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 itself is unsupervised and only requires a small representative dataset for calibration purposes after training of the VAE. Numerical simulations show that the proposed method clearly outperforms classical methods and even reaches or beats a supervised approach depending on the considered snapshots.

翻译：传统的模型阶次选择方法在低信噪比或快拍数较少的情况下常常失效。基于深度学习的方法作为应对此类挑战性场景的替代方案具有良好前景，因为它们通过在大规模数据集上进行训练，弥补了观测数据中信息不足的问题。本文提出了一种利用变分自编码器（VAE）进行模型阶次选择的方法。其核心思想是在VAE解码器中学习一个参数化的条件协方差矩阵，使其逼近真实的信号协方差矩阵。该方法本身属于无监督学习，在VAE训练完成后，仅需少量代表性数据集用于校准。数值仿真结果表明，所提方法明显优于传统方法，甚至根据不同的快拍数条件，能够达到或超越有监督方法的性能。