# Bi-Objective Power Optimization of Radio Stripe Uplink Communications
## 4 Simulation Results
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Value** & **Description** \\ \hline \(f_{c}\) & 2 GHz & Carrier frequency \\ \hline \(h_{d}\) & 5 m & AP/UE height difference \\ \hline \(\sigma_{sh}^{2}\) & 4 dB & Variance of the shadow fading term \\ \hline \(\Delta\) & 0.5 & AP/UE shadowing contributions \\ \hline \(d_{c}\) & 9 m & Decorrelation distance \\ \hline \(d_{sh}\) & 50 m & Shadow fading distance \\ \hline \(D\) & 125 m & Size of simulation area \\ \hline \(D_{u}\) & 100 m & Size of the UE positioning area \\ \hline \(L\) & 12 & Number of APs \\ \hline \(d_{H}\) & \(\frac{\lambda}{2}\) m & Antenna spacing \\ \hline \(N\) & 2 & Number of antennas per AP \\ \hline \(K\) & \(\{6,12,20\}\) & Number of UE \\ \hline \(\tau_{p}\) & \(\{5,10,16\}\) & Number of orthogonal pilots \\ \hline \(\tau_{c}\) & 2000 & Number of samples per coherent block \\ \hline \(P_{max}\) & \(\{5,50\}\) mW & UE maximum power \\ \hline \(B\) & 100 MHz & Communication bandwidth \\ \hline \(\sigma^{2}\) & \(-92\) dBm & Noise power \\ \hline \(\sigma_{\phi}\) & \(15^{\circ}\) & Std of the angle from multipath components \\ \hline \hline \end{tabular}
\end{table} 
Table 2: System parameters. The RS networks employed in the simulation assessment allow for the evaluation of the SO and MO optimization algorithms in \(N_{in}\) different instances with distinct UE densities:  
* One with high UE density (scenario 1) of approximately 80% of the total antennas \(LN=24\), i.e., \(K=20\),;
* One with a medium UE density (scenario 2), with 50% of UE with respect to \(LN\), i.e., \(K=12\);
* One with a low UE density (scenario 3), by considering that the total number of UE is equal to 25% of \(LN\), i.e., \(K=6\). Figure 1 shows the three different RS networks considered in this section. It should be mentioned that to also take into account the pilot contamination interference, the total number of orthogonal pilots, \(\tau_{p}\), is adjusted to 80% of the total number of UE. This means that \(\tau_{p}=\lceil 0.8\times K\rceil\). Furthermore, to evaluate the performance of the optimization procedures with different UE technologies, in each RS scenario from Figure 1, two different values of \(P_{max}\) are considered: one with low maximum power of \(P_{max}=5\) mW and one with high maximum power of \(P_{max}=50\) mW. In Figures 2-4 the max-min fairness, max-sum rate and bi-objective power optimization are performed in a high, medium and low UE density RS network with high and low maximum power, respectively. The SE values in both axis are obtained by taking the mean value for the \(N_{a}\) realizations. The 95% confidence intervals are presented. Along with the main SE results, a tendency curve is presented to illustrate an approximation of the non-dominated front. This curve is plotted through a quartic (4 th degree) polynomial fitting function. Figure 2a shows the advantage of using an MO approach to unveil the trade-offs between the OFs. The max-min fairness optimization leads to a solution in which the network operates in a state where the worst UE has 1.21 bit/s/Hz. However, this is achieved at the expense of the sum rate, which is 24.2 bit/s/Hz for this solution. At the other end, the max-sum rate optimization achieves a total UL throughput of 104 bit/s/Hz, but the worst UE has \(2.67\times 10^{-7}\) bit/s/Hz of SE. The MO optimization approach enables unveiling SE trade-offs between these two extreme operation points. Figure 2a presents all \(N_{arch}\) states of network operation computed using the MO version of the DE developed. For reference, it is also displayed the case where there is no power optimization, which means that all UE employ the maximum power, \(P_{max}\), (which in this case is 50 mW) in the UL. For this case, the worst UE has a SE of 0.318 bit/s/Hz, while the network sum rate is 56.8 bit/s/Hz.