In this paper, we investigate a full-duplex (FD) cell-free massive multiple-input multiple-output (mMIMO) system. To cope with the cross-link interference, especially the interaccess point (inter-AP) interference, we formulate a sum spectral efficiency maximization problem by jointly optimizing the digital and analog beamforming at FD AP and digital precoder at the uplink user equipment. To solve it, we present a fully digital design first by utilizing successive convex approximations and majorization-minimization to obtain a closed-form solution in each iteration. After that, we exploit the Riemannian manifold to get a hybrid design, which is shown to approximate the fully digital one well. Simulation results show that the proposed design enhances the sum spectral efficiency as well as uplink performance effectively when compared to other benchmarks.

This paper aims to develop a Newton-type method to solve a class of nonconvex composite programs. In particular, the nonsmooth part is possibly nonconvex. To tackle the nonconvexity, we develop a notion of strong prox-regularity which is related to the singleton property and Lipschitz continuity of the associated proximal operator, and we verify it in various classes of functions, including weakly convex functions, indicator functions of proximally smooth sets, and two specific sphere-related nonconvex nonsmooth functions. In this case, the problem class we are concerned with covers smooth optimization problems on manifold and certain composite optimization problems on manifold. For the latter, the proposed algorithm is the first second-order type method. Combining with the semismoothness of the proximal operator, we design a projected semismooth Newton method to find a root of the natural residual induced by the proximal gradient method. Due to the possible nonconvexity of the feasible domain, an extra projection is added to the usual semismooth Newton step and new criteria are proposed for the switching between the projected semismooth Newton step and the proximal step. The global convergence is then established under the strong prox-regularity. Based on the BD regularity condition, we establish local superlinear convergence. Numerical experiments demonstrate the effectiveness of our proposed method compared with state-of-the-art ones.