Classical methods for model order selection often fail in scenarios with low SNR or few snapshots. Deep learning-based methods are promising alternatives for such challenging situations as they compensate lack of information in the available observations with training on large datasets. This manuscript proposes an approach that uses a variational autoencoder (VAE) for model order selection. The idea is to learn a parameterized conditional covariance matrix at the VAE decoder that approximates the true signal covariance matrix. The method is unsupervised and only requires a small representative dataset for calibration after training the VAE. Numerical simulations show that the proposed method outperforms classical methods and even reaches or beats a supervised approach depending on the considered snapshots.

翻译：经典模型阶数选择方法在低信噪比或少量快拍场景下常常失效。基于深度学习的方法凭借大规模数据集训练弥补观测信息不足，成为此类挑战性场景的有力替代方案。本文提出一种利用变分自编码器（VAE）实现模型阶数选择的新方法。其核心思想是在VAE解码器中学习参数化的条件协方差矩阵，以逼近真实信号协方差矩阵。该方法属于无监督学习，训练完成后仅需少量代表性数据集即可完成校准。数值仿真表明，所提方法优于经典方法，并且在特定快拍条件下能达到甚至超越有监督方法的性能。