This correspondence is concerned with source localization and classification for scenarios where both the far-field and near-field narrowband sources may coexist. We propose an efficient MUSIC-based solution that requires neither a multidimensional search nor high-order statistics (HOS). We also derive the stochastic Cramér-Rao bound (CRB) for the problem under consideration. The performance of the proposed method is compared with an existing method and with the CRB.

The electromagnetic vector sensor (EMVS) embedded multiple-input multiple-output (MIMO) radar, named EMVS-MIMO radar, offers a unique perspective on target localization, providing both two-dimensional (2D) angle and polarization status estimations of targets. However, the current frameworks limit the EMVS-MIMO radar's ability to achieve high-resolution 2D direction finding while maintaining low complexity. To address this limitation, this paper proposes a uniform rectangular array-based methodology with the inter-sensor spacing of the receiving array greater than half-wavelength, along with a high-resolution estimation strategy based on a parallel factor (PARAFAC) model. To optimize the identifiability of the PARAFAC model, the array measurement is first arranged into a third-order tensor, and the 6 possible PARAFAC tensor models are established. Factor matrices are then estimated via PARAFAC decomposition, and 2D direction finding is achieved by combining the spatial rotational invariance technique with the normalized vector-cross product technique. The proposed PARAFAC algorithm can be extended to other sparse uniform geometries, such as L-shaped arrays and parallel linear arrays. The larger array aperture and inherent tensor gain of the proposed PARAFAC approaches offer superior estimation performance compared to existing frameworks. Additionally, the flexibility of the PARAFAC model may make it suitable for single snapshot scenarios. Finally, the improvements of the proposed approaches are validated by numerical simulations.

The large-scale multiple-input-multiple-output (MIMO), also known as massive MIMO, is one of the key techniques for the fifth-generation (5 G) mobile communications. Due to large-scale antenna systems equipped at the basestations, the user-basestation distance in massive MIMO systems may be within the so-called Rayleigh distance. This would cause challenges in developing algorithms for user localization, because both near-field (NF) and far-field (FF) sources (users) may coexist. To solve this problem, most of existing algorithms are based on a simplified source-sensor spatial model, where the sensor-magnitude is assumed to be equal and the spatial phase is approximated by the Taylor polynomial. In contrast, a new algorithm based on the exact spatial geometry is developed, where no model simplification is made. The new algorithm is termed as MIxed Localization using the Exact model (MILE) in that it sets up a unified (non-approximation) model framework to the problem under consideration, and solves this problem in a mathematically quite simple manner. In fact, the MILE has the following three important advantages: (1) it is not restricted to exploit equally spaced arrays, (2) it can accommodate any arbitrary propagation loss, and (3) it does not suffer the model mismatch caused performance loss. All these advantages are not offered by current state-of-the-art techniques. The matlab codes for replication of the results in this study are available at: https://github.com/jinhesjtu/MILE.git.

The problem of passive localization of mixed near-field (NF) and far-field (FF) source signals in the presence of array gain-phase uncertainties is addressed. A new algorithm is aimed to use partly calibrated nonuniform linear arrays (NLAs), in which only three sensors have been fully-calibrated. Most of the existing algorithms deal with this problem by exploiting uniform linear arrays (ULAs). Moreover, they assume a simplified source-array model, in which the propagation magnitude scaling is completely neglected and the spatial phase difference is approximated by Taylor’s polynomial. As an opposite, the proposed algorithm is employed to accommodate a more general situation: the exact spatial geometries and nonuniform linear arrays. In the proposed algorithm, three cumulant matrices are firstly defined to construct two matrix pencils. Unambiguous range and angle parameter estimates of the NF sources are then obtained from the generalized eigenvalues of the two defined matrix pencils. After that, these estimates are utilized to calibrate array gain-phase errors. Finally, a spectrum-MUSIC like approach is applied to accomplish the angle estimation for the FF sources. The new algorithm is shown to be readily simple and effective and will be verified both mathematically and numerically.

This paper aims to estimate the two dimensional (2D) direction-of-arrival (DOA) using a polarized uniform rectangular array (URA) under multipath propagation. To leverage the tensorial nature, a parallel factor (PARAFAC) model is established, in which it comprises two spatial response matrices, the polarization response matrix, and the source matrix. Unfortunately, the source matrix exhibits rank-deficiency, hindering effectively PARAFAC decomposition. Our analysis reveals that the rank-deficiency can be easily resolved by taking the KhatriRao product with a full column rank factor matrix. Consequently, three rearranged PARAFAC tensors are obtained that are free of the source matrix's rank-deficiency. The estimation of 2D-DOA is then performed using the vector cross product-auxiliary rotational invariance technique (VCPARIT). The proposed algorithms are insensitive to inter-sensor distance and are suitable for a one-snapshot scenario. Furthermore, they outperform existing smoothing methods from the perspective of estimation accuracy. Theoretical advantages of the proposed algorithms are corroborated by the simulations.

The problem of near-field partially polarized electromagnetic source localization using an array of cross-dipoles, each of which consists of one x-axis dipole and one y-axis dipole, is addressed. The maximum likelihood (ML) algorithm for estimating the angle and range parameters is developed. This algorithm requires no search over the polarization parameters. We also show that the ML algorithm can be implemented by processing the x-axis dipole data and the y-axis dipole data separately. In addition, a subspace-based algorithm, which is based on the ideas of MUSIC and generalized ESPRIT, is presented. This algorithm decouples the two-dimensional (2D) search into two successive one-dimensional (1D) searches, where the angle and range parameters are estimated in succession. The deterministic Cramer-Rao bound (CRB), for the problem under consideration, is also derived. The performance of the subspace-based algorithm is evaluated and compared with that of the ML algorithm and the CRB.