Estimation of ambiguity functions with limited spread

Authors:
Heidi Hindberg;Sofia C. Olhede
Affiliations:
Northern Research Institute Tromsø, Norway and Department of Physics and Technology, University of Tromsø, Tromsø Norway;Department of Statistical Science, University College London, London, U.K.
Venue:
IEEE Transactions on Signal Processing
Year:
2010

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Abstract

In this correspondence, we propose a class of estimators of the ambiguity function of a discrete-time process using thresholding. To this purpose, the distributional and moment properties of the empirical ambiguity function for a realization of an analytic random process are derived, and the moments for the special cases of stationary, uniformly modulated, and deterministic signals immersed in noise processes are determined. Suitable thresholds are chosen based on the distributional properties of the empirical ambiguity function, and the procedure is tested on simulated data.