Multicast Capacity of XL-RIS Assisted Hybrid Near- and Far-Field mmWave Communications

Multicast transmission in millimeter-wave (mmWave) networks is fundamentally limited by the weakest user, and blockages further exacerbate this problem. Large-scale reconfigurable intelligent surfaces (XL-RIS) offer a promising solution by providing high array gain to overcome blockages. However, the large aperture of XL-RIS significantly expands the near-field region, creating a hybrid-field scenario where some users lie in the near-field while others remain in the far-field. Existing hybrid-field studies on XL-RIS have primarily focused on channel estimation and deployment optimization, leaving multicast capacity analysis unexplored. This paper investigates the fundamental capacity limits of XL-RIS-assisted multicast communications in hybrid-field scenarios. For the fundamental two-user case consisting of one near-field and one far-field user, we derive the optimal closed-form covariance matrix and optimize the RIS phase shifts via manifold optimization. We establish that the multicast capacity scales as $\Theta(\log_2(MN))$ as the number of transmit antennas M and/or RIS elements N grow large, and prove this scaling is order-tight. Numerical results validate the bounds and show the impact of M, $N$, and distance on the multicast rate.