Near-Field Range-Angle Estimation and Power Allocation for Cell-Free Massive MIMO ISAC With Extremely Large Arrays

Abstract

The deployment of extremely large-scale antenna arrays (ELAAs) at the access points (APs) of cell-free (CF) massive multiple-input multiple-output (MIMO) networks extends the near-field Rayleigh boundary to several hundred metres, invalidating the conventional plane-wave assumption for both communications and radar sensing. This paper develops a near-field cell-free integrated sensing and communications (NF-CF-ISAC) framework for joint target range-angle estimation and region-aware power allocation while serving multiple user equipments (UEs) under per-AP power constraints. Relative to existing near-field and cell-free ISAC studies, this work develops a closed-form analytical framework whose Cramér–Rao lower bound (CRLB) depends only on the large-scale fading, enabling per-AP power and focal-range allocation under per-target CRLB constraints in a distributed deployment. We derive the spherical-wavefront near-field steering vector and a region-aware ISAC beamformer, obtain an analytical ergodic achievable rate under maximum-ratio transmission (MRT) and zero-forcing (ZF) precoding, and establish a joint <inline-formula> <tex-math notation="LaTeX">$(r,\theta,\phi)$ </tex-math></inline-formula> CRLB whose range component scales as <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(L^{-1}N_{t}^{-3})$ </tex-math></inline-formula> in the asymptotic regime <inline-formula> <tex-math notation="LaTeX">$N_{t}\to \infty $ </tex-math></inline-formula> for targets at fixed range <inline-formula> <tex-math notation="LaTeX">$r\geq r_{F}$ </tex-math></inline-formula>, while the angle CRLB scales as <inline-formula> <tex-math notation="LaTeX">$\mathcal {O}(L^{-1}N_{t}^{-1})$ </tex-math></inline-formula>. Building on these results, we formulate a joint per-AP power and beam-focus-distance allocation problem and solve it with a low-complexity two-level alternating algorithm comprising an inner successive-convex-approximation (SCA) loop and an outer one-dimensional focal-range search, with provable convergence to a KKT point. Monte Carlo simulations over 500 independent channel realisations show up to 12% sum-rate improvement over far-field-assumption baselines at the same CRLB target, with the range CRLB reaching the sub-metre regime for targets within the Rayleigh distance.