In this paper, we consider an intelligent reflecting surface (IRS)-aided cell-free massive multiple-input multiple-output system, where the beamforming at access points and the phase shifts at IRSs are jointly optimized to maximize energy efficiency (EE). To solve EE maximization problem, we propose an iterative optimization algorithm by using quadratic transform and Lagrangian dual transform to find the optimum beamforming and phase shifts. However, the proposed algorithm suffers from high computational complexity, which hinders its application in some practical scenarios. Responding to this, we further propose a deep learning based approach for joint beamforming and phase shifts design. Specifically, a two-stage deep neural network is trained offline using the unsupervised learning manner, which is then deployed online for the predictions of beamforming and phase shifts. Simulation results show that compared with the iterative optimization algorithm and the genetic algorithm, the unsupervised learning based approach has higher EE performance and lower running time.

翻译：在本文中,我们考虑的是智能反射表面(IRS)辅助无细胞帮助的大规模多输入多输出产出系统,在这个系统中,对接入点的光束和IRS的阶段转移进行优化,以最大限度地提高能源效率。为了解决EEE最大化问题,我们建议使用二次变换和拉格朗吉亚的双变换,来找到最佳的波束成形和阶段变换。然而,提议的算法有很高的计算复杂性,这阻碍了它在一些实际情景中的应用。对此,我们进一步提议了一种基于深层次学习的办法来联合波形成形和阶段变换换。具体地说,一个两阶段深神经网络在离线上培训,使用不受监督的学习方式,然后在网上部署,用于预测波形变和阶段变换。模拟结果表明,与迭代优化算法和基因变法相比,基于非超强的学习方法具有更高的 EE性能和较低的运行时间。