Low-Level Sinusoidal Signal Detection From a High-Resolution Virtual Spectral Image Using Autoregressive Vector Extrapolation

Abstract

A new high-resolution virtual spectral imaging technique is able to resolve a closely spaced dominant and low-level sinusoidal signal (power spread of up to 15 dB) in harsh signal-tonoise ratio environments with limited samples where a highresolution 2-D autoregressive (AR) spectral estimation algorithm failed. This feat is accomplished by applying a 2-D fast Fourier transform to an expanded 2-D measurement data set (which consists of the original measurements extended by vectorextrapolated virtual measurements). The virtual measurement data are created from the original 2-D measurements using an innovative virtual-data vector extrapolation algorithm. A special 2-D AR model is used to model the measurements and then used to extrapolate measurements a vector at a time. Simulations compare our virtual spectral image with a high-resolution 2-D AR spectral image and a spectral image of the truth (the measurements that the extrapolation algorithm is trying to predict). The virtual measurement data are also compared with the true measurement data. We analytically show that the virtual measurements are a function of the true measurements plus some residual error terms. Mean-squared-error simulations show that the extrapolated measurements are well behaved for our problem space and provide a cost example.

Constrained Sensor System Resolves Closely Spaced Obscured Low-SNR Sources Using Virtual Beamforming

“…It can be zero-filled (as was done in [15]) or extrapolated using a 1-D linear prediction technique as was done in [21] and [22]. A vector extrapolation technique [24] was applied by the authors to enhance spectral estimation in [17] and [18], which overcomes this limitation. The vector extrapolation technique uses the existing measurement data to predict a vector of measurements at a time.…”

“…The virtual measurement data is partitioned in the original measurement data and the extrapolated measurement data. Because the extrapolation is trying to predict the signals, it has been shown in [17] and [18] that the extrapolated measurement data is just the truth plus some error terms, which is presented…”

“…First, we improve upon the current DOA estimation by demonstrating a high-resolution capability of a constrained sensor system, where the measurements are limited. The environment differs from [18] and [19] because the data is narrowband and there are three closely spaced sources instead of two. We cover three different environmental cases a high-SNR case, and two low-SNR cases.…”

“…By close, we mean that the sources are within one beamwidth of the array and unresolvable by a CBF and high-resolution algorithms. Second, is that we apply different algorithms than those of [18] and [19] to address a different problem space, narrow-band DOA estimation. Here, we use the CBF instead of a 2-D fast Fourier transform.…”

High-resolution digital beamforming of UWB signals based on Caratheodory representation for delay compensation and array extrapolation

“…However, there are more and more constraints in extending the aperture of an array, so the array extrapolation technique is a considerable option, especially for a small-scale array [18,19]. One typical extrapolation method is the vector extrapolation based on two dimensional autoregressive model (2D-ARVE) [20,21]. However, this method utilizes a linear model and makes use of multiple snapshots to create virtual measurement data, so the real-time performance is affected.…”