Enhanced User-Fairness in CAPA-Based Systems Using CoV-Based Optimization

Continuous Aperture Array (CAPA) systems offer high spatial resolution and efficient beam control for next-generation wireless networks. While most existing works have focused on maximizing the sum-rate performance to design CAPA beamforming, user fairness has been largely overlooked. To address this challenge, we incorporate two alternative fairness-oriented objectives into the CAPA beamforming framework: maximizing the geometric mean of users’ rates (GMR) and maximizing a soft minimum rate function (SMR). Both problems are reformulated into tractable forms and efficiently solved using calculus of variations (CoV). Simulation results show that the proposed SMR approach improves the minimum user rate by over 300% compared to conventional sum-rate-based methods at moderate user densities. Meanwhile, the GMR method retains up to 88% of the sum-rate performance while significantly enhancing fairness. These findings highlight the practical value of fairness-oriented optimization for CAPA systems.