Mixed Near-field and Far-field Localization in Extremely Large-scale MIMO Systems

In this paper, we study efficient \emph{mixed near-field and far-field} target localization methods in extremely large-scale multiple-input multiple-output (XL-MIMO) systems Compared with existing works, we address two new challenges in target localization of MIMO communication systems via using decoupled subspace methods, arising from the half-wavelength antenna spacing constraint and \emph{hybrid uniform planar array} (UPA) architectures.To this end, we propose a new three-step mixed-field localization method. First, we reconstruct the equivalent signals received at UPA antennas by judiciously designing analog combining matrices over time with minimum recovery errors.Second, based on recovered signals, we extend the modified multiple signal classification (MUSIC) algorithm to the UPA architectures by constructing a new covariance matrix of a virtual sparse UPA (S-UPA) to decouple the 2D angles and range estimation.Due to the structure of the S-UPA, there exist ambiguous angles when estimating true angles of targets.In the third step, we design an effective classification method to distinguish mixed-field targets, determine true angles of all targets, as well as estimate the ranges of near-field targets.In particular, angular ambiguity is resolved by showing an important fact that the three types of estimated angles (i.e., far-field, near-field, and ambiguous angles) exhibit significantly different patterns in the range-domain MUSIC spectrum.Furthermore, to characterize the estimation error lower-bound, we obtain a matrix closed-form Cram\'er-Rao bounds for mixed-field target localization.Finally, numerical results demonstrate the effectiveness of our proposed mixed-field localization method, which improves target-classification accuracy and achieves a lower root mean square error than various benchmark schemes.