Qi Wang

Qi Wang, Xiaoming Chen, Qiao Qi et al.

This paper proposes a novel continuous aperture array (CAPA)-assisted integrated communication and navigation (ICAN) framework for low Earth orbit (LEO) satellite constellations. Within this framework, an electromagnetic-based collaborative transmission model is developed, in which multiple satellites equipped with CAPAs simultaneously radiate downlink data streams and navigation reference signals over shared spectrum. Building upon this, the achievable communication rate and the navigation Cramer-Rao bound (CRB) are derived, which explicitly characterize the intrinsic coupling between the dual-function beamformers and system performance. To improve the positioning accuracy with communication quality of service guarantee, a joint beamforming optimization problem is formulated to minimize the average CRB subject to transmit power budgets and minimum rate constraints. To tackle the inherent infinite-dimensionality of the CAPA beamformer design, an ICAN channel subspace is introduced to equivalently transform the formulation into a tractable finite-dimensional problem, which is then efficiently solved via an iterative convex optimization algorithm. Finally, numerical results demonstrate that the proposed CAPA-assisted beamforming design algorithm significantly outperforms conventional discrete phased array architectures and other benchmark schemes, yielding notable improvements in ICAN performance.

Xuelong Gu, Qi Wang

The skew-gradient embedding (SGE) framework~\cite{GuWangSGE2025} reformulates a thermodynamically consistent system as a generalized gradient flow by embedding its zero-energy contribution in a skew-symmetric operator. In a time-discrete scheme, the profiles defining this operator may be evaluated at previous time levels. The resulting operator remains skew-symmetric, so its contribution to the discrete energy balance vanishes; this explicit treatment often decouples multiphysics systems. We show that this operator is not unique: the admissible gauges form an affine space, and we call the resulting family generalized skew-gradient embeddings (GSGE). For any positive definite metric, least squares selects a unique minimum-Hilbert--Schmidt gauge, and the native metric recovers SGE. This construction also gives regularized approximations, corrections of non-neutral residuals, and gauges that preserve prescribed invariants. For rank-two gauges, we use a necessary and sufficient Jacobi criterion. Applying this criterion to a compatible MAC discretization of the incompressible Navier--Stokes equations gives a finite-dimensional rank-two Poisson--GENERIC formulation at the semi-discrete level; the implicit midpoint rule preserves this rank-two GENERIC structure at the fully discrete level and satisfies the exact discrete energy law. For the Cahn--Hilliard--Navier--Stokes system, the regularized GSGE--BDF2 scheme preserves mass, dissipates the discrete energy unconditionally, and admits a decoupled implementation.