Sample Rate Offset Compensated Acoustic Echo Cancellation For Multi-Device Scenarios

Emanuel A. P. Habets; Oliver Thiergart; Srikanth Korse

REVIEW 2 major objections 5 minor 27 references

Sample Rate Offset Compensated Acoustic Echo Cancellation For Multi-Device Scenarios

T0 review · 2 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Sample rate offsets between devices no longer have to break acoustic echo cancellation.

desk verdict A solid empirical integration paper whose real contribution is the decoupling finding for correlated playback; the ideal-VAD dependence and lack of error bars are the soft spots, not the math. read the letter →

arxiv 2507.05399 v1 pith:BJ4B7RZJ submitted 2025-07-07 eess.AS

Srikanth Korse , Oliver Thiergart , Emanuel A. P. Habets This is my paper

classification eess.AS

keywords acousticechocancellationsamplerateoffsetKalmanfilteringmulti-deviceteleconferencingcoherencedriftresamplingclockdouble-talk

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper claims that acoustic echo cancellation across multiple loudspeaker devices can be made to work despite sample rate offsets by treating the setup as a two-channel filtering problem, estimating the offset between device clocks, and resampling the auxiliary far-end reference to match the primary device's clock. In a simulated two-device room with uncorrelated playback, the proposed system recovers the same echo return loss enhancement and speech quality as a system with no offset, and it matches an oracle that knows the true offset. With correlated playback, the paper shows that an independent single-channel AEC error must drive the SRO estimator, otherwise the estimator and multi-channel filter interfere and performance stays near the uncompensated baseline. This matters because multi-device teleconferencing over Bluetooth or WiFi currently loses echo cancellation quality to clock drift, and a synchronous reference-based fix would avoid changing the devices or the network.

What carries the argument

The load-bearing object is the frequency-domain phase-rotation model $\Lambda(k,m)$, which turns a drifting auxiliary signal into a stationary reference at the primary device's clock. The DWACD algorithm estimates $\epsilon_{1,2}$ from the phase slope of the complex coherence between the auxiliary reference and a chosen error signal, using golden-search refinement for the fractional time lag; the estimated rotation then resamples $X_2$ to produce $\tilde X_2$ for the two-channel Kalman filter. The second key piece is Variant 2's independent single-channel AEC, whose error $E_0$ removes the primary device's own echo before coherence estimation, decoupling SRO estimation from the slow-converging multi-channel filter.

What would settle it

Use the same setup but replace the clean pre-transmission $X_2$ with the delayed or mixed signal a primary device could actually observe after transmission; if ERLE and PESQ no longer recover to the no-SRO baseline, the pre-transmission-access assumption, not the SRO-estimation and resampling method, is what carries the result.

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Extended reading notes

Core claim

The central claim is that the divergence of a multi-channel Kalman AEC filter under sample rate offset can be mitigated by estimating the offset with the dynamic weighted average coherence drift algorithm and resampling the auxiliary far-end signal before filtering. Concretely, the SRO appears in the frequency domain as the phase rotation $\Lambda(k,m) = e^{-j2\pi k/N_w \cdot mN_h \epsilon_{1,2}/f_1}$ on $X_2(k,m)$, so resampling means multiplying the auxiliary reference by this rotation and using $\tilde X_2 = X_2\Lambda$ as the second channel's input to the partitioned-block Kalman filter. In two-device experiments, this restores no-offset ERLE and PESQ for uncorrelated playback, and for correlated playback the decoupled Variant 2 matches oracle performance in echo-only; a residual gap in double-talk is attributed to less robust SRO estimation when near-end speech is present.

Load-bearing premise

The primary device must have access to the auxiliary far-end signal $X_2$ before it is transmitted, so the SRO estimator and resampler always see a clean reference; if only a delayed, mixed, or post-transmission copy is available, the synchronous compensation chain cannot be set up.

Editorial extensions

If this is right

For uncorrelated playback, SRO compensation makes the two-device Kalman AEC reach the no-SRO baseline for offsets within at least ±75 ppm and keeps most of that gain up to ±150 ppm.
For correlated playback, the SRO estimator must be fed by an independent single-channel AEC; without that decoupling, the proposed system performs no better than doing no compensation.
SRO estimates remain stable across echo path changes in echo-only conditions, so moving a device or switching a microphone does not force re-convergence of the offset estimate.
The resampling-based compensation does not add algorithmic delay, since the SRO estimate uses two previous 0.512-second segments.
In double-talk with correlated playback, even the oracle-SRO system leaves a performance gap, indicating that SRO estimation robustness, not the Kalman structure alone, is the remaining bottleneck.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The same phase-rotation and resampling recipe should generalize to $Q$ devices by estimating each auxiliary SRO independently, but the paper only validates the two-device case, so behavior across many devices is untested.
The energy-based ideal VAD used for coherence gating means real-world noise and double-talk may weaken SRO estimates; a robust voice activity detector or a non-speech reference would be a natural next test.
A fully blind setup, where the primary device only hears the auxiliary loudspeaker through the microphone instead of receiving a clean reference, escapes the paper's access assumption and is the main scenario the method cannot yet serve.
If SRO estimation accuracy is the double-talk bottleneck, improving the coherence estimator, for example by longer temporal smoothing or a multi-tap lag search, could close the correlated-playback gap without changing the two-channel Kalman structure.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper is an integration of two known components—DWACD SRO estimation and a partitioned-block Kalman AEC—into a two-device echo cancellation setting. That integration is the contribution, and it is a legitimate one. The authors show that for uncorrelated playback the SRO-compensated two-channel Kalman filter recovers the no-SRO baseline, and they identify a genuinely useful empirical fact: when the two devices play correlated content, the SRO estimator should be fed from an independent single-channel AEC error rather than from the multichannel error. That decoupling is the paper's real finding, and the SRO-versus-time plots make the point convincingly.

The paper is also honest. The abstract's claim about double-talk is stronger than what the body reports: for correlated playback in double-talk, Variant 2 still leaves a gap relative to the oracle, and the authors say so. That kind of reporting makes the rest of the results easier to trust.

Soft spots, in order of importance. First, the SRO estimator relies on an energy-based ideal VAD. The coherence function in Eq. (5) is computed only when speech is detected in both the reference and the input. The VAD knows ground truth. In echo-only that is a non-issue, but the headline claim covers double-talk, and there the oracle VAD is doing real work: it is selecting exactly the frames where the echo-to-near-end ratio is usable. The paper gives no sensitivity analysis or ablation with a realistic VAD. The stress-test note is right that this is the load-bearing assumption; it doesn't sink the paper, but it caps the strength of the double-talk claim.

Second, all results are averages over 50 simulated files with no error bars, and the SRO is constant-valued per file. Those are presentation choices rather than errors, but they make it harder to judge how robust the advantage of Variant 2 is. Third, the assumption that the primary device has the auxiliary reference before transmission is stated clearly, but it does restrict practical deployment to setups with that coordination.

The math in the signal model and the Kalman-filter update is standard and consistent. The citation pattern is appropriate: the DWACD and Kalman sources are the right prior art, and the paper positions itself correctly against the single-device SRO-AEC literature.

Who this is for: AEC researchers and engineers working on spatial teleconferencing with multiple Bluetooth or WiFi speakers. A serious referee should spend time on it, mainly to push for a non-oracle VAD ablation and error bars. I would accept it for peer review.

Referee Report

2 major / 5 minor

Summary. The paper addresses acoustic echo cancellation in a two-device scenario where an auxiliary loudspeaker runs on an independent clock, introducing sample rate offset (SRO) between the far-end reference and the primary device's microphone. The authors propose a synchronous compensation scheme: estimate the SRO using the DWACD algorithm and resample the auxiliary signal before feeding it to a two-channel frequency-domain Kalman AEC. Two variants are presented: Variant 1 uses the two-channel AEC error for SRO estimation, while Variant 2 uses the error of an independent single-channel AEC to decouple SRO estimation from filter convergence. Experiments with 50 simulated two-device settings compare these variants against no-SRO, no-compensation, and oracle-SRO baselines for both uncorrelated and correlated playback, in echo-only and double-talk scenarios. The results show that for uncorrelated playback both variants reach the no-SRO baseline, whereas for correlated playback Variant 2 matches the oracle in echo-only but leaves a performance gap in double-talk.

Significance. If the results are reproducible, the paper offers a practical step toward handling clock drift between consumer devices in spatial teleconferencing, and the Variant 2 decoupling idea is a useful design insight. The authors are honest about the correlated double-talk gap and the limitations at higher SRO values, and they link to an online resource for reproducibility. The treatment is empirical rather than analytical, but the experimental design is reasonable for the scope. The main qualification is that the SRO estimator relies on an energy-based ideal VAD, which makes the double-talk claims weaker than they first appear for real systems.

major comments (2)

[Sec. 3.1, Eqs. (5)-(9)] The SRO estimator is gated by an 'energy-based ideal VAD' that knows the ground-truth speech activity in I(k,m). In the double-talk experiments this oracle makes the estimator immune to near-end speech interference, because frames containing near-end speech are excluded from the coherence updates. The abstract claims the system 'mitigates the divergence ... during ... double-talk', but Fig. 5 shows that Variant 2 already falls short of the oracle-SRO baseline in double-talk for correlated playback; with a practical VAD, misclassified speech-active frames would corrupt the GCC phase in Eq. (9) and likely enlarge the gap. Please add an ablation that replaces the ideal VAD with a realistic speech-activity detector (or with a VAD at controlled error rates) and report whether the double-talk results are preserved. Without this, the double-talk claim is not established for non-oracle conditions.
[Sec. 4.2, Figs. 4-5] All ERLE and PESQ values are reported as averages over 50 test files with no measure of variance. The claim in Sec. 4.2 that Variant 2 and the oracle have 'almost identical performance' in the echo-only correlated case is a comparison of two point estimates; without error bars or paired significance testing, the reader cannot judge whether the small differences around ±75-150 ppm are meaningful. Report per-SRO standard deviations or confidence intervals, or provide a statistical test for the key comparisons.

minor comments (5)

[Sec. 3.2, sentence after Eq. (12)] The passage 'we use ˜X2 (k, m) instead X2 (k, m) of as the reference signal' is ungrammatical; rewrite as 'we use ~X2(k,m), instead of X2(k,m), as the reference signal.'
[Sec. 4.2, correlated playback paragraph] The sentence 'the filter bH1,1 and bH1,2 do not converge to the true AIR H1,1 and H2,2 respectively' contains an index typo: H2,2 should be H1,2.
[Sec. 4.2, SRO estimation description] The statement 'For the estimation of the SRO, two previous segments, each of length 8192 samples corresponding to 0.512 s, are used' is unclear: are the two segments overlapping or disjoint, and is the SRO estimate updated every 8192 samples? Please clarify the update schedule.
[References] Reference [19] is cited for the WSJ0 corpus but is actually a speech-separation paper; please cite the WSJ0 corpus directly (e.g., Garofolo et al., 1993).
[Eq. (4), condition following it] The condition m Nh epsilon_1,2 / f1 << Nw is stated but never checked for the experimental parameters (e.g., SRO ±150 ppm, hop 256, 36 s signals). Please confirm that the condition is satisfied for the farthest evaluated frame.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the SRO estimator and the AEC are evaluated against external metrics and ground-truth SRO values.

full rationale

The paper's claimed derivation chain is self-contained and does not reduce to its inputs. The SRO estimate is obtained from the coherence-drift method in Eqs. (5)-(9), using the input signal I(k,m) and reference X2(k,m); it is then validated directly against the simulated true SRO in Figs. 6-7 and indirectly through ERLE and PESQ in Figs. 4-5. The two-channel AEC is a standard partitioned-block Kalman filter, and the proposed variants differ only in which error signal feeds the SRO estimator. The resampled reference is constructed from the estimated SRO and then used by the AEC; this is the intended signal-processing loop, not a fitted parameter renamed as a prediction, because the SRO estimate is not optimized to maximize the reported metrics and the AEC performance is measured by independent quality measures. The only self-reference appears to be the RIR generator tool by one of the authors, used for synthesizing test room impulse responses; this is a standard simulation utility and is not load-bearing for any conclusion. The use of an 'energy-based ideal VAD' is an oracle assumption that raises a practical robustness concern for double-talk operation, but it does not make the evaluation circular: the SRO estimator could fail under non-ideal VADs without the paper's claims being true by construction. No circularity is found.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The paper introduces no new physical entities. The experimental claims rest on standard adaptive-filter assumptions, a constant-SRO model, simulated room acoustics, and an idealized voice-activity detector; the free parameters are algorithm constants, not fitted to the test data.

free parameters (4)

Smoothing factor alpha = 0.95
Temporal smoothing of the phase function P(k,m) in Eq. (7). Chosen by hand; standard for coherence-drift SRO estimators.
Kalman transition factor A = 0.999
State-space transition in Eqs. (10)-(12), adopted from Kuech et al. [4].
Filter taps, FFT length, hop size = 10 taps, 512, 256
Gives a 160 ms time-domain filter length; selected without tuning to test data.
SRO estimator segment length = 8192 samples (0.512 s)
Used for coherence estimation; follows [13] and adds no extra delay.

assumptions (5)

domain assumption The resampled auxiliary signal can be approximated as a phase ramp e^{-j 2 pi k/Nw * m Nh epsilon/f1}, valid when m Nh epsilon/f1 << Nw.
Used in deriving Eq. (4). The tested parameters satisfy the condition, but it is an approximation for large offsets or long frames.
domain assumption Filter partitions are mutually uncorrelated with zero mean; process noise covariance and transition factor A are known.
From [4], stated before Eqs. (10)-(12).
domain assumption The SRO is constant, and there is no packet loss, sampling time offset, or variable SRO.
Stated in Section 2 as out of scope.
ad hoc to paper Energy-based ideal VAD provides ground-truth speech activity to gate coherence estimation.
Used in Section 3.1; not available in a real system, so experiments are idealized.
domain assumption The room impulse responses are simulated with a generator rather than measured.
Section 4.1 uses [20]; results may not carry over exactly to real rooms.

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Cite this review

Pith. "Pith review of Sample Rate Offset Compensated Acoustic Echo Cancellation For Multi-Device Scenarios." pith.science (2026). https://pith.science/paper/BJ4B7RZJ

@misc{pith2026250705399,
  author       = {Pith},
  title        = {Pith review of: Sample Rate Offset Compensated Acoustic Echo Cancellation For Multi-Device Scenarios},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BJ4B7RZJ}},
  note         = {Machine review of arXiv:2507.05399}
}

read the original abstract

Acoustic echo cancellation (AEC) in multi-device scenarios is a challenging problem due to sample rate offset (SRO) between devices. The SRO hinders the convergence of the AEC filter, diminishing its performance. To address this , we approach the multi-device AEC scenario as a multi-channel AEC problem involving a multi-channel Kalman filter, SRO estimation, and resampling of far-end signals. Experiments in a two-device scenario show that our system mitigates the divergence of the multi-channel Kalman filter in the presence of SRO for both correlated and uncorrelated playback signals during echo-only and double-talk. Additionally, for devices with correlated playback signals, an independent single-channel AEC filter is crucial to ensure fast convergence of SRO estimation.

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Reference graph

Works this paper leans on

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Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

In spatial teleconferencing systems [5] using multiple devices, as il- lustrated in Fig

INTRODUCTION Acoustic echo cancellation (AEC) is a critical acoustic signal pro- cessing technique employed to mitigate the echo caused by the acoustic coupling between loudspeakers and microphones [1–4]. In spatial teleconferencing systems [5] using multiple devices, as il- lustrated in Fig. 1, a primary device (such as a smartphone or a laptop) is typic...

work page

[2] [2]

Sample Rate Offset Compensated Acoustic Echo Cancellation For Multi-Device Scenarios

MULTI-DEVICE SCENARIO Let us consider a room with Q devices. Without loss of generality, we assume one microphone and one loudspeaker per device. The time-domain microphone signal of the primary device with index arXiv:2507.05399v1 [eess.AS] 7 Jul 2025 ++ ˆH1,2ˆH1,1 ResamplingSRO Estimation ˆϵ1,2 ˜X2(k,m ) E1(k,m )Y1(k,m ) X1(k,m ) X2(k,m ) E(k,m ) −− Fig...

work page Pith review arXiv 2025

[3] [3]

2 and 3, respectively

PROPOSED METHOD The two variants of the proposed two-device AEC envisioned as a two-channel AEC system with SRO compensation are shown in Figs. 2 and 3, respectively. The SRO compensation comprises of SRO estimation and resampling, which is described in Sec. 3.1. The two-channel AEC filter is described in detail in Sec. 3.2. The main difference between th...

work page

[4] [4]

EXPERIMENTAL RESULTS The performance of our proposed system is evaluated under both correlated cases, where the devices are playing back the same sig- nal, and uncorrelated cases, where the devices are playing back different signals. In the echo-only scenario, echo return loss en- hancement (ERLE) [1] is used to evaluate the performance whereas, perceptua...

work page 2024

[5] [5]

We showed that for uncorrelated playback signals, it is possible to compensate for SRO and reach the perfor- mance of the system with no SRO

CONCLUSION We proposed two variants of two-channel AEC for addressing the two-device AEC problem in the presence of SRO and evaluated them for both uncorrelated or correlated playback signals in echo-only and double-talk scenarios. We showed that for uncorrelated playback signals, it is possible to compensate for SRO and reach the perfor- mance of the sys...

work page

[6] [6]

Hansler and G

E. Hansler and G. Schmidt, Acoustic Echo and Noise Control: A Practical Approach, Wiley-Interscience, USA, 2004

work page 2004

[7] [7]

Frequency-domain adaptive Kalman filter for acoustic echo control in hands-free telephones,

G. Enzner and P. Vary, “Frequency-domain adaptive Kalman filter for acoustic echo control in hands-free telephones,” Sig- nal Processing, vol. 86, no. 6, pp. 1140–1156, June 2006

work page 2006

[8] [8]

Recursive Bayesian Control of Multi- channel Acoustic Echo Cancellation,

S. Malik and G. Enzner, “Recursive Bayesian Control of Multi- channel Acoustic Echo Cancellation,” IEEE Signal Processing Letters, vol. 18, no. 11, pp. 619–622, Nov. 2011

work page 2011