Power Control with QoS Guarantees: A Differentiable Projection-based Unsupervised Learning Framework

Deep neural networks (DNNs) are emerging as a potential solution to solve NP-hard wireless resource allocation problems. However, in the presence of intricate constraints, e.g., users' quality-of-service (QoS) constraints, guaranteeing constraint satisfaction becomes a fundamental challenge. In this paper, we propose a novel unsupervised learning framework to solve the classical power control problem in a multi-user interference channel, where the objective is to maximize the network sumrate under users' minimum data rate or QoS requirements and power budget constraints. Utilizing a differentiable projection function, two novel deep learning (DL) solutions are pursued. The first is called Deep Implicit Projection Network (DIPNet), and the second is called Deep Explicit Projection Network (DEPNet). DIPNet utilizes a differentiable convex optimization layer to implicitly define a projection function. On the other hand, DEPNet uses an explicitly-defined projection function, which has an iterative nature and relies on a differentiable correction process. DIPNet requires convex constraints; whereas, the DEPNet does not require convexity and has a reduced computational complexity. To enhance the sum-rate performance of the proposed models even further, Frank-Wolfe algorithm (FW) has been applied to the output of the proposed models. Extensive simulations depict that the proposed DNN solutions not only improve the achievable data rate but also achieve zero constraint violation probability, compared to the existing DNNs. The proposed solutions outperform the classic optimization methods in terms of computation time complexity.