Joint Antenna Geometry and Transmit Covariance Design for Near-Field Multicast ISAC with Pinching Antenna Arrays
Abstract: PASS provide a flexible waveguide-based architecture for reconfiguring wireless propagation environments and creating geometry-dependent radiating apertures. This paper investigates a near-field multicast ISAC system enabled by a lossy multi-waveguide PASS, where a base station transmits a common message to multiple communication users while simultaneously sensing one or multiple targets. The PA positions along the waveguides and the feed-domain transmit covariance matrix are jointly designed to improve sensing accuracy under multicast communication constraints. We first develop a near-field multicast ISAC signal model that accounts for waveguide attenuation, equal-radiated-power operation, geometry-dependent free-space propagation, and monostatic sensing. Then, we derive the FIM for target parameter estimation and obtain a compact projected-Jacobian representation by exploiting the block-diagonal PA transfer structure. This representation reveals how the PA geometry and transmit covariance jointly affect the CRB. Based on this structure, we further characterize the per-waveguide and cross-waveguide FIM contributions, the loss-aperture tradeoff, the identifiability condition, and the communication-sensing phase conflict. To minimize the CRB, we formulate a joint PA-position and transmit-covariance optimization problem subject to a multicast rate constraint, a feed-power budget, and PA deployment constraints. An alternating optimization algorithm is developed, where the covariance subproblem is solved as a semidefinite program and the PA-position subproblem is handled by waveguide-wise block coordinate descent.