Nelder–Mead enhanced MUSIC algorithm for efficient position estimation in ISAC systems

Accurate user-position estimation is essential in integrated sensing and communication systems, where sensing accuracy must be balanced against sampling and computational costs. This paper considers two-dimensional localization of a single ground-plane user through a known elevated uniform rectangular array and the multiple signal classification pseudo-spectrum. The proposed Nelder–Mead MUSIC method combines a uniform coarse search with derivative-free simplex refinement, thereby avoiding an exhaustive fine-grid evaluation of the complete search region. Exact Euclidean antenna–user distances and free-space amplitude decay are retained in the steering vector so that the pseudo-spectrum depends on the candidate position rather than only on direction of arrival. A Cramér–Rao bound that accounts for the unknown signal phase and amplitude is derived as a theoretical performance benchmark, and Monte Carlo simulations examine the effects of signal-to-noise ratio, sample count, array elevation, coarse-grid density, and refinement iterations. The numerical results indicate that, under the modeled line-of-sight single-user conditions, the estimator approaches the adopted bound at sufficiently high signal-to-noise ratios for well-conditioned user geometries, while requiring substantially fewer pseudo-spectrum evaluations than a dense exhaustive search.