Linear frequency modulation (LFM) waveforms have been widely adopted due to their excellent performance characteristics, such as good Doppler tolerance and ease of physical implementation. However, LFM waveforms suffer from high autocorrelation sidelobes (ACSLs) and limited design flexibility. Phase-coded frequency modulation (PCFM) waveforms can be used to design waveforms similar to LFM, offering greater design flexibility to optimize ACSLs. However, it has been found that the initial PCFM waveform experiences spectral expansion during the ACSL optimization process, which reduces its similarity to LFM. Therefore, this article jointly optimizes the ACSLs and spectrum of the initial PCFM waveform, establishes an optimized mathematical model, and then solves it using the heavy-ball gradient descent algorithm. Numerical experiments indicate that the proposed method effectively addresses the problem of waveform similarity degradation caused by spectral expansion while reducing waveform ACSLs. At the same time, a balance between reducing waveform ACSLs and preserving waveform similarity can be achieved by adjusting the parameters.
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