Abstract: Phase-shifting interferometry with finite bandwidth light sources is a key technique for high-precision measurement of ultra-smooth optical components. However, influenced by vibrations, moving devices, and spectral bandwidth, the interference fringes exhibit not only random phase-shifting errors but also intra- and inter-frame nonlinear and non-uniform variations in modulation amplitude, which degrades the phase retrieval accuracy of existing random phase-shifting algorithms. To solve this problem, we propose a spatiotemporally decoupled iterative algorithm (SDIA). This method decouples the spatiotemporally varying modulation amplitude via multi-order Taylor expansion, stepwise separating the time-dependent and space-dependent variables in two distinct iterative steps to construct linear equations without variable coupling, thereby achieving high-precision phase retrieval via the least-squares alternating iteration. Simulations and experiments validated the feasibility and high accuracy of the proposed algorithm. The experimental results demonstrate that, for randomly phase-shifted interferograms under 40 nm bandwidth illumination, the retrieval residual errors of a planar smooth mirror are below 1 nm (PV) and 0.1 nm (RMS), respectively. To the best of our knowledge, this is the first time that such a spatiotemporal decoupling iterative algorithm using multi-order Taylor expansion has been proposed, which can address both random phase-shifting errors and spatiotemporally coupled modulation variations under finite bandwidth illumination conditions.

Abstract: For large-scale eigenvalue problems requiring many mutually orthogonal eigenvectors, traditional numerical methods suffer substantial computational and communication costs with limited parallel scalability, primarily due to explicit orthogonalization. To address these challenges, we propose a quasi-orthogonal iterative method that dispenses with explicit orthogonalization and orthogonal initial data. It inherently preserves quasi-orthogonality (the iterates asymptotically tend to be orthogonal) and enhances robustness against numerical perturbations. Rigorous analysis confirms its energy-decay property and convergence of energy, gradient, and iterate. Numerical experiments validate the theoretical results, demonstrate key advantages of strong robustness and high-precision numerical orthogonality preservation, and thereby position our iterative method as an efficient, stable alternative for large-scale eigenvalue computations.

Abstract: Unmanned Aerial Vehicles (UAVs) have attracted significant interest recently in wireless communication due to their flexible deployment and low cost. This paper investigates a multi-UAV enabled wireless relay network where multiple UAVs are employed as regenerative relays to provide communication service for a group of sensors far off the base station in a three-dimensional (3D) coordinate system. In order to improve the stability of the entire system over Rayleigh-fading channels, we jointly optimize sensors' communication scheduling and UAV trajectory to minimize the maximum average outage probability among all sensors. To tackle the formulated mixed integer non-convex problem, we decouple the problem into two sub-problems, which can be iteratively solved by utilizing the inexact block coordinate descent and successive convex optimization techniques. Moreover, an efficient iterative algorithm has been proposed with rigorous proof of convergence. To verify the efficiency of the proposed algorithm in practical wireless relay systems, especially for large-scale networks, we conducted extensive experiments and analysis under different UAV/sensor deployment scenarios. Numerical results show that the outage probability of the proposed algorithm is significantly lower than that of the other trajectories for the UAV relay.

Abstract: The Kaczmarz method is successfully used for solving discretizations of linear inverse problems, especially in computed tomography where it is known as ART. Practitioners often observe and appreciate its fast convergence in the first few iterations, leading to the same favorable semi-convergence that we observe for simultaneous iterative reconstruction methods. While the latter methods have symmetric and positive definite iteration operators that facilitate their analysis, the operator in Kaczmarz's method is nonsymmetric and it has been an open question so far to understand this fast initial convergence. We perform a spectral analysis of Kaczmarz's method that gives new insight into its (often fast) initial behavior. We also carry out a statistical analysis of how the data noise enters the iteration vectors, which sheds new light on the semi-convergence. Our results are illustrated with several numerical examples.

Abstract: Expectation propagation with successive updating (EP-SU) offers a symbol-wise, layering-like update, enhancing the detection performance for massive MIMO. Nevertheless, this layered potential has not yet been exploited in iterative detection and decoding (IDD). To address this gap, we propose a jointly-layered IDD algorithm for LDPC-coded massive MIMO systems, termed EP-SU-JL. By restructuring EP-SU in a layered manner and embedding it within a jointly-layered IDD framework, the proposed approach facilitates more frequent and efficient iterative information exchange between the detector and decoder, accelerating convergence and enhancing performance. Additionally, a sorting and grouping scheme is introduced to optimize the symbol update process. Numerical simulations demonstrate that the proposed EP-SU-JL consistently outperforms state-of-the-art (SOA) EP-based IDD algorithms across various MIMO scenarios while maintaining comparable complexity.

Abstract: Vehicle localization is an important part of autonomous vehicles, traditional localization methods often rely on Taylor series expansions and iterative techniques to estimate positions accurately. However, it relies on a good initial estimation and has a computational complexity that increases with the number of iterations. Aiming at this problem, we introduce a Closed-Form Least Squares (CFLS) algorithm that estimates positions within a single epoch, eliminating the need for iterative processing. In multi-system settings, a direct algebraic solution is not feasible. We reformulate the problem to obtain approximate closed-form solutions by intermediate variables. It scales to multiple systems, in contrast to existing intermediate-variable methods restricted to single or dual systems. Although squaring the measurements can increase sensitivity to noise, our CFLS algorithm achieves positioning accuracy close to the Cramér-Rao Lower Bound (CRLB). Experimental results using three satellite systems at 50 reference stations show that the CFLS algorithm provides accuracy comparable to that of conventional iterative least squares methods while reducing average processing time by 35.11%, making it highly suitable for real-time applications.