A time-frequency training-based approach for robust classification of unknown transients with unknown arrival time and doppler shift

We present a training-based approach for the classification of noisy unknown transient signals with arbitrary range and Doppler shift (time and frequency shifts). The ambiguity function, which is the 2-D inverse Fourier transform of the Wigner time-frequency distribution of the signal, is utilized to remove the unknown time and frequency shifts. An ambiguity domain template is then generated from labeled training data (tens of observations), and classification is performed using an inner product. The method is tested on synthetic transient signals in Gaussian noise and performs as well as or better than another recently proposed time-frequency based method, and an energy detector, particularly when limited training data are available.