Computationally Efficient Unsupervised Deep Learning for Robust Joint AP Clustering and Beamforming Design in Cell-Free Systems

In this paper, we consider robust joint access point (AP) clustering and beamforming design with imperfect channel state information (CSI) in cell-free systems. Specifically, we jointly optimize AP clustering and beamforming with imperfect CSI to simultaneously maximize the worst-case sum rate and minimize the number of AP clustering under power constraint and the discrete constraint of AP clustering. Through transformations, the intractable simultaneous optimization of continuous and discrete variables is reduced to optimizing only the sparsity of the continuous variables, facilitating a computationally efficient unsupervised deep learning algorithm. In addition, to further reduce the computational complexity, a computationally effective unsupervised deep learning algorithm is proposed to implement robust joint AP clustering and beamforming design with imperfect CSI in cell-free systems. Numerical results demonstrate that the proposed unsupervised deep learning algorithm achieves a higher worst-case sum rate under a smaller number of AP clustering with computational efficiency.