# CNN-Transformer with Sigmoid Label for High-Resolution Sub-Degree DOA Estimation

arXiv: https://arxiv.org/abs/2610.13433 · HTML: https://mlsanity.com/paper/2610.13433/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 16 references that are in the map.
- First posted on arXiv 9 Oct 2026.

## Builds on (most cited first, 3 of 3)

- [Deep Neural Networks for Multiple Speaker Detection and Localization](https://mlsanity.com/paper/1711.11565/) (2017)
- [Deep Networks for Direction-of-Arrival Estimation in Low SNR](https://mlsanity.com/paper/2011.08848/) (2020)
- [SDOA-Net: An Efficient Deep Learning-Based DOA Estimation Network for Imperfect Array](https://mlsanity.com/paper/2203.10231/) (2022)

## Abstract (arXiv)

This paper addresses the grid quantization error of deep-learning (DL)-based direction-of-arrival (DOA) estimation. Classification- based DOA methods discretize the continuous angular space into a grid, so that with a peak-based read-out, the accuracy and resolution are limited by the grid step and by the width of the label peak. To address this issue, we propose a sigmoid label that encodes the sources' DOAs as the sum of angle-shifted monotonic sigmoid functions. Differentiating the output of a CNN-Transformer network trained with the sigmoid label produces sharp spectral peaks at the source DOAs. Combined with a moderately refined grid step of 0.25 degrees, the CNN-Transformer with the proposed sigmoid label attains sub-degree accuracy and a 1-degree resolution, breaking the limit of the grid quantization error. Under the unified CNN-Transformer backbone, we compare the proposed Sigmoid label with the Gaussian label, the 0-1 hard label, and the binary cross-entropy (BCE) baseline. Numerical results demonstrate that the Sigmoid label attains the highest accuracy and superior resolution compared to other labels.