# Power Optimization in Multi-Tier Heterogeneous Networks Using Genetic Algorithm
## 9 Results and Discussion  
This paper evaluated the performance of the suggested model by using a power optimization technique. The optimal weight was calculated to improve the system's performance. The simulation was performed using MATLAB. The power transmission of the access point and the relay node was fixed at 43 dBm and 23 dBm, respectively. A Monte Carlo simulation with 5000 iterations was carried out. The simulation model involved multiple macrocell and multiple femtocells, picocells, and users evenly spread out within the coverage area of the macrocell as shown in Figure 8. A network area of 2.5 \(\times\) 2.5 km with 100-400 randomly placed access points was utilized. The users were evenly spread within the coverage area. The simulation was run with different parameter variations and power optimization techniques. The \(PL^{ABG}(f,d)[\text{dB}]\) in Equation (20) was utilized for the path losses \(P_{A,R}\) (access point to relay node), \(P_{R,R}\) (relay to relay node), and \(P_{R,U}\) (relay to user node) for the implementation in the MATLAB simulation. The simulation parameters are listed below in Table 2.  
\(SIR_{T}\) is an important metric for ensuring the reliability of wireless communication systems and is used in conjunction with the SIR to maintain a minimum quality threshold for a reliable communication. When the \(SIR\) decreases below a given threshold, the signal becomes weak and is unable to be detected at the receiver, leading to errors. Hence, the condition \((SIR_{CU_{i}}\geq SIR_{T})\) should be met for the proper communication between a pair of a transmitter and a receiver. The SIR is a bottleneck for any transmitter and receiver pair in wireless networks. We made the assumption that the background noise is zero, and hence, the \(SINR\) is equal to the \(SIR\). For a successful transmission, the \(SIR\) of each cellular user \(SIR_{CU_{i}}\) should be greater than the \(SIR\) threshold \(SIR_{T}\). The condition \((SIR_{CU_{i}}\geq SIR_{T})\) is also known as the coverage probability. Hence, \(SIR_{T}\) is set for a given system, and then, performance metrics such as power consumption and spectral efficiency are calculated for those users that meet the condition \((SIR_{CU_{i}}\geq SIR_{T})\). Similarly, the power consumption and spectral efficiency are calculated for a set of \(SIR_{T}\) and plotted. A comparison of various related works with proposed algorithm has been done and is presented in tabular format in Table 3. In table, it points out the methodology, strategies, algorithms and performance metrics that has been used in related works as compared to that of proposed model. Figure 9 shows that the modified genetic algorithm converged faster than the other algorithms and the best cost for the modified GA was 0.000013698. The modified GA evaluates solutions as chromosomes, classifying them as \"good\" or \"bad\" based on the fitness function. The proposed algorithm's results indicated that it reduced the power consumption and increased the network spectral efficiency, as compared to other methods such as equal power allocation, particle swarm optimization, and genetic algorithm. \begin{table}
\begin{tabular}{c c} \hline
**Parameter** & **Default Value** \\ \hline Frequency (f) & 2.3 GHz \\ Bandwidth & 20 MHz \\ \(T_{c}\) (Coherence time) & 2 ms \\ \(B_{c}\) (Coherence bandwidth) & 100 kHz \\ A & 100 \\ \(\sigma^{2}\) & \(-94\) dBm \\ Transmit power & 46 dBm \\ Fading model & Rayleigh fading \\ Path loss exponent & 3 \\ Transmission range & 500 m \\ SIR threshold (\(SIR_{T}\)) & \(-10\) dB to 30 dB \\ Transmit antenna & 2 \\ Receive antenna & 2 \\ Population size & 50 \\ Crossover fraction & 0.85 \\ Mutation probability & 1 \\ Function tolerance & \(1\times 10^{8}\) \\ Iteration & 100 \\ \(w_{d}\) & 0.5 \\ \(w_{\beta}\) & 0.5 \\ \(a_{A}\) & 2 \\ \(\beta_{B}\) & 31.4 dB \\ \(\gamma_{C}\) & 2.1 \\ \(\sigma_{X}\) & 2.9 dB \\ \hline \end{tabular}
\end{table} 
Table 2: Parameter specification. Figure 8: Simulation model of a heterogeneous network.