Curved Beam Enabled Wireless Communications: Modeling, Analysis and Optimization

In this paper, the problem of using curved beams to improve wireless communication performance in the presence of a blockage is studied. In particular, a transmitter equipped with a continuous aperture array can generate curved beams to serve multiple receivers by allowing signals to propagate along both straight and curved paths. To optimize the weighted sum-rate, a curved beam model is developed for controlling the beam steering, beam focusing, and beam curving functions, along with a segmented channel model to characterize practical channels induced by the blockage. Based on the introduced curved beam model, an optimization problem is posed with the goal of maximizing the weighted sum-rate of all users under a transmit power budget and physical constraints of curved beams. To solve this problem, the continuous aperture is first converted into finite summations via a discrete sampling of the continuous coordinate. Then, the performance gap between the ideal continuous aperture design and its practical discrete aperture approximation is analyzed. Based on the above discrete approximation, an iterative algorithm is developed to optimize curved beam control parameters. In particular, the original problem is reformulated as a trackable form via fractional programming (FP). Then, the transformed problem is solved by designing an enhanced block coordinate ascent (BCA) method which determines a surrogate-construction point leveraging the local descent from previous iterations, thereby accelerating convergence. Then, a proximal regularization term is included into the surrogate function to control the update magnitude and suppress aggressive update, thereby improving updates stability. Finally, the beam amplitudes are computed based on the effective channel gains. Simulation results show that the proposed method can improve the weighted sum-rate compared to using only straight beam.