Direct Localization of High-Order QAM Sources With Multiple Anchors: Dual Atomic Norm Minimization Framework

Direct localization (DL) of high-order quadrature amplitude modulation (QAM) sources is a pivotal challenge in wireless communications, particularly in environments characterized by complex multipath propagation and the presence of multiple sensor array-based anchors. This paper introduces a novel solution based on dual atomic norm minimization (DANM) framework that capitalizes on the fourth-order cumulant property of QAM signals to suppress Gaussian noise and expand the effective array aperture. Unlike traditional DL frameworks based on discrete Fourier transform (DFT) and spatial smoothing pre-processing (SSP) techniques, the proposed framework enhances localization accuracy and improves robustness against multipath effects. By framing the localization problem as a semidefinite program that utilizes dual atomic norm properties, our solution eliminates the need for prior knowledge of the number of sources and achieves a favorable balance between computational complexity and localization performance. Simulation results reveal that the DANM-based DL algorithm outperforms existing DFT- and SSP-based DL methods in terms of localization accuracy, with its root mean square error (RMSE) closely approaching the Cramér-Rao bound (CRB) even under challenging conditions. These findings underscore the potential of DANM in advancing high-precision DL for high-order QAM sources, thereby paving the way for more reliable and precise wireless communication systems.