A Novel NLFM Waveform With Low Sidelobes Based on Modified Chebyshev Window

It is well known that the nonlinear frequency modulation (NLFM) chirp waveform can shape advantageously the power spectrum density (PSD) such that the autocorrelation function exhibits reduced sidelobes as the window function. However, differences between the PSD and window function due to the Gibbs effects caused by the Fresnel integral would lead to deteriorative performance of the NLFM chirp waveform. In particular, the correlation function of NLFM waveform with Chebyshev PSD is seriously inconsistent with the lowest sidelobe level of the Chebyshev window function possesses. To overcome the inconsistency, therefore, in this letter, a novel NLFM waveform with modified Chebyshev window PSD is proposed, which combines the Chebyshev with edge distortion compensation, allowing, in theory, low sidelobe level as Chebyshev window. Using theoretical analysis also confirmed by simulation, this letter shows that the novel NLFM waveform possesses low sidelobes without high computational complexity in design.