# Binary PSO with Classification Trees Algorithm for Enhancing Power Efficiency in 5G Networks
## 3 System Model  
Consider 5G HetNet with densely deployed Voronoi SCs, where the SCs are deployed within the MCs coverage area. In this scenario, the MCs and the SCs utilize different frequency bands, mitigating the cross-tier interference between them. The MCs stay active to maintain the coverage of the network when the SCs are turned off. On the other hand, the SCs are either active (on) or asleep (off). When the SC is turned off, regular discovery signals are sent by the SC to be detected by any potential user. Each UE reports its channel state information and its reference signal received power (RSRP) to its SC. The SC sub-band allocation and the SC switching is organized by a main controller, or the MC if the main controller is absent, to collect the data from the SCs, allocate the sub-bands to the SCs, and determine the on/off switching decisions of the SCs. Furthermore, it is assumed that all UEs in every SC are located inside the coverage area of the SC. In case of the existence of any coverage holes in the SCs, relay nodes can be utilized to cover these holes [49]. However, this is not considered in our paper. Nomenclature lists the described symbols utilized in this paper. An SC on/off indicator \(\gamma\) is defined, where \(\gamma_{m}=1\) when the SC \(m\) is active; otherwise, \(\gamma_{m}=0\). The number of SCs is denoted by \"\(M\)\" and the number of UEs in SC \(m\) is denoted by \"\(U_{m}\)\". The UE association indicator \(\sigma_{m,k}=1\) if UE \(k\) is associated with SC \(m\); otherwise, \(\sigma_{m,k}=0\). The signal to interference and noise ratio (SINR) of UE \(k\) in SC \(m\) can be calculated as [14]:  
\[SINR_{k,m}=\frac{\gamma_{m}P_{m}G_{m,k}}{\sum_{n\
eq m,\;\;n\;\in\;M}\gamma_{n }P_{n}G_{n,k}+N} \tag{1}\]  
where \(P_{m}\) and \(P_{n}\) are the transmission powers of the serving SC \(m\) and the interfering SC \(n\), respectively. The channel gain between UE \(k\) and serving SC \(m\) is \(G_{m,k}=d_{m,k}-^{\alpha}\), where \(d_{m,k}\) is the distance between SC \(m\) and UE \(k\) and \(\alpha\) is the path loss exponent [50]; the channel gain between UE \(k\) and interfering SC \(n\) is \(G_{n,k}\) and \(N\) is the noise power. The data rate \(R_{k,m}\) of UE \(k\) in SC \(m\) is also calculated by [PERSON]'s formula as [13]:  
\[R_{k,m}=B_{k}\;\log_{2}(1+SINR_{k,m}) \tag{2}\]  
where \(B_{k}=B_{RB}L_{k,m}\) is the bandwidth allocated to UE \(k\), while the resource block (RB) bandwidth is \(B_{RB}\) and \(L_{k,m}\) is the number of requisite RBs for UE \(k\) in SC \(m\) to achieve the minimum data rate [14]. While the total throughput of the system is given by [9]:  
\[C_{sys}=\sum_{m=1}^{M}\gamma_{m}\sum_{k=1}^{U_{m}}R_{k,m} \tag{3}\]  
Due to the dense deployment of the SCs, some SCs can be turned off without affecting the QoS of the UEs. Thus, the total power consumption of SC \(m\) can be calculated as [13]:  
\[P_{m_{tot}}=\beta P_{m_{tot}}+(1-\beta)P_{m_{tot}}\gamma_{m}+\theta_{m}P_{m_{ tot}}\gamma_{m} \tag{4}\]  
where \(P_{m_{tot}}\) and \(P_{m_{tot}}\) are the baseline and the transmission power consumption, respectively, while \(\beta\) is the inactive level of the SC, such that \(P_{m_{off}}=\beta P_{m_{tot}}\), and \(\theta_{m}\) is the portion of power consumption that is due to the feeder losses and power amplifier of SC \(m\)[51]. The total power consumption of the system (\(P_{sys}\)) is the sum of the power consumption of all SCs. The PE of the system is given by [9]:  
\[PE_{sys}=\frac{C_{sys}}{P_{sys}} \tag{5}\]  
To improve the PE, the SCs on/off switching decisions using BPSO is proposed in this paper. The PSO is an iterative population-based search algorithm inspired by the hunting behavior of a flock of flying birds [52; 53; 54]. In PSO, every particle is considered a bird of the flock and represents a possible solution to the problem [55; 56; 57; 30]. The search begins with an initial set of particles and attempts to find the best solution by searching around the solution space.