# Power Control Techniques for Interference Management-
## 4 Power Control Technique Evaluation  
### Power Control Theories  
The main power control theories are classified according to their specific applications. The classification encompasses mathematical programming theory, neural networks, game theory, deep learning, dynamic control theory, machine learning, and network protocol heuristics, as shown in Figure 5.  
Most power control problems in wireless networks can be formulated as optimization problems by applying linear programming theory [7]. For instance, maximizing system throughput is subject to QoS requirements from users [8]. In a complex application where a system is dynamic, like in a multi-hop wireless system, an optimization problem can be an NP-hard problem [9]. Network protocol heuristics are applied to reduce the complexity of a dynamic power control theory (DPCT) problem [10]. Some of the power optimization problems are focused on solving the SINR. For instance, in [11], a DPCT algorithm is proposed to maximize the SINR subject to maximum power constraints. The algorithms proposed in [12; 13] minimize power consumption in the event of large-scale fading. Another power control application is found in [14], where total power transmitted is minimized over discrete power levels. In [15; 16], the SIR outage probability is minimized by total transmission power. In [18], the authors developed an efficient _graph neural network_ (GNN) architecture that is scalable and generates the same output for the transformed input function. Their algorithm addresses interference challenges amongst multiple access points  
Figure 4: Power control techniques obtained from the databases. Figure 5: Classification of power control techniques. Adapted from [17]. (APs) and a UE group. Compared to the baseline algorithms, the technique verifies that adaptability to minimum-capacity constraints of network configurations and channel conditions is achieved. The authors in [79] proposed applying the _graph neural network_ (GNN) technique to address radio resource management challenges in wireless networks. A comparative study of this technique was performed with the family of distributed optimization algorithms. The method was performed to simulate power control and beamforming. The results showed that a GNN performs better than traditional optimization-based techniques without domain knowledge. Furthermore, it has been demonstrated that a GNN satisfies the permutation equivariance property [134; 135], can generalize large-scale problems [136], and improve high computational efficiency [137]. The application of _game theory_ in wireless networks is commonplace. Game theoretic power control techniques can be modelled using _cooperative_ or _non-cooperative_ approaches. These approaches are extensively discussed in [138; 139]. For instance, the authors in [140] combined successive interference cancellation (SIC) algorithms [141] and non-cooperative game theory [138] approaches to save energy and improve network throughput. They presented a non-cooperative game theory power control approach based on CDMA wireless sensor networks (WSNs) in their groundbreaking study. Sensor node energy consumption is reduced, and network lifetime is increased when this method is used in conjunction with other power control techniques in WSNs. Mobile operators deploy more small cells to support users with varied data rate requirements in 5G mobile communication systems. Microcell users attached to small cells use the same frequency band to enhance capacity. As a result of this deployment, co-channel interference is likely to occur, which in turn causes poor network performance. To address this challenge, the authors of [142] proposed a game theory-based power control technique to optimize femtocell user power. The technique improves the sum rate and reduces outage and interference compared to the typical power control schemes. A power control strategy based on game theory was proposed in [143] to remove interference between D2D lines and cellular user devices.