Orthogonal Discrete Frequency-Coding Waveform Set Design with Minimized Autocorrelation Sidelobes

The autocorrelation sidelobe peak (ASP) levels of discrete frequency-coding waveform with fixed frequency pulses (DFCW-FF) is very large, which is about 0.21 or - 13.2 dB. Replacing the fixed frequency pulses with linear frequency modulated (LFM) pulses can lower the ASP. We investigate the autocorrelation function (ACF) and cross-correlation function (CCF) for DFCW with arbitrary frequency firing order. It is shown that DFCW-LFM has different ACF expression from the DFCW-FF, and the CCF of DFCW-LFM changes distinctly with different frequency firing order. By setting the relationships between the frequency step Delta f, LFM bandwidth B and subpulse duration T, we can reduce the ASP, as well as nullify the grating lobes. Then, a modified genetic algorithm (GA) is proposed to numerically search optimal frequency firing order for DFCW-LFM. Some of the designed results are presented. Their correlation properties are effectively improved. Both simulation results and comparisons show that the method of mitigating ASP and the proposed search algorithm are effective for the design of DFCWs with superior aperiodic correlation.