Comparative study of single-channel algorithms
for blind reverberation time estimation
Heinrich W. Löllmann, Andreas Brendel, and Walter Kellermann
Friedrich-Alexander University Erlangen-Nürnberg, Germany{Heinrich.Loellmann, Andreas.Brendel, Walter.Kellermann}@FAU.de

Abstract
Knowledge about the reverberation time (T60) is exploited by numerous algorithms, e.g., for automatic speech
recognition, speech dereverberation, or as a feature for acoustic scene classification. This contribution provides
a comprehensive survey about various state-of-the-art methods to estimate the reverberation time blindly from anoisy and reverberant speech signal and compares their estimation performance for different acoustic scenarios.
The evaluation considers different acoustic conditions regarding the signal-to-noise ratio (SNR) and directto-reverberation ratio (DRR), and uses databases with room impulse responses measured in different acoustic
enclosures. The findings of the Acoustic Characterisation of Environments (ACE) challenge are extended bytaking into account algorithms and acoustic scenarios which are not considered in this benchmarking campaign,and by using a much larger set of reverberant speech signals.
Keywords: Reverberation time, blind estimation, single-channel, survey

1

Introduction

The reverberation time (RT) T60 is an important and widely used quantity for the characterization of acoustic enclosures [1]. Knowledge about the RT is exploited for various applications such as automatic speech
recognition (ASR), e.g., [2–4] or speech dereverberation, e.g., [5–7]. For such applications, the (possibly timevarying) RT can typically not be obtained by intrusive methods, e.g., by estimating it from a measured room
impulse response (RIR) by the Schroeder method [8] or its variants [9], but needs to be estimated blindly froma reverberant speech signal, usually in the presence of background noise. Various reverberation time estimators (RTEs) to address this challenging task were developed in the past two decades, e.g., [10–34].
The growing research interest in blind RT estimation also fuels the interest in comparative studies of different methods. In [35], three state-of-the-art methods [16, 17, 19] are compared using simulated and measured
RIRs. In [30], an analytical and experimental analysis of three common decay rate estimators [10, 12, 18] ispresented which are the main building blocks of many modeled-based RTEs. The variety of concepts for blind
RT estimation has motivated the Acoustic Characterisation of Environments (ACE) challenge, which provided
an objective benchmarking of RT and direct-to-reverberant energy ratio (DRR) estimators [36, 37].
This contribution presents a survey of various methods for blind RT estimation and evaluates the performanceof selected methods corresponding to different classes of algorithms for T60 estimation and, thus, aims at complementing previous benchmarking efforts. The investigation is based on the evaluation dataset and performancemeasures used for the ACE challenge to complement its findings by also investigating algorithms which were
not evaluated in that challenge. In addition, a second database is used generated by more than 700 measured
RIRs to cover a larger range of RTs and DRRs than for the ACE challenge to investigate how well different
methods perform for various acoustical scenarios.
The paper is organized as follows: In Sec. 2, a survey of different approaches to blind RT estimation is provided.
The datasets used for the evaluation are described in Sec. 3 and Sec. 4 presents evaluation results for various
RTEs. The paper concludes with a summary of the main results in Sec. 5.

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2

Methods for Blind RT Estimation

This section provides a survey over various methods for blind RT estimation from single-channel speech recordings.
2.1 Model-based methods without training
Many approaches to model-based blind RT estimation were inspired by the work of Lebart et al. [10]. They
have in common that speech pauses in which the signal energy decays gradually due to the room reverberationneed to be detected followed by an estimation of the RT from the decay behavior. It is furthermore assumed
that the signal decay can be described by a statistical modeldm (k) = A v(k) e−ρ k Ts ε(k)(1)

with sample index k, amplitude A > 0, decay rate ρ, unit step sequence ε(k), sampling period Ts and v(k) representing a sequence of i.i.d. standard-normally distributed random variables. The decay rate ρ is then estimatedby linear regression from the logarithm of the smoothed energy envelope of the reverberant speech signal within
the detected decay interval.1 The RT is obtained from the decay rate by the relation T60 = 3/(ρ log10 (e)) suchthat both terms can be used interchangeably.
In [12], the model of Eq. (1) is used to derive a maximum-likelihood (ML) estimator for the decay rate. Decay
rates are estimated continuously from speech frames (of 200 ms duration) shifted by one sample instant. The
final decay rate estimate is determined by applying an order statistics filter to a histogram of all decay rateestimates, i.e., the maximum of the histogram yields the final decay rate estimate as detailed in [12]. A benefitof this approach is that no speech decay detection is needed. However, the ML estimate of [12] is not given by
a closed-form solution, but has to be calculated by numerical optimization. In [13], two efficient solutions arepresented for this: A fast online algorithm is proposed which compares the values of the log-likelihood function
for a finite set of candidate decay rates to determine its approximate maximum. As an alternative, a fast block
algorithm is proposed (but not evaluated) which finds the maximum of the log-likelihood function iteratively bya gradient-based method. However, a suitable step size has to be found to ensure convergence of the algorithm.
The use of an ML estimator to determine the RT from a noisy reverberant speech signal by means of a priordenoising step is discussed in [18]. Based on this work, an efficient scheme to estimate a time-varying RT by
ML estimation is presented in [19]. A pre-selection of promising speech decays is performed to reduce thecomputational complexity and the number of outliers for the T60 estimation. In [20], it is proposed to determine
the fullband RT by an energy-weighted average of ML-estimates determined from the subband signals of an
octave filter bank. As shown in [20, 36], this method provides a higher estimation accuracy at the cost ofincreased computational complexity relative to the scheme of [19].
Various authors have derived ML estimators for the RT which are based on variants of the statistical decay
model of Eq. (1). In [18], an ML estimator is derived which allows to estimate the decay rate from a measured
RIR distorted by additive noise. An improvement of this estimator is presented in [30] which achieves a similar
estimation accuracy, but involves a significantly lower computational complexity. However, such estimators relyon an accurate estimation of the noise variance. In [21], an ML estimator is derived from a statistical modelfor the magnitude of the reverberant speech decay which leads to a closed-form solution for the T60 estimate.
The obtained RTE achieves a similar estimation accuracy as the method of [20], but with a considerably lower
computational complexity. In [14], an ML estimator is presented which extends the model of Eq. (1) to accountfor different decay rates for the early and late reflections. In [24] and [33], ML estimators for the RT are
derived which assume a sequence of Laplace- and Gamma-distributed random variables, respectively, for v(k)in Eq. (1).
In [25], a speech model-based algorithm is presented where the decay rate is estimated from the residual signal
obtained by a linear prediction (LP) filter. This approach is based on the assumption that the signal after LP
1 In [10], there is no scheme described for detecting the speech pauses.

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filtering contains a residual speech signal convolved with the RIR, but not with the vocal tract filter any more.
In this case, the auto-correlation of the signal after LP filtering contains decays, which can be modeled by
Eq. (1) and estimated by an ML estimator as presented in [12]. An LP filter is also used in [32] to obtain an
estimate of the RIR from which the RT is calculated by the Schroeder method.
Besides ML estimation, the use of linear regression is another common method to obtain the RT from detectedspeech decays [10]. In [22], RT estimation is performed in the discrete magnitude short-time Fourier transform(STFT) domain by estimating the decay rate by linear regression from detected decay regions. The median of
the subband estimates is mapped to the fullband estimate by a linear function. A modification of this scheme ispresented in [23] to account for additive noise. It should be noted that model-based RTEs which obtained thefullband estimate by a mapping of subband estimates [20,23] scored among the best at the ACE challenge [37].
The RTE presented in [29] operates in the modulation domain. The modulation coefficients are obtained by adiscrete Fourier transform (DFT) of the magnitude of the discrete STFT coefficients of the reverberant speech
signal calculated over the STFT frequency bands. The decay rate is determined by minimizing the meansquare error (MSE) between the modulation coefficients of the reverberant speech and the representation of thestatistical RIR of Eq. (1) in the modulation domain for a detected sound decay.
2.2 Methods based on single feature mapping with training
The previously discussed model-based approaches have in common that the decay rate is estimated directly via
linear regression or ML estimation from a speech decay interval, an auto-correlation sequence or an estimateof the RIR. In contrast, methods based on feature mappings derive the RT from a distinct parameter calculated
from the reverberant speech which changes with the T60 . The RT is then obtained by a learned mapping function
between the calculated feature and the T60 , e.g., [15–17, 26–28].
In [15], a pitch-based method is proposed for the estimation of short RTs (up to 0.6 s). It is based on theobservation that reverberation changes the harmonic structure of voiced speech and the pitch strength measure
is introduced to quantify this change. The RT is finally obtained by a learned mapping function which relates
the pitch strength to the T60 .
In [16], the variance corresponding to the negative side of the distribution of measured decay rates is mapped to
the RT by a second-order polynomial function whose coefficients are found by training with a few reverberant
speech files. The distribution of the decay rates is obtained by estimating decay rates in the discrete magnitude
STFT domain via linear regression for each frame without sound decay detection. Various improvements of thisalgorithm have been proposed: In [26], the method of [16] is extended by including an LP-based prewhitening
step to obtain a better fit for the model assumption of Eq. (1). In [28], the estimation accuracy and robustness
towards noise is improved by learning a data-driven representation of the decay rates based on training forseveral room configurations. In [27], the complexity of the RTE of [16] is reduced by calculating the decay
rates in Mel frequency bands instead of STFT frequency bands. The robustness towards noise is improved byintroducing a dependency on the signal-to-noise ratio (SNR) for the T60 calculation.
2.3 Methods based on multiple features with training
This class of RTEs maps multiple features to the RT, typically by using an artificial neural network (ANN). In
contrast to approaches based on single feature mapping, these methods usually require a much larger training
and do typically not rely on the statistical RIR model of Eq. (1).
An early attempt to estimate the RT with ANNs is presented in [11] which was trained on noiseless reverberant
speech. In [17], two approaches to estimate the RT are presented where various features are mapped to the
RT by support vector regression (SVR). In the first method, the cepstral coefficients of the reverberant speech
signal are used for the feature calculation. As an algorithmic variant, the reverberation-to-speech modulationenergy ratio (RSMR) is introduced, which is calculated in the modulation domain and used as feature for RT
estimation.
More recently, the joint room parameter estimator (jROPE) has been presented in [34] which jointly estimates

96the RT and early-to-late reverberation ratio (ELR) by an ANN. A multi-layer perceptron maps auditory-inspired
temporal modulation features to binned classes for the RT and ELR.

3

Datasets

The data corpus of the ACE challenge [36, 37] has become a common dataset for the evaluation of RT and
DRR estimators. The evaluation dataset contains 4500 noisy reverberant speech files with a sampling frequencyof 16 kHz and SNRs of −1 dB, 12 dB and 18 dB. The files were generated by convolving RIRs measured infive different rooms with anechoic speech signals and adding noise recorded in the same rooms. The development dataset contains 288 sound files generated by measured RIRs and recorded noise obtained for two rooms
different from those considered for the evaluation dataset.
The evaluation dataset of the ACE challenge provides very realistic recordings, but comprises only a rather
small set of acoustic environments due to the cumbersome recording procedure. Therefore, a new, larger datasetwith noisy reverberant speech signals was created for this study, termed as large evaluation dataset (LED). It is
used in addition to the ACE evaluation dataset to account for a larger range of RTs and DRRs. As for the ACE
challenge dataset, only measured RIRs and no simulated RIRs were used to generate the reverberant speech.
The measured RIRs were mainly obtained from publicly available databases which do not provide separate
noise recordings for the rooms in which the RIRs were measured. Therefore, the ambient noise was generated
by convolving the late reverberant part of the RIRs with either white Gaussian noise or babble noise, cf., [34].
Thus, the noisy reverberant speech signals were obtained as follows
L−1

L−1

l=0

m=0

(m) n j (k − m)y p,i, j,α (k) = ∑ s p (k − l) hi (l) + α ∑ h(late)i(2)with indices p ∈ {1, . . . , 4}, i ∈ {1, . . . , 782} and j ∈ {1, 2} denoting the used anechoic speech signals s p (k), measured RIRs hi (k) and noise signals n j (k), respectively. Two male and two female speech files each with a lengthof 14 − 16 s were used obtained by concatenating speech files of the CSTR VCTK1 database [38] downsampled
to 16 kHz. Babble noise for an anechoic environment can be created by adding up non-reverberant speech signals, e.g., [34]. Here, 7 male and 7 female speech sequences using concatenated files of the CSTR VCTK1
database were added for this. The temporal segment of the RIR beginning 50 ms after the first dominant peak(m). The scaling factor α ≥ 0 was adjusted to obtain a predefined segwas taken as late reverberant part h(late)imental SNR between reverberant speech and additive noise. The active speech level for the segmental SNR
calculation was determined according to ITU-T P.56 [39] as provided by the MATLAB toolbox Voicebox [40].
Segmental SNR values of −5 dB, 5 dB, 15 dB and the case of no added noise were considered for the generationof the dataset.
The RIRs to generate the LED were mainly obtained from publicly available databases, namely, the Aachen
impulse response (AIR) database [41], the multichannel acoustic reverberation database at York (MARDY) [42],the multichannel impulse reponse database (MIRD) [43] and the OpenAirLib database [44]. Only RIRs with a
RT of less than 1.5 s were considered. Moreover, RIRs measured in the acoustic laboratory, a seminar room
and a hallway of the Chair of Multimedia Communication and Signal Processing of the University ErlangenNuremberg have been used with RTs ranging from 0.2 to 0.9 s.
A scatter plot showing the RTs and DRRs of the 782 RIRs included in the LED is provided by Fig. 1. The
T60 was determined by the Schroeder method [8] using least-squares (LS) fitting. The DRR was determinedaccording to [37] (but without equalization prior to the peak search). The RIRs of the ACE challenge were notused for generating the LED, but their RTs and DRRs are shown in Fig. 1 for comparison. The used databases
often provide various RIRs measured in the same room at different positions which is reflected by the different
DRR values for the same RT.
Four scenarios were considered for generating the LED: A male or female speech signal in the presence ofeither diffuse noise or babble noise. Hence, the database for each segmental SNR value comprised 3128 audio
files and the complete database with its 12512 files has a total duration of 75 hours.

97

ACE
Own
AIR
MARDY
MIRD
OpenAirLib

1.4
1.2

T60 /s

1
0.8
0.6
0.4
0.2
0

−14 −12 −10 −8

−6

−4

−2

0

2
4
DRR/dB

6

8

10

12

14

16

18

20

Figure 1. RTs and DRRs of the RIRs used for the large evaluation dataset (LED) and the ACE challenge data
corpus (evaluation and development dataset).
Table 1. Overall estimation accuracy of various fullband RTEs.
Algorithm
FAO [13]
LM RTE [24]
ML RTE [19]OSB RTE [20]SFM RTE [27]
jROPE II [34]4

ACE evaluation dataset
Bias
MSE
Cp
-0.161 0.193 0.169
0.294 0.216 0.285-0.046 0.111 0.384-0.106 0.072 0.751-0.051 0.095 0.502
0.124 0.129 0.661

Large evaluation dataset
Bias
MSE
Cp
-0.215 0.168 0.572
0.220 0.140 0.635
0.010 0.065 0.770
0.046 0.066 0.758-0.010 0.062 0.778
0.312 0.374 0.489

Evaluation

As representatives for the large class of model-based approaches without training, the fast online algorithm(FAO) of [13], the Laplace distribution-based estimator (LM RTE) of [24], the ML estimation-based RTE(ML RTE) of [19] (which served as baseline algorithm in the ACE challenge) and the octave subband-based
RTE (OSB RTE) of [20] are considered in this evaluation.2 The single feature mapping-based RTEs are represented by the algorithm of [27] (SFM RTE) and the jROPE II algorithm [34, 46] represents a method for RT
estimation based on multiple feature mapping. The estimation performance is assessed by the bias, MSE andPearson correlation coefficient Cp as used also for the ACE challenge [37] which also allows to compare theevaluation results with those of [37]. The Pearson correlation coefficient quantifies how closely the estimation
results are correlated with the ground truth values, cf., [37].
The evaluation results for the considered estimators and datasets are listed in Table 1. The OSB RTE andSFM RTE show a high estimation performance for both datasets where the OSB RTE achieves the highest
performance of all RTEs for the ACE challenge dataset w.r.t. MSE and Pearson correlation coefficient, and
2 A MATLAB implementation of the ML RTE is available online [45] where the results for the ACE challenge [37] were created with a modified
version which used a different parameter setting and included a prior noise suppression.

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Table 2. Estimation accuracy for different segmental SNRs and DRRs for the LED.
Algorithm
OSB RTE [20]SFM RTE [27]

jROPE II [34]Measure
Bias
MSE
Cp
Bias
MSE
Cp
Bias
MSE
Cp

-5
0.188
0.131
0.606
0.096
0.066
0.799
0.591
0.638
0.372

segmental SNR [dB]515∞0.055 -0.010 -0.050
0.054
0.039
0.040
0.827
0.889
0.899
-0.018 -0.028 -0.092
0.048
0.055
0.079
0.851
0.831
0.754
0.452
0.179
0.025
0.502
0.239
0.119
0.450
0.631
0.689

DRR
< 5 dB > 5 dB
0.017
0.089
0.075
0.052
0.770
0.525
-0.047
0.043
0.079
0.037
0.772
0.586
0.285
0.351
0.342
0.422
0.533
0.312

the SFM RTE achieves the highest estimation accuracy of all treated estimators for the LED. In contrast,
the estimation performance of the ML RTE is less consistent for both databases as it achieves a marginallybetter estimation performance than the OSB RTE for the LED, but a significantly lower accuracy for the ACE
challenge dataset.
Like the ML RTE, the FAO and the LM RTE are also ML-based methods, but do not account for additivenoise which explains their lower estimation performance in comparison to the ML RTE that performs a noise
reduction prior to the RT estimation. The jROPE II estimator achieves a rather good estimation performancefor the ACE challenge dataset with the second highest Pearson correlation coefficient of all estimators, but thelowest estimation performance of all approaches for the LED. The LED contains a much larger variety of
DRRs and RTs than the ACE challenge dataset such that the mismatch between training and evaluation data
can become more pronounced.
More detailed results for the OSB RTE, the SMF RTE and the jROPE-II estimator (as representatives for thepreviously discussed three classes) for the LED are provided by Table 2. The estimation performance of the
jROPE II estimator decreases for decreasing SNRs most likely due to a mismatch between the noise used for
the LED and the noise used in the training, cf., [34]. A mismatch between training and evaluation dataset could
also explain the lower estimation performance for higher DRRs than for lower DRRs.3 A similar tendency
can also be observed for the OSB RTE whose estimation performance decreases for low SNR values of 5and −5 dB. The prior noise suppression can only partly remove the noise, especially at low SNRs, and theremaining noise contained in the detected speech decays leads to an increased bias and estimation error since
the assumed statistical model of Eq. (1) becomes less valid. This statistical model does also not model earlyreflections which explains the lower Pearson correlation coefficient for higher DRRs. The same can be observed
for the SFM RTE which is also derived based on the statistical model of Eq. (1). However, the estimation
performance of this RTE does not decrease significantly for low SNRs compared to the OSB RTE which canbe attributed to the SNR-dependent RT calculation.

5

Conclusions

This contribution has presented a comprehensive survey on single-channel algorithms for blind RT estimation
and an evaluation of selected algorithms representing different approaches to RT estimation by using the evaluation dataset of the ACE challenge and a second dataset which covers a larger range of RTs and DRRs. Most
model-based approaches for RT estimation are derived by assuming a statistical model for the sound decay andrequire no training phase. The evaluation of four such approaches [13, 19, 20, 24] has shown that the energy
3 The non-blind RT estimation from a measured RIR by the Schroeder method [8] is also less reliable for a high DRR as the assumption of alogarithmic energy decay is less valid.

99

weighted averaging of subband estimates [20] leads to a higher overall estimation performance than the RT
estimation in the time-domain as done in [13, 19, 24] (at the cost of a higher computational complexity). RTEs
based on single feature mapping require typically a training phase for a small set of room configurations suchas [27]. This RTE and the RTE of [20] have achieved a rather high estimation performance for both considered
database. However, both methods are derived by a statistical model for the sound decay and show performancedegradations if this model becomes less valid due to noise or for high DRRs. The evaluation has shown that
adapting the RT calculation based on the SNR in [27] achieves a higher noise robustness than a prior denoising
as used in [20].
RTEs based on the mapping of multiple features to the reverberation time, e.g., by an ANN, require much moretraining data than single feature-based approaches, but do not rely on an explicit signal model. The evaluationof the jROPE II estimator [34] has shown that a mismatch between training and evaluation dataset can lead toa significant decrease of the estimation accuracy.

Acknowledgment
The authors gratefully acknowledge the contributions of Apurva Kriti in evaluating the various estimators. The
authors are also thankful to Feifei Xiong (University of Oldenburg) for providing the code for the jROPE II
RTE [34], and James Eaton (Imperial College) for providing a MATLAB implementation for [27] and the ACE
challenge data corpus. This work was partly supported by DFG under contract no. <Ke890/10-1> within the
Research Unit FOR2457 "Acoustic Sensor Networks".

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