# Power Optimization in Multi-Tier Heterogeneous Networks Using Genetic Algorithm
## 9 Results and Discussion
### Spectral Efficiency Performance  
The average spectral efficiency [40] is determined by dividing the total throughput of all users by the effective bandwidth and the number of transreceivers (\(T_{Rx}\)). If there are N users, each with M \(T_{Rx}\), and they are transmitting with a \(BW\) effective bandwidth, the average spectral efficiency \(\
u_{avg}\) can be calculated as follows:  
\[\
u_{avg}=\frac{\sum_{i=1}^{N}R_{i}(T)}{T,BW,M} \tag{29}\]  
Figure 11: Power consumption vs. the \(SIR_{T}\) for different Power optimization techniques. Figure 10: Power consumption vs. number of users for different optimization techniques. where \(R_{i}(T)\) is the number of correctly received bits by user \(i\) over a period of time \(T\) and \(BW\) is the bandwidth. In our proposed weight-based user-scheduling algorithm, we took into consideration both the distance and received signal strength to select a user by a particular access point. Basically, for downlink transmission, low transmission power is allocated to the user near the base station and high power is assigned to the user away from the base station [41]. Similarly, transmission power is allocated based on the channel gain of the user. If a user has a low channel gain, he/she receives a high transmission power, and if a user has a high one, he/she receives a low transmission power. Boosting the transmission power improves the data rate and signal-to-noise ratio and increases interference to nearby stations. Thus, it is important to allocate the transmission power optimally to enhance the network efficiency. Thus, this paper considered both the distance and received signal strength for a user to select an access point. Equal weight is provided to both the distance and received signal strength, and the base station calculates the resultant value depending on which access point decides which user to be selected. The weight is essential in selecting a user and improving the spectral efficiency. In our research, we took equal weights; however, future work can study the varying of the weight. Here, throughput increased with the increase in the signal-to-noise ratio of each individual user, and hence, the spectral efficiency shown in Figure 12 increased, whereas the power optimization was carried out to allocate the optimal power for each user; the SIC-based receiver led to better interference suppression in a multi-tier heterogeneous environment, resulting in improved spectral efficiency (SE) performance. The optimal power allocation optimized the combined spectral efficiency of a set of users by allocating the appropriate transmission power, resulting in increased spectral efficiency for most of the users. In Figure 13, spectral efficiency is analyzed for three different scheduling algorithms in a multi-tier heterogeneous network. The SIC-based receiver was used for a weight-based scheduling algorithm, and optimal power allocation for the users associated with a particular access point was performed using a modified genetic algorithm. In contrast, in the minimum distance scheduling and maximum channel gain algorithm, the local minimum-mean-squared error (LMMSE) precoding [27] technique was used. It uses fractional power allocation for optimal power allocation. In the minimum distance scheduling algorithm, the  
Figure 12: Spectral efficiency with respect to \(SIR_{T}\) for different power optimization techniques. user \(u\) is assigned to access point \(A^{*}\) based on the shortest distance between them. The user with the shortest distance is assigned the highest power, while the user with the farthest distance is assigned the lowest power using fractional power allocation. Therefore, the spectral efficiency is better for MDS at lower distances. In the case of maximum channel gain scheduling (MCS) algorithm, the maximum power is allocated to the user with strong channel conditions and the minimum power to users with the worst conditions.