular coverage footprint, ensuring extensive and uniform service delivery to user devices. In contrast, the backhaul link, tasked with establishing connections among nodes and between nodes and donors, employs fixed directional links. The employment of fixed directional links amplifies link reliability, curtails interference, and bolsters capacity. Therefore, we use circular representation for omni-directional coverage and use straight lines when considering backhaul links. Our primary goal remains to determine the minimum number of these conceptual circles required for full coverage. Such a modeling perspective finds its roots in prior scholarly research [18].