The estimation of the frequency of a single tone signal is a classical problem. The Cramér-Rao lower bound (CRB) on the frequency estimates has been well studied for the case of additive Gaussian noise. In practical applications, however, the probability density function of the noise is rarely Gaussian, or known. Moreover, non-linear effects, as quantization, are often present, making the Gaussian CRB unreachable. In this paper we propose a data-driven approach for evaluating the CRB on frequency estimation with unknown noise and other degradation. Using a learned normalizing flow model, we model the distribution of the measurements by a neural network and obtain an approximate CRB, referred to as a Generative CRB (GCRB). We demonstrate the GCRB on frequency estimation both in cases where the CRB has been previously evaluated, showing the accuracy of the GCRB empirically, and on complex cases where the CRB cannot be evaluated analytically or numerically.
|Title of host publication||2022 IEEE 12th Sensor Array and Multichannel Signal Processing Workshop, SAM 2022|
|Publisher||IEEE Computer Society|
|Number of pages||5|
|State||Published - 2022|
|Event||12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022 - Trondheim, Norway|
Duration: 20 Jun 2022 → 23 Jun 2022
|Name||Proceedings of the IEEE Sensor Array and Multichannel Signal Processing Workshop|
|Conference||12th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2022|
|Period||20/06/22 → 23/06/22|
Bibliographical noteFunding Information:
Acknowledgement: The work of Yoram Bresler was part by US Army MURI Award W911NF-15-1-0479.
© 2022 IEEE.
- deep learning
- Generative model
- normalizing flow
- parameter estimation