## 4 Proposed Technique
### BS-Sw Techniques  
While the dual decomposition method is applied to solve the PA part of the formulated problem, three other methods are proposed to determine the BS switching status. One of them evaluates an optimal set of sleeping SBSs by adopting binomial theorem to maximise the EE function, whereas the other two proposed heuristic methods (i.e., distance-based and random BS-Sw schemes) provide a sub-optimal solution as shown in step 3 of Algorithm 1. The computational complexity of the optimal technique (binomial theorem) increases exponentially as the number of SBSs is increased while the heuristic techniques have a constant and smaller computational complexity. Since the BS-Sw and PA are intertwined problems where their optimisations are interdependent, the PA and BS-Sw schemes can be integrated as a single algorithm (PABS-Sw). Depending on the BS on/off status attained through the BS-Sw method, the transmit power allocation is evaluated. Thereafter, the EE is determined through [PERSON]'s method. These processes are carried out until an optimal EE value is achieved through the iterative algorithm as shown in step 10-16 of Algorithm 1. The binomial theorem is used to obtain the BS on/off statuses where all possible combinations (i.e., \(2^{5 BS}-1\)) of SBS on/off is evaluated as shown in Algorithm 2. It is worth noting that the MBS is always on in this work, i.e., \(b_{j\in\ell\backslash\{1\}}\). The best output that yields the highest EE is chosen from the results as indicated in step 6 of Algorithm 2; therefore, this method is regarded as the optimal BS-Sw technique. ```
1:Declare two arrays of (\(2^{SBS}-1\)), (i) combination & (ii) EE. 2:for\(\forall\) combination. do
3: Off SBSs of the combination. 4: Evaluate EE of the combination. 5:endfor
6: Off combination of SBSs with highest EE. ```  
**Algorithm 2** Binomial method. In order to satisfy the target QoS of the user with higher channel gain, allocating less transmit power is sufficient [30]. Consequently, the total power consumption will be decreased, leading to a higher EE. Higher channel gain is viable through decreased path loss, which is achievable through shorter distance between BS and user [31]. The example shown in Figure 3 consists of four small cells (SCs) located randomly within the coverage of the MBS. The distance of SBS \(j\) from MBS is indicated by \(D_{j}\), whereas \(d_{i}\) represents the distance of user \(i\) from MBS and \(\sum_{i}d_{i}^{j}\) is the sum of distances of all users of the particular SBS \(j\) to MBS. The SBS with lowest \(\sum_{i}d_{i}^{j}\) value is considered to be switched off. As the number of users per cell increases, the possibility for the SBS to be switched off will be consequently reduced, in other words, the number of users per cell is taken into consideration while switching off the SBSs. The proposed BS-Sw strategy employs two distance-based thresholds, \(D_{j}^{t}hr\) and \(d_{i}^{t}hr\), to determine the on/off state of an SBS. \[\text{Threshold of distance of SBS from MBS}:\ D_{j}^{thr}=\text{median}(D_{j}, \forall j)\] \[\text{Threshold of sum user distance from MBS}:\ d_{i}^{thr}=\text{median} \big{(}\sum_{i}d_{i}^{j},\forall j\big{)}\]  
If \(D_{j}<D_{j}^{thr}\) or \(\sum_{i}d_{i}^{j}<d_{i}^{thr}\) or both of the conditions are satisfied, then the SBSs that fall in the category and the combination of the SBSs are shortlisted to be switched off as shown in step 4 of Algorithm 3. Thereafter, the EE of those combinations are evaluated and the combination that provides the best EE among them is chosen to be switched off, i.e., \(b_{j}=0\). For instance, in Table 3, the highlighted cells indicate the SBSs that fulfil the value less than the threshold value for the example shown in Figure 3. From Table 3, we can deduce that SBS 1 or SBS 2 or both SBS 1 and SBS 2 can be considered to be switched off. Thus, after evaluating the highest EE obtained by switching off the mentioned combinations of SBSs, the switching decision is made.