Compressive time delay estimation off the grid

Abstract

This paper describes a time delay estimation (TDE) technique using compressive sensing (CS) off the grid, which estimates the channel impulse response in a continuous time domain. The TDE can be formulated into a sparse signal reconstruction problem where the CS technique can be applied. Previous works have used standard finite dimensional CS with evenly discretized grids. However, the actual time delays will not always lie on the discrete grid, and this mismatch between the actual and discretized time delays results in reconstruction degradation. To overcome the basis mismatch, a TDE technique using an off the grid CS framework is proposed by modifying the scheme in the off the grid direction of arrival (DOA) estimation [Xenaki and Gerstoft, J. Acoust. Soc. Am. 137(4), 1923-1935 (2015)]. The effectiveness of the suggested method is demonstrated on real data from a water tank experiment. The off the grid CS TDE is shown to have super-resolution, which enables close arrivals to be distinguished.

Multiple snapshot grid free compressive beamforming

“…In general, n is unknown so selecting a proper value for e s is critical depending on the purpose. 27 Herein, the CVX program 34 (available in MATLAB) is an efficient tool to solve SDP [Eq. (8) Fig.…”

“…In underwater acoustic signal processing, the grid free CS technique has shown its superiority in its high resolution and robustness to the basis mismatch compared to the conventional CS technique. 26,27 The goal of DOA estimation can be to estimate the DOAs which are stationary across sequential multiple snapshot data. For multiple snapshot processing, the conventional CS DOA estimation technique has provided high resolution, outperforming the widely used classical superresolution techniques such as MVDR and MUSIC.…”

Compressive Sound Speed Profile Inversion Using Beamforming Results

“…After applying a simple delay-and-sum beamforming [11], DOAs are revealed in a time domain, which have much higher intensities compared to regions around them. It is helpful to refine the DOAs to exploit frequency-domain beamforming based on advanced techniques [14][15][16][17][18] and high-resolution channel impulse response [21] for the center of the array simultaneously with the delay-and-sum beamforming result. Practically, the DOAs should be used with the compressive SSP inversion.…”

“…To enhance the CS inversion performance, the errors in DOAs should be suppressed via refining beamforming results through advanced schemes [14][15][16][17][18]21]. Furthermore, the sparsity in the solution can be exploited with probability distribution of the errors as well as its probability distribution (i.e., sparse Bayesian learning) [25].…”

“…A is a sensing matrix that shows the linear relation between x and y, and these are defined differently according to the given problem. In underwater acoustics, CS has been applied to obtain a high-resolution DOA with a limited number of sensors in an array [14][15][16][17][18], and the applicability of CS has been expanded to source localization [19,20] and ocean parameter inversion [10,21,22].…”