# Bi-Objective Power Optimization of Radio Stripe Uplink Communications
## 4 Simulation Results
In the non-dominated front, we can obtain a point with the same SE for the worst UE, but with a total sum rate of approximately 96.7 bit/s/Hz, and the same sum rate of 56.8 bit/s/Hz, with the worst UE having a SE of approximately 0.976 bit/s/Hz. In these cases, there is a 70.2% gain in the sum rate and a 20% gain in the max-min fairness, respectively, if the network is optimized using the bi-objective approach. Figure 1: AP and UE positions in a high (**a**) medium (**b**) and low (**c**) UE density RS network. Figure 3: _Cont_. Figure 2: Bi-objective power optimization, max-min fairness and max–sum rate OF in a high UE density RS network with (**a**) high and (**b**) low maximum power. Figure 4: Bi-objective power optimization, max–min fairness and max–sum rate OF in a low UE density RS network with (**a**) high and (**b**) low maximum power. Figure 3: Bi-objective power optimization, max–min fairness and max–sum rate OF in a medium UE density RS network with (**a**) high and (**b**) low maximum power. In Figure 2b the max-min fairness optimization has a SE of 1.17 bit/s/Hz for the worst UE and a sum rate of 23.5 bit/s/Hz, while the max-sum rate optimization achieves a total of 67 bit/s/Hz with the worst UE having \(3.09\times 10^{-7}\) bit/s/Hz. The point with no power optimization, with \(P_{max}=5\) mW, has 0.139 bit/s/Hz for the worst UE and a sum rate of 43.2 bit/s/Hz. The bi-objective approach obtains the same SE for the worst UE with a sum rate of approximately 63.7 bit/s/Hz and the same sum rate with the worst UE having a SE of approximately 0.875 bit/s/Hz. This represents a 47.5% gain in the sum rate and a 529% gain in the max-min fairness, respectively. The same trade-offs are observable in Figure 3a where the max-min fairness optimization provides the worst UE with 3.68 bit/s/Hz but a poor sum rate of 44.1 bit/s/Hz, while the max-sum rate optimization achieves a total of 75 bit/s/Hz with the worst UE having \(3.58\times 10^{-7}\) bit/s/Hz of SE. For reference, the point with no power optimization for \(P_{max}=50\) mW is able to obtain 1.64 bit/s/Hz for the worst UE and 51.5 bit/s/Hz of network throughput. The MO approach can obtain the same SE for the worst UE with approximately 71 bit/s/Hz of sum rate, and the same throughput with the worst UE having a SE of approximately 3.53 bit/s/Hz. In both cases, there is a 37.9% gain in the sum rate and a 115% gain in the max-min fairness, respectively. In Figure 3b the max-min fairness outputs 2.26 bit/s/Hz for the worst UE and a sum rate of 27.1 bit/s/Hz, while the max-sum rate outputs 46 bit/s/Hz, with the worst UE having \(4.14\times 10^{-7}\) bit/s/Hz. The point with full power, with \(P_{max}=5\) mW, outputs 1.46 bit/s/Hz for the worst UE and a sum rate of 36.8 bit/s/Hz. With the MO approach, the same SE for the worst UE is obtained with a sum rate of approximately 40.9 bit/s/Hz, and the same sum rate is obtained with the worst UE having a SE of approximately 1.84 bit/s/Hz. The gains are 11.1% and 26% for the max-sum rate and the max-min fairness, respectively. Figure 4a displays the max-min fairness optimization providing 5.03 bit/s/Hz for the worst UE with a total sum rate of 30.2 bit/s/Hz, while the max-sum rate optimization achieves a total of 40.4 bit/s/Hz, with the worst UE having 2.96 bit/s/Hz. In this case, by transmitting with full power, with \(P_{max}\)=50 mW, a SE of 4.57 bit/s/Hz is obtained for the worst UE and the network has a total of 33.6 bit/s/Hz. The bi-objective approach for the same SE of the worst UE increments the sum rate to approximately 37 bit/s/Hz and for the same throughput increments the SE of the worst UE to approximately 4.89 bit/s/Hz, thus obtaining gains of about 10.1% and 7% in the sum rate and max-min fairness, respectively. Finally, Figure 4b shows that it is possible to obtain the extreme points with 4.12 bit/s/Hz for the worst UE and 24.7 bit/s/Hz sum rate for the max-min fairness optimization and 28.5 bit/s/Hz for sum rate combined with 2.36 bit/s/Hz for the worst UE for the max-sum rate optimization.