Coherent Direct D-MIMO Localization: Analysis of Coherence Levels

Abstract

Distributed multiple-input multiple-output (D-MIMO) offers favorable geometry for localization and sensing, with its greatest potential arising from joint coherent processing across panels. However, stringent frequency-synchronization and phase-calibration requirements, together with multimodal likelihood functions, complicate the estimation problem. Consequently, most existing methods process the panels noncoherently, potentially sacrificing localization accuracy. We present a unified family of Bayesian state filters based on concentrated Type-I and marginal Type-II likelihoods for wideband near-field D-MIMO systems. The Type-I filters realize (i) noncoherent, (ii) coherent, and (iii) carrier-phase-based processing. We show that a zero-mean Type-II model is inherently noncoherent under distributed processing, whereas observation stacking restores coherence. A recently proposed nonzero-mean Type-II model adapts to the coherence available in the data, a property termed ``soft coherence.''We derive posterior Cram\'er--Rao lower bounds (PCRLBs) for all three coherence levels and show that each level is fundamentally tied to the number of phase parameters used for positioning or treated as nuisance parameters. Numerical results show that the filters closely approach their respective PCRLBs and that coherent processing substantially outperforms noncoherent processing. Our particle-based implementations parallelize over particles and panels, scale linearly with the observed data, and achieve runtimes of tens of milliseconds per time step under GPU acceleration.