Location-based Training with Complementary Folded Linear Orderings for Multichannel Speech Separation

Kaixuan Yang; Stijn Kindt; Nilesh Madhu

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Location-based Training with Complementary Folded Linear Orderings for Multichannel Speech Separation

Kaixuan Yang, Stijn Kindt, Nilesh Madhu

arXiv:2609.12629v1Sep 11, 2026eess.AS

TL;DR

For planar-array multichannel speech separation, circular ordering's wrap-around discontinuity can increase learning complexity and limit effective use of spatial cues. The paper introduces folded linear orderings and a complementary azimuth-guided selection framework. The selected framework yields modest but consistent gains over circular-ordering LBT, with reported robustness to azimuth estimation errors.

Problem
Planar-array LBT uses full-range circular ordering, whose wrap-around discontinuity may increase learning complexity and limit effective use of spatial cues.
Source: §1 · p. 1, §2.3 · p. 2
Method
The paper introduces folded linear orderings and selects among complementary LBT-FLOs using azimuth-guided scoring, including a boundary-distance score.
Source: §1 · p. 1, §2.3 · p. 2, §3 · p. 3
Results
CLBT-FLOs improve performance over individual LBT-FLOs and LBT-CO, with modest but consistent average gains over LBT-CO and paired-test effect sizes r > 0.36.
Source: §5 · p. 4
Takeaways & Limitations
Across planar-array geometries and realistic conditions, the framework shows modest but consistent gains over circular ordering and strong robustness to azimuth estimation errors.
Source: §6 · p. 4
For J > 2, LBT-FLOs may collapse sources with widely separated azimuths; this generalization is outside the current scope.
Source: §4.1 · p. 3

Abstract

from arXiv · show

Location-based training (LBT) effectively resolves the output permutation problem in multichannel speech separation by imposing deterministic spatial orderings. For planar microphone arrays, LBT typically adopts circular azimuth ordering to cover the full spatial range. However, the resulting cyclic topology introduces a discontinuity at the wrap-around point, increasing learning complexity and limiting the effective use of spatial cues. This work investigates this limitation by introducing location-based training with folded linear orderings (LBT-FLOs), which collapse circular azimuths into controlled linear orderings. While individual LBT-FLOs exhibit front-back ambiguity, each provides enhanced spatial discriminability over specific azimuth regions. Exploiting their complementarity, we propose an ensemble-style framework that selects among multiple LBT-FLOs using azimuth-guided scoring. Experiments across planar array geometries and reverberant conditions show modest but consistent improvements over circular-ordering LBT, with robustness to azimuth estimation errors.

1. INTRODUCTION

Speech separation recovers individual sources from mixtures, but multichannel systems must resolve output permutation ambiguity while using spatial cues. The paper studies how circular ordering can burden planar-array LBT and proposes complementary folded linear orderings.

1. INTRODUCTION

Speech separation aims to recover individual sources from mixtures, supporting human listening and machine processing in applications such as hearing-assistive devices and voice-controlled interfaces.Interfering speech and background noise reduce target intelligibility and quality.Source: §1 · p. 1
PIT addresses output permutation ambiguity by dynamically matching estimated outputs to reference sources, while multichannel systems can additionally exploit array-captured spatial cues.The supplied passage reports that LBT uses spatial priors to determine output permutation and outperforms PIT-based approaches in multichannel scenarios.Source: §1 · p. 1
Planar-array circular ordering spans the full azimuth range, but its 360°/0° discontinuity may increase learning burden and degrade separation.The paper proposes controlled folded linear orderings and a complementary selection framework to address this limitation.Source: §1 · p. 1
CLBT-FLOs combine complementary folded linear orderings using azimuth-guided score-based selection and are evaluated across planar-array geometries and azimuth configurations in reverberant conditions.The study frames this as an investigation of ordering-induced trade-offs in LBT.Source: §1 · p. 1

2. SIGNAL MODEL AND LOCATION-BASED TRAINING

The section describes the multichannel mixture and azimuth-based output ordering, then examines how circular ordering's wrap-around discontinuity relates to separation performance. Folded linear orderings offer an alternative topology with complementary strengths and front–back ambiguity.

2.1. Multi-Channel Signal Model

The signal model assumes a compact array captures concurrent static speakers; each microphone signal includes direct-path speech and combined reverberation and background noise, with dry speaker signals estimated at a reference microphone.The signal is described in the STFT domain.Source: §2.1 · pp. 1–2

2.2. Location-based Training

Azimuth-based LBT assigns a deterministic output permutation; planar-array circular ordering sorts speakers across 360°, whereas linear ordering projects azimuths onto a 180° interval before sorting.The linear ordering uses an orientation azimuth θ.Source: §2.2 · p. 2

2.3. Limitations of Conventional LBT

Circular ordering maps directions on opposite sides of its wrap-around boundary to opposite ordering ends, so small angular changes can cause abrupt order flips and increase learning complexity.Folding azimuths around a controlled orientation instead gives a continuous, monotonic linear ordering within a bounded interval.Source: §2.3 · p. 2
Across azimuth configurations, at least one LBT-FLO outperforms LBT-CO, although each FLO has symmetric performance notches around its orientation from front–back ambiguity.The comparison is under anechoic conditions, and the passage presents the result as empirical support for the hypothesis that circular ordering diverts capacity toward enforcing an artificial topology.Source: §2.3 · p. 2

3. PROPOSED METHOD

The proposed CLBT-FLO framework selects a complementary folded-linear-ordering network for each mixture using estimated spatial configuration. Its score combines local crowding and distance from linear-ordering boundaries.

3. PROPOSED METHOD

CLBT-FLOs select one complementary LBT-FLO network per mixture from the estimated spatial configuration, rather than evaluating multiple networks in parallel.The framework is presented as an ensemble-style selection policy.Source: §3 · pp. 2–3
The network selection policy uses a local-crowding score to quantify how closely spaced ordering coordinates are, since separation performance depends strongly on their proximity.The final score weights local crowding at 1.0 and boundary distance at 0.2, then selects the candidate with the maximum score.Source: §3 · p. 3
The selection score includes a boundary-distance term because source pairs farther from linear-ordering boundaries are more effectively separated as gains tend to diminish near those boundaries.The boundary-distance score is combined with the local-crowding score.Source: §3 · p. 3

4. EXPERIMENTAL SETTINGS

The experiments train and evaluate location-based speech separation methods using simulated mixtures, a shared network backbone, and planar microphone arrays. They compare performance under specified reverberant settings and azimuth conditions.

4.1. Training Data and Settings

Training uses 40,320 acoustic scenarios per epoch across 10 rooms with T60 ranging from 0.20 s to 0.80 s, one- or two-speaker mixtures, and SNRs from 0 to 30 dB.Clean speech comes from TIMIT and PTDB-TUG; the arrays are PET-3 and URA-4+ configurations on a 3×3 grid.Source: §4.1 · p. 3, Figure 4 · p. 3
The proof of concept focuses on J = 2; for J > 2, FLOs may collapse widely separated sources, and generalization remains out of scope.Source: §4.1 · p. 3

4.2. Network Model

A CRUSE encoder–GRU–decoder uses trigonometric spatial and detrended log-magnitude features, with a hybrid magnitude/phase source representation.Training uses a power-compressed complex error loss and AdamW; module-wise complexity is tabulated for LBT-CO and CLBT-FLOs.Source: §4.2 · p. 3

4.3. Evaluation Settings

Evaluation uses 16 TSP speaker pairs in a simulated meeting room with T60 = 0.65 s, sampling reference azimuths and exhaustively varying the second speaker across the azimuth range.Reference azimuths are sampled from 0° to 340° in 20° steps; performance is compared using SI-SDR and ESTOI across ordering and guidance conditions.Source: §4.3 · pp. 3–4, Figure 5 · p. 4

5. EXPERIMENTAL RESULTS

Oracle-guided CLBT-FLOs consistently outperform individual LBT-FLOs and LBT-CO, with modest gains over LBT-CO and robustness to azimuth-estimation errors. The selection policy favors advantageous orderings across azimuth pairs.

Oracle-guided CLBT-FLOs consistently improve SI-SDR and ESTOI relative to individual LBT-FLOs and LBT-CO; gains over LBT-CO are modest, with paired Wilcoxon effect sizes r > 0.36.Source: §5 · p. 4
With random ±20° azimuth errors, CLBT-FLOs remain comparable to the lower-bound condition and closely approach oracle selection performance.Source: §5 · p. 4
Across 16 speaker-pair averages, Fig. 6 shows the selection policy favoring advantageous LBT-FLOs over azimuth pairs for both array geometries.Source: Figure 6 · p. 4, §5 · p. 4

6. CONCLUSION

The conclusion identifies cyclic topology as a limitation of LBT-CO for planar arrays and presents complementary folded linear orderings as an alternative. Experiments show modest, consistent gains and robustness to azimuth-estimation errors.

The proposed CLBT-FLO framework combines complementary folded linear orderings through azimuth-guided selection.Source: §6 · p. 4
Across planar array geometries and realistic conditions, the framework yields modest but consistent gains over circular-ordering LBT and robustness to azimuth-estimation errors.Source: §6 · p. 4
Future work will extend the framework to multi-speaker scenarios and parameter-efficient implementations.Source: §6 · p. 4