Angular resolution limit for deterministic correlated sources

This paper is devoted to the analysis of the angular resolution limit (ARL), an important performance measure in the directions-of-arrival estimation theory. The main fruit of our endeavor takes the form of an explicit, analytical expression of this resolution limit, w.r.t. the angular parameters of interest between two closely spaced point sources in the far-field region. As by-products, closed-form expressions of the Cram\'er-Rao bound have been derived. Finally, with the aid of numerical tools, we confirm the validity of our derivation and provide a detailed discussion on several enlightening properties of the ARL revealed by our expression, with an emphasis on the impact of the signal correlation

MIMO Radar Target Localization and Performance Evaluation under SIRP Clutter

Multiple-input multiple-output (MIMO) radar has become a thriving subject of research during the past decades. In the MIMO radar context, it is sometimes more accurate to model the radar clutter as a non-Gaussian process, more specifically, by using the spherically invariant random process (SIRP) model. In this paper, we focus on the estimation and performance analysis of the angular spacing between two targets for the MIMO radar under the SIRP clutter. First, we propose an iterative maximum likelihood as well as an iterative maximum a posteriori estimator, for the target's spacing parameter estimation in the SIRP clutter context. Then we derive and compare various Cram\'er-Rao-like bounds (CRLBs) for performance assessment. Finally, we address the problem of target resolvability by using the concept of angular resolution limit (ARL), and derive an analytical, closed-form expression of the ARL based on Smith's criterion, between two closely spaced targets in a MIMO radar context under SIRP clutter. For this aim we also obtain the non-matrix, closed-form expressions for each of the CRLBs. Finally, we provide numerical simulations to assess the performance of the proposed algorithms, the validity of the derived ARL expression, and to reveal the ARL's insightful properties.Comment: 34 pages, 12 figure

Performance analysis of an improved MUSIC DoA estimator

This paper adresses the statistical performance of subspace DoA estimation using a sensor array, in the asymptotic regime where the number of samples and sensors both converge to infinity at the same rate. Improved subspace DoA estimators were derived (termed as G-MUSIC) in previous works, and were shown to be consistent and asymptotically Gaussian distributed in the case where the number of sources and their DoA remain fixed. In this case, which models widely spaced DoA scenarios, it is proved in the present paper that the traditional MUSIC method also provides DoA consistent estimates having the same asymptotic variances as the G-MUSIC estimates. The case of DoA that are spaced of the order of a beamwidth, which models closely spaced sources, is also considered. It is shown that G-MUSIC estimates are still able to consistently separate the sources, while it is no longer the case for the MUSIC ones. The asymptotic variances of G-MUSIC estimates are also evaluated.Comment: Revised versio

Cramer-Rao bounds in the estimation of time of arrival in fading channels

This paper computes the Cramer-Rao bounds for the time of arrival estimation in a multipath Rice and Rayleigh fading scenario, conditioned to the previous estimation of a set of propagation channels, since these channel estimates (correlation between received signal and the pilot sequence) are sufficient statistics in the estimation of delays. Furthermore, channel estimation is a constitutive block in receivers, so we can take advantage of this information to improve timing estimation by using time and space diversity. The received signal is modeled as coming from a scattering environment that disperses the signal both in space and time. Spatial scattering is modeled with a Gaussian distribution and temporal dispersion as an exponential random variable. The impact of the sampling rate, the roll-off factor, the spatial and temporal correlation among channel estimates, the number of channel estimates, and the use of multiple sensors in the antenna at the receiver is studied and related to the mobile subscriber positioning issue. To our knowledge, this model is the only one of its kind as a result of the relationship between the space-time diversity and the accuracy of the timing estimation.Peer ReviewedPostprint (published version

The azimuth structure of nuclear collisions -- I

We describe azimuth structure commonly associated with elliptic and directed flow in the context of 2D angular autocorrelations for the purpose of precise separation of so-called nonflow (mainly minijets) from flow. We extend the Fourier-transform description of azimuth structure to include power spectra and autocorrelations related by the Wiener-Khintchine theorem. We analyze several examples of conventional flow analysis in that context and question the relevance of reaction plane estimation to flow analysis. We introduce the 2D angular autocorrelation with examples from data analysis and describe a simulation exercise which demonstrates precise separation of flow and nonflow using the 2D autocorrelation method. We show that an alternative correlation measure based on Pearson's normalized covariance provides a more intuitive measure of azimuth structure.Comment: 27 pages, 12 figure