用概率建模解决无线资源分配中的离散变量难题

While deep learning (DL)-based methods have achieved remarkable success in continuous wireless resource allocation, efficient solutions for problems involving discrete variables remain challenging. This is primarily due to the zero-gradient issue in backpropagation, the difficulty of enforcing intricate constraints with discrete variables, and the inability in generating solutions with non-same-parameter-same-decision (non-SPSD) property. To address these challenges, this paper proposes a general DL framework by introducing the support set to represent the discrete variables. We model the elements of the support set as random variables and learn their joint probability distribution. By factorizing the joint probability as the product of conditional probabilities, each conditional probability is sequentially learned. This probabilistic modeling directly tackles all the aforementioned challenges of DL for handling discrete variables. By operating on probability distributions instead of hard binary decisions, the framework naturally avoids the zero-gradient issue. During the learning of the conditional probabilities, discrete constraints can be seamlessly enforced by masking out infeasible solutions. Moreover, with a dynamic context embedding that captures the evolving discrete solutions, the non-SPSD property is inherently provided by the proposed framework. We apply the proposed framework to two representative mixed-discrete wireless resource allocation problems: (a) joint user association and beamforming in cell-free systems, and (b) joint antenna positioning and beamforming in movable antenna-aided systems. Simulation results demonstrate that the proposed DL framework consistently outperforms existing baselines in terms of both system performance and computational efficiency.