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 observations with repeated 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.

Identification is a communication paradigm that promises some exponential advantages over transmission for applications that do not actually require all messages to be reliably transmitted, but where only few selected messages are important. Notably, the identification capacity theorems prove the identification is capable of exponentially larger rates than what can be transmitted, which we demonstrate with little compromise with respect to latency for certain ranges of parameters. However, there exist more trade-offs that are not captured by these capacity theorems, like, notably, the delay introduced by computations at the encoder and decoder. Here, we implement one of the known identification codes using software-defined radios and show that unless care is taken, these factors can compromise the advantage given by the exponentially large identification rates. Still, there are further advantages provided by identification that require future test in practical implementations.

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