Linear frequency-modulated signal detection using Radon-ambiguity transform

A novel time-frequency technique for linear frequency modulated (LFM) signal detection is proposed. The design of the proposed detectors is based on the Radon transform of the modulus square or the envelope amplitude of the ambiguity function (AF) of the signal. A practical assumption is made that the chirp rate is the only parameter of interest. Since the AF of LFM signals will pass through the origin of the ambiguity plane, the line integral of the Radon transform is performed over all lines passing through the origin of the ambiguity plane. The proposed detectors yield maxima over chirp rates of the LFM signals. This reduces the two-dimensional (2-D) problem of the conventional Wigner-Ville distribution (WVD) based detection or the Radon-Wigner transform (RWT) based detector to a one-dimensional (1-D) problem and consequently reduces the computation load and keeps the feature of "built-in" filtering. Related issues such as the finite-length effect, the resolution, and the effect of noise are studied. The result is a tool for LFM detection, as well as the time-varying filtering and adaptive kernel design for multicomponent LFM signals.