PCFM Radar Waveform Design with Spectral and Correlation Considerations

This paper considers the polyphase-coded FM (PCFM) waveform design with good spectral compatibility and correlation performance. In getting the desired PCFM waveform, we first design its sampled sequence with spectral and correlation considerations. To be specific, the power in prescribed stopbands is minimized to improve spectral compatibility, and correlation performance is enhanced by minimizing the integrated mainlobe energy (IME) and integrated sidelobe energy (ISE) of the autocorrelation function, which, respectively, control the range resolution and range sidelobe level. We deduce the optimal power spectrum density (PSD) condition for the considered problem and write the objective function as the residual error between the sequence's PSD and the optimal one. We also devise a way to employ fast Fourier transform (FFT) in calculating the gradient of the PSD residual error such that it can be efficiently minimized using a general gradient descent method. With the designed sequence, we propose a new sequence-to-waveform implementation to reconstruct the PCFM waveform. Unlike sequences designed in many existing studies, the PCFM waveform is much closer to the real emission and thus expected to suffer less distortion in physical implementation.