Joint Hybrid Beamforming and Antenna Positioning for Fluid Antenna Enabled Wideband MIMO Radar

Hybrid beamforming (HBF) is a key enabler for wideband MIMO radar and integrated sensing and communication (ISAC) systems, yet precise space-frequency beampattern shaping remains challenging due to the dichotomy between analog and digital domains and the constant-modulus (CM) constraints on analog precoders. Conventional designs with fixedposition antenna (FPA) suffer from static geometries that restrict the degrees of freedom (DoFs) available for beampattern control. Fluid antenna (FA) overcome this by enabling repositioning, but entail challenging geometry optimization under bounded minimum spacing (BMS) constraints. To address this, we propose a Riemannian-aware mapped penalization (RAMP) framework for holistic joint design, combining (i) a differentiable mapping that embeds BMS into unconstrained parameterization and (ii) a scaled augmented direction method of multipliers (ADMM) with variable splitting to decouple analog-digital design. This reformulation enables unconstrained optimization on a Riemannian product manifold, jointly optimizing all variables with convergence to a Karush-Kuhn-Tucker (KKT) point. We further introduce a lightweight variant, PAMP-Fix, which reduces complexity by employing a quadratic penalty followed by a normalization step, for which we establish a bounded-error guarantee. Numerical results show that the proposed method reduces beampattern matching error by 2.71 dB over the FPA benchmark, and even surpasses the theoretical fully-digital FPA limit.