Bias Analysis of Spatial Coherence-Based RTF Vector Estimation for Acoustic Sensor Networks in a Diffuse Sound Field

TL;DR

This paper provides a theoretical bias analysis of a spatial coherence-based RTF vector estimation method for acoustic sensor networks, revealing the dependence of optimal weights on input SNR and highlighting practical estimation errors.

Contribution

It derives an analytical expression for the weights in the RTF estimation method, showing they are real-valued and SNR-dependent, and compares model-based and GEVD-based weights.

Findings

Optimal weights are real-valued and SNR-dependent

GEVD-based and model-based weights show good agreement in simulations

Estimation errors in practice are not fully accounted for by the model

Abstract

In many multi-microphone algorithms, an estimate of the relative transfer functions (RTFs) of the desired speaker is required. Recently, a computationally efficient RTF vector estimation method was proposed for acoustic sensor networks, assuming that the spatial coherence (SC) of the noise component between a local microphone array and multiple external microphones is low. Aiming at optimizing the output signal-to-noise ratio (SNR), this method linearly combines multiple RTF vector estimates, where the complex-valued weights are computed using a generalized eigenvalue decomposition (GEVD). In this paper, we perform a theoretical bias analysis for the SC-based RTF vector estimation method with multiple external microphones. Assuming a certain model for the noise field, we derive an analytical expression for the weights, showing that the optimal model-based weights are real-valued and only depend on the input SNR in the external microphones. Simulations with real-world recordings show a good accordance of the GEVD-based and the model-based weights. Nevertheless, the results also indicate that in practice, estimation errors occur which the model-based weights cannot account for.