# Multi-channel Narrow-band Deep Speech Separation with Full-band Permutation Invariant Training

arXiv: https://arxiv.org/abs/2110.05966 · HTML: https://mlsanity.com/paper/2110.05966/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Oct 2021.

## Built on by (most cited first, 4 of 4)

- [ReZero: Region-customizable Sound Extraction](https://mlsanity.com/paper/2308.16892/) (2023)
- [Deep Neural Mel-Subband Beamformer for In-car Speech Separation](https://mlsanity.com/paper/2211.12590/) (2022)
- [Unsupervised Multi-channel Speech Dereverberation via Diffusion](https://mlsanity.com/paper/2508.02071/) (2025)
- [SpatialEmb: Extract and Encode Spatial Information for 1-Stage Multi-channel Multi-speaker ASR on Arbitrary Microphone Arrays](https://mlsanity.com/paper/2601.18037/) (2026)

## Abstract (arXiv)

This paper addresses the problem of multi-channel multi-speech separation based on deep learning techniques. In the short time Fourier transform domain, we propose an end-to-end narrow-band network that directly takes as input the multi-channel mixture signals of one frequency, and outputs the separated signals of this frequency. In narrow-band, the spatial information (or inter-channel difference) can well discriminate between speakers at different positions. This information is intensively used in many narrow-band speech separation methods, such as beamforming and clustering of spatial vectors. The proposed network is trained to learn a rule to automatically exploit this information and perform speech separation. Such a rule should be valid for any frequency, thence the network is shared by all frequencies. In addition, a full-band permutation invariant training criterion is proposed to solve the frequency permutation problem encountered by most narrow-band methods. Experiments show that, by focusing on deeply learning the narrow-band information, the proposed method outperforms the oracle beamforming method and the state-of-the-art deep learning based method.