CNN-Transformer with Sigmoid Label for High-Resolution Sub-Degree DOA Estimation
Authors: Lifeng Wang, Xintong Li, Aifei Liu
Organizations: Academy of AI and Advanced Technology, Xi’an Jiaotong-Liverpool University, Taicang 215400, China · Department of Electrical and Computer Engineering, Western University, London, ON N6A 3K7, Canada
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.
Figures & tables
Figure 1: The proposed Sigmoid label and its first derivative for two sources at −43.7∘ and −41.7∘ (separation 2∘ , w=0.2∘ ). (a) The Sigmoid label (before derivative) forms a monotonic CDF. (b) The first derivative (after derivative) forms two sharp peaks at the source angles.
Figure 2: Output spectra at a 2∘ separation (SNR =5 dB) for two sources at −48.1∘ and −46.1∘ : (a) the Gaussian and Sigmoid-derivative spectra; (b) the 0-1 hard, BCE and MUSIC spectra.
Figure 3: RMSE versus SNR of the proposed Sigmoid label, the three baselines and MUSIC, for a small ( 2∘ , left) and a large ( 20∘ , right) angular separation.
Figure 4: Probability of resolution versus angular separation of the proposed Sigmoid label, the three baselines, and MUSIC, at an SNR of 0 dB (left) and 5 dB (right).
Center for Connected Autonomy and AI and the Dept. of Electrical Engineering and Computer Science, Florida Atlantic University, Boca Raton, FL 33431 USA · Air Force Research Laboratory, AFRL/RI, Rome, NY 13441 USA
Department of Electronics and Communication Engineering, Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham, India · Department of Electronic Systems Engineering, Indian Institute of Science, Bangalore, India