Sub-Nyquist sensing of Gaussian pulse streams with unknown shape factor based on information fitting.

Gaussian pulse streams can be characterized by a finite number of unit-time parameters, and classical Finite Rate of Innovation (FRI) sampling enables sub-Nyquist sensing of these signals. However, prior knowledge of its shape factor is required, limiting FRI's applicability. This paper proposes a solution to the FRI sampling problem of Gaussian pulse streams with an unknown pulse shape factor. We aim to fit pulse shape information from sub-Nyquist samples and reconstruct parameters using spectral estimation methods. We first demonstrate the feasibility of fitting the shape factor from sub-Nyquist samples and provide the fitting algorithm and related fitting errors in detail. This paper also provides the Cramer-Rao lower bound (CRLB) on parameter estimation accuracy of Gaussian pulse streams under analog white Gaussian noise, offering a statistical perspective of our proposed information fitting method's performance. We qualitatively demonstrate that the information-fitting method can also be applied to a wider range of FRI pulse stream forms. Simulation experiments show that our proposed information fitting method achieves high accuracy in parameter estimation of the signal when the pulse shape factor is unknown. [ABSTRACT FROM AUTHOR]