Cramér-Rao Bound Analysis of Underdetermined Wideband DOA Estimation Under the Subband Model via Frequency Decomposition

Abstract

This is a repository copy of Cramr-Rao bound analysis of underdetermined wideband DOA estimation under the subband model via frequency decomposition.

Speech Enhancement With Robust Beamforming for Spatially Overlapped and Distributed Sources

“…Here, we take p = 1 for exploiting also the sparsity property of the spectrogram of the speech, and add the entropy function defined in (11) of the output of the microphone array for extracting the signal component which is the least Gaussian. We propose to define the Beamforming filter as the solution: (15) where Y(ω) ∈ C M ×D are the samples of the signals received at the microphone array at frequency band ω after the short time Fourier transform (STFT), y d is the d th column of the matrix Y(ω), ω is omitted in the following as all the algorithms are studied in the same sub-frequency band, D is the number of samples at each sub-frequency band, λ 1 is the sparsity penalization weighting parameter, δ w is the constraint that we impose on the norm of the Beamforming filter, c 1 and c 2 are assumed to be the steering vectors corresponding to the target source and the interference, respectively. The problem (15) can be solved by the CVX toolbox directly.…”

“…We propose to define the Beamforming filter as the solution: (15) where Y(ω) ∈ C M ×D are the samples of the signals received at the microphone array at frequency band ω after the short time Fourier transform (STFT), y d is the d th column of the matrix Y(ω), ω is omitted in the following as all the algorithms are studied in the same sub-frequency band, D is the number of samples at each sub-frequency band, λ 1 is the sparsity penalization weighting parameter, δ w is the constraint that we impose on the norm of the Beamforming filter, c 1 and c 2 are assumed to be the steering vectors corresponding to the target source and the interference, respectively. The problem (15) can be solved by the CVX toolbox directly. However, the CVX toolbox solves the entropy family functions such as ( 12)-( 14) using an experimental successive approximation method which is slower and less reliable than the method employed for other problems.…”

“…However, the CVX toolbox solves the entropy family functions such as ( 12)-( 14) using an experimental successive approximation method which is slower and less reliable than the method employed for other problems. To solve this problem, we reformulate (15) with only linear constraints as the problem (16), where the entropy replaces the contrast function. Note that the problem ( 16) is non-convex and non-continuous, we solve this problem by the LPADMM which is faster and more accurate.…”

“…2) As explained before, c 2 is an approximate model for the ID interference. To compensate for the error introduced by this approximation, we relax the equality constraint on the steering vectors in (15) to an inequality constrained by δ 2 . We propose to define the Beamforming as the solution:…”

“…Most of Beamforming techniques mentioned above as well as other array processing techniques [15] are developed in the scenario of point source. However, for many applications, the source can no longer be considered as point source and angular spreads should be taken into consideration.…”