Signal-to-noise Ratio Of Arrays Research Articles

Resolving power of MUSIC-like algorithms for circular or rectilinear correlated sources in CES data models

The concept of threshold array signal-to-noise ratio (ASNR) which is defined as the minimal SNR at which specific high-resolution algorithms are able to resolve two closely spaced far-field sources, allows to quantify and to compare sensors array performance in localizing remote targets. This paper generalizes and extends the expressions of the threshold ASNR given in the literature for the conventional and non-circular (NC) MUSIC direction-of-arrival (DOA) estimation algorithms in the context of uncorrelated stochastic circular or rectilinear Gaussian sources and circular complex Gaussian (C-CG) noise, in a more general stochastic framework. We assume that the sources are correlated with an arbitrary distribution, which is inherent in a context of multipath or smart jammers, and that the noise is circular complex elliptically symmetric (C-CES) distributed, which can model impulsive noise with heavy-tailed distributions. The C-CES and NC-CES distributed observations are also considered to quantify the gain in resolution provided when the sample covariance matrix (SCM) of the observations is replaced by M-estimates of this matrix. Asymptotic approaches and perturbation analysis have been performed to derive closed-form expressions of the mean null spectra of the two considered MUSIC algorithms for both observation models, which allow us to derive, for the first time, general unified explicit analytical expressions of the threshold ASNR along the Cox and the Sharman and Durrani criteria. These expressions allow us to quantify the impact of the non-Gaussianity of noise and observations, as well as of the phase and magnitude of the correlation on the resolution threshold, and to quantify the benefit provided when the SCM is replaced by M-estimates of this covariance matrix for CES observations. Finally, numerical illustrations are included to support our theoretical analysis.

Phase Coherent EM Array Measurements in a Refractive Environment

Phase-coherent measurements of the pilot tone from a digital television (DTV) station were taken by a 24-element vertical array 168 km from the transmitter. Measurements were recorded over 15 days in Southern California, a region known for ducting events in which abnormal atmospheric refractivity patterns allow for the exceptionally long-range propagation of electromagnetic (EM) waves. The DTV station was positioned over the horizon (OTH) relative to the receiver array such that the line of sight was obstructed; thus, significant diffraction loss was expected. Direction-of-arrival (DOA) estimation was performed on the measurements. The measurement campaign objective was to collect the first long-term data set of DOA and the array-signal-to-noise ratio (ASNR) from signals propagating OTH through a refractive channel, toward the goal of enhancing the fidelity of atmospheric refractivity estimates. The analysis of the collected data shows that ASNR is correlated with atmospheric parameters related to refractivity.

Approaching Ultimate Intrinsic SNR in a Uniform Spherical Sample with Finite Arrays of Loop Coils.

We investigated to what degree and at what rate the ultimate intrinsic (UI) signal-to-noise ratio (SNR) may be approached using finite radiofrequency detector arrays. We used full-wave electromagnetic field simulations based on dyadic Green's functions to compare the SNR of arrays of loops surrounding a uniform sphere with the ultimate intrinsic SNR (UISNR), for increasing numbers of elements over a range of magnetic field strengths, voxel positions, sphere sizes, and acceleration factors. We evaluated the effect of coil conductor losses and the performance of a variety of distinct geometrical arrangements such as "helmet" and "open-pole" configurations in multiple imaging planes. Our results indicate that UISNR at the center is rapidly approached with encircling arrays and performance is substantially lower near the surface, where a quadrature detection configuration tailored to voxel position is optimal. Coil noise is negligible at high field, where sample noise dominates. Central SNR for practical array configurations such as the helmet is similar to that of close-packed arrangements. The observed trends can provide physical insights to improve coil design.