# Bi-Objective Power Optimization of Radio Stripe Uplink Communications
## 4 Simulation Results  
In this section, the SE performances are evaluated while considering both the SO and the MO optimization for the OSLP detection scheme. The path loss and shadow fading included in the propagation model follow the 3 rd Generation Partnership Project (3 GPP) Urban Microcell model ([25] Table B.1.2.1-1) where the large-scale fading coefficient takes into consideration the APs and the UE antenna's heights, being defined in dB by  
\[\beta_{kl}=-36.7\log_{10}\left(\sqrt{d_{kl}^{2}+h_{d}^{2}}\right)-22.7-26\log_ {10}(f_{c})+F_{kl}, \tag{24}\]  
where \(d_{kl}\) is the horizontal distance between UE \(k\) and AP \(l\), \(f_{c}\) denotes the carrier frequency in GHz and \(h_{d}\) represents the height difference (in meters) between the AP and UE antennas. The term \(F_{kl}\sim\mathcal{N}\left(0,\sigma_{sh}^{2}\right)\) only appears when \(d_{kl}>d_{sh}\) and follows a shadowing correlation model [4] given by  
\[\mathbb{E}\left\{F_{kl}F_{ij}\right\}=\sigma_{sh}^{2}\left(\Delta 2^{-\frac{\
u_{kl}}{2\varepsilon}}+(1-\Delta)2^{-\frac{ \zeta_{lj}}{2\varepsilon}}\right), \tag{25}\]  
where \(\
u_{kl}\) is the distance between UE \(k\) and UE \(i\), \(\zeta_{lj}\) is the distance between AP \(l\) and AP \(j\) and \(0\leq\Delta\leq 1\) denotes the AP/UE shadowing contributions. The RS network is deployed around the perimeter of a squared \(D\times D\) m\({}^{2}\) area and consists on \(L\) equidistant APs equipped with \(N\) antennas. Furthermore, \(K\) UE are concentrated in a smaller squared \(D_{u}\times D_{u}\) m\({}^{2}\) area within the far-field regarding the antenna's operation region. It is also assumed that there are \(\tau_{p}\) orthogonal pilots available. Additionally, the maximum UE transmission power in mW is \(P_{max}\), the communication bandwidth in MHz is \(B\) and the coherence block has \(\tau_{c}\) samples. The total noise power in dBm is [4]  
\[\sigma^{2}=Bk_{B}T_{0}\sigma_{f}^{2} \tag{26}\]  
where \(\sigma_{f}^{2}=1.9741\) dB is the noise figure, \(k_{B}=1.381\times 10^{-23}\) J/K is the Boltzmann constant and \(T_{0}=290\) K is the noise temperature. The UE pilot assignment is performed according to a greedy algorithm described in ([4] Sec. IV.A) with \(\tilde{p}=P_{max}\). Each multi-antenna AP includes a uniform linear array with antenna spacing \(d_{H}\). Moreover, each AP antenna receives multipath components which follow a Gaussian distribution in the angular domain with a \(\sigma_{\phi}\) degree std around the nominal angle to the UE [2; 9; 11]. The results were obtained by considering \(N_{a}=10\) independent realizations in \(N_{in}=3\) different independent instances with randomly placed UE. The constant of Equation (23), \(C_{p}\), is calculated by the quotient between the average value of \(f_{2}(\mathbf{p})\) for the max-min fairness optimization and the average value of \(f_{1}(\mathbf{p})\) for the max-sum rate optimization considering the \(N_{a}\) realizations. All simulations were performed in the same machine (Intel [EMAIL_ADDRESS] GHz) using Matlab. The DE algorithm parameters are displayed in Table 1. The network simulation parameters are presented in Table 2, where \(\lambda\) denotes the wavelength. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Variable** & **Value** & **Description** \\ \hline \(N_{pop}\) & 40 & Population size \\ \hline \(C_{max}\) & 1 & Maximum value of the control parameter \\ \hline \(C_{r}\) & 0.9/100 iter. & Decreasing rate of the control parameter \\ \hline \(\lambda\) & 0.5 & Weighting factor to the best population individual \\ \hline \(F_{0}\) & 0.8 & Nominal value of the scaling parameter \\ \hline \(\alpha\) & 0.01 & Std value of the scaling parameter \\ \hline \(N_{in}\) & 1000 & Maximum number of iterations \\ \hline \(N_{i}\) & 100 & Maximum number of iteration with no improvement of both OFs \\ \hline \(\varepsilon\) & \(10^{-5}\) & Algorithm’s tolerance \\ \hline \(N_{arch}\) & 100 & Population archive size \\ \hline \hline \end{tabular}
\end{table} 
Table 1: DE parameters.