Nonlinear frequency modulation using fourier sine series

Nonlinear Frequency Modulated (NLFM) waveforms utilize a nonlinear modulation function to achieve a tapered spectrum which results in low Auto-Correlation Function (ACF) sidelobes. Previous efforts in the literature have mostly focused on designing NLFM modulation functions which result in a spectral shape that closely resembles the many known amplitude tapering functions encountered in spectral analysis. This work presents a NLFM waveform design method where the modulation function possesses a Linear FM (LFM) component plus a nonlinear perturbation expressed as a Fourier sine series. The Fourier coefficients are used as a discrete set of parameters that may be adapted to directly synthesize NLFM waveforms with low ACF sidelobes. This paper evaluates this method by synthesizing NLFM waveforms for a variety of Time-Bandwidth Products (TBPs) and additionally analyzes the Doppler sensitivity of the resulting NLFM designs.