[Paper Review] Estimation of the direct-to-reverberant Energy Ratio using a spherical microphone array

Hanchi Chen, Prasanga N. Samarasinghe+2 more|arXiv (Cornell University)|Oct 30, 2015

Speech and Audio Processing10 references7 citations

TL;DR

This paper proposes a blind estimation method for the direct-to-reverberant energy ratio (DRR) using a spherical microphone array (Eigenmike) without requiring prior knowledge of the source signal. By leveraging spherical harmonic decomposition to estimate sound pressure and particle velocity components, and exploiting the coherence between pressure and velocity, the method achieves ±3 dB DRR accuracy across 199–2511 Hz, even in low-SNR and high-reverberation conditions.

ABSTRACT

This paper proposes a practical approach to estimate the direct-to-reverberant energy ratio (DRR) using a spherical microphone array without having knowledge of the source signal. We base our estimation on a theoretical relationship between the DRR and the coherence estimation function between coincident pressure and particle velocity. We discuss the proposed method's ability to estimate the DRR in a wide variety of room sizes, reverberation times and source receiver distances with appropriate examples. Test results show that the method can estimate the room DRR for frequencies between 199 - 2511 Hz, with $\pm$ 3 dB accuracy.

Motivation & Objective

• To develop a practical, blind method for estimating the direct-to-reverberant energy ratio (DRR) in reverberant rooms without requiring prior knowledge of the source signal or impulse response.
• To overcome limitations of existing DRR estimation techniques that rely on time-domain impulse response measurement or require accurate direction-of-arrival (DOA) estimation as a priori input.
• To improve DRR estimation accuracy in low-SNR and high-reverberation environments by utilizing spatial averaging and frequency-smoothed MUSIC for DOA estimation.
• To validate the method across diverse room sizes, reverberation times, and source-receiver distances using the ACE Challenge database.

Proposed method

• The method uses a 32-element Eigenmike spherical microphone array to record sound fields and computes spherical harmonic coefficients from the measured pressure data using discrete spherical harmonic decomposition.
• First-order spherical harmonics are derived to represent particle velocity components along orthogonal axes at the array's center, enabling estimation of the velocity component along the direct path direction.
• The direction of arrival (DOA) of the direct path is estimated using a frequency-smoothed MUSIC algorithm applied in the spherical harmonic domain to mitigate coherence between direct and reverberant components.
• The DRR is estimated using the magnitude-squared coherence between the estimated particle velocity and the sound pressure, based on a theoretical relationship from Kuster (2013).
• Spatial averaging of multiple velocity estimates is applied to improve robustness, particularly at higher frequencies where single-estimate performance degrades.
• Fullband DRR is computed by averaging subband DRR estimates from 199 Hz to 2511 Hz, excluding unreliable low- and high-frequency bands.

Experimental results

Research questions

• RQ1 Can the DRR be accurately estimated in real-time using only a spherical microphone array without prior knowledge of the source signal or impulse response?
• RQ2 How does the proposed method perform across varying room sizes, reverberation times, and source-to-receiver distances?
• RQ3 What is the impact of spatial averaging and frequency-smoothed DOA estimation on DRR estimation accuracy?
• RQ4 How does the method perform under low signal-to-noise ratio (SNR) conditions?
• RQ5 To what extent does the method maintain accuracy in high-reverberation environments?

Key findings

• The proposed method achieves ±3 dB DRR estimation accuracy across the frequency band of 199–2511 Hz, even in challenging acoustic conditions.
• Spatial averaging of four velocity estimates significantly improves accuracy, reducing deviation from ground truth to less than 2 dB in most subbands, especially at higher frequencies.
• At 18 dB SNR, the mean estimation error across all subbands is within ±3 dB, with standard deviation below 3 dB, and the error decreases with increasing frequency.
• At −1 dB SNR, the mean error increases across all subbands, and the standard deviation rises to around 4 dB, with no improvement at higher frequencies, indicating noise sensitivity.
• Fullband DRR estimation maintains error within ±3 dB for all room configurations at 18 dB SNR, with only two setups exceeding 3 dB mean error, primarily in long-distance, high-reverberation conditions.
• The method demonstrates robustness in high-reverberation scenarios, though accuracy slightly degrades when the ground-truth DRR is very low, as seen in long-distance lecture room recordings.