Abstract
Blind estimation of the direction of arrival (DOA) and delay of room reflections from reverberant sound may be useful for a wide range of applications. However, due to the high temporal and spatial density of early room reflections and their low power compared to the direct sound, existing methods can only detect a small number of reflections. This paper presents PHALCOR (PHase ALigned CORrelation), a novel method for blind estimation of the DOA and delay of early reflections of a single source in a room that overcomes the limitations of existing solutions. PHALCOR is based on a signal model in which the reflection signals are explicitly modeled as delayed and scaled copies of the direct sound. A phase alignment transform of the spatial correlation matrices is proposed; this transform can separate reflections with different delays, enabling the detection and localization of reflections with similar DOAs. It is shown that the DOAs and delays of the early reflections can be estimated by separately analysing the left and right singular vectors of the transformed matrices using sparse recovery techniques. An extensive simulation study of a speaker in a reverberant room, recorded by a spherical array, demonstrates the effectiveness of the proposed method.
Highlights
E STIMATION of the direction of arrival (DOA) and delay of room reflections is useful for many tasks in signal processing, such as speech enhancement and dereverberation [1], [2], source separation [3], optimal beamforming [4] and room geometry inference [5]
A microphone array can be used to estimate the coefficients of the spherical Fourier transform (SFT) of the plane wave amplitude density (PWAD) with order less than or equal to N, by inverting the linear transformation (3), a process known as plane wave decomposition
6) Computational Complexity: We focus in the analysis on part 1 of PHALCOR since the pre-processing steps and part 2 are standard and shared among many methods
Summary
E STIMATION of the direction of arrival (DOA) and delay of room reflections is useful for many tasks in signal processing, such as speech enhancement and dereverberation [1], [2], source separation [3], optimal beamforming [4] and room geometry inference [5]. Subspace methods, such as MUSIC or ESPRIT [11]–[14], can often provide higher resolution than beamformers These methods require the sources to be uncorrelated, while in the case of early reflections, since all sources are delayed copies of the direct sound, reflected narrowband signals are highly correlated. Since for a given array geometry the dictionary remains fixed, the performance improves as the actual number of sources is reduced, and, in practice only the first few reflections are recoverable with practical arrays Another type of methods that can localize correlated sources is based on modeling the source signals as deterministic unknowns. This paper presents PHALCOR (PHase ALigned CORrelation), a novel method for blind estimation of the DOA and delay of early reflections of a single source in a room. A simulation study and conclusions are presented in Sections VI and VII, respectively
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