# Bi-Objective Power Optimization of Radio Stripe Uplink Communications
## 1 Introduction
### Contributions  
Power allocation algorithms are essentially methods that solve an optimization problem where the decision variables are the power coefficients that are allocated at each UE terminal, in case of UL. The constraints are usually related to the maximum transmission power that each UE can support, and the objective function (OF) is related to a network metric that should be optimized. In all papers mentioned in the previous subsection, the power optimization is performed in CF mMIMO systems. Moreover, only one metric is considered at a time, i.e., the UL power optimization problem is SO. The state-of-the-art solutions have focused on the development of exact algorithms that are able to compute the optimal solution for a given SO optimization problem. However, in practical scenarios, multiple network metrics must be optimized. Thus, in order to enhance the system performance and provide flexibility, we consider multi-objective (MO) optimization for the RS scenario. In this work, we deal with two competing OFs, max-min fairness and max-sum rate, which means that a non-dominated solution front should be sought rather than an optimal solution. The output of the MO UL power optimization model is a set of power coefficients vectors for UL transmission, each one assigned to an UE. Each vector provides a specific trade-off between the OFs. To the best of the authors' knowledge, there is no prior work focusing on MO UL power optimization in an RS network. Thus, the main contribution of our work is considering a MO UL power optimization approach simultaneously taken into account two metrics of evaluation of solution quality.  
In order to tackle the computation costly nature of such optimization problems, customized MO programming using a MH approach [21] can output high quality solutions displaying network performance trade-offs. In this work, we adopt the differential evolution (DE) MH approach [22] to solve a MO optimization problem aiming to optimize the UE SE considering the max-min fairness and the maximum sum rate metrics, in a UL RS scenario, while employing the OGLP combining scheme [11]. Since no exact algorithm can efficiently solve this bi-objective optimization problem, the main motivation for the use of DE is its good performance in continuous optimization problems, capability of making the solution population to evolve towards the non-dominated front, and easiness of implementation. The computational complexity of the DE algorithm is much lower than the one of exact algorithms, with DE being capable of finding high-quality and near-optimal solutions much faster, as shown in [21] for an SO problem. This is critically important when the number of UE is high, which significantly increases the computation complexity. The SE of each UE is an important key performance indicator that depends on the power coefficient, equalization vector, noise and channel estimation. Since the DE algorithm only relies on the UE SE measurements across the network, this means that the set of possible solutions provided by the algorithm is reasonable for multiple time-frequency intervals, i.e., those solutions are valid for a coherent block wherein the channel stays constant. This means that DE lends itself well to (near) real-time applications that can adapt to the network environment and only needs to update the power vectors once per coherent block.