This paper discusses the design of phase coded waveforms with ultra-low autocorrelation sidelobes in desired intervals.These waveforms can be used as interference suppression and signal synchronization waveforms for radar

sonar and communication systems.An algorithm based on power spectral density (PSD) approximation is proposed.According to the relationship between aperiodic autocorrelation sequence and the waveform PSD

the autocorrelation design object is translated into a PSD design object.The method transforms and projects the design waveform in the time and the frequency domain iteratively.Thus the PSD of the design waveform approximates the ideal PSD iteratively in order to generate the desired waveform.Compared with the general nonlinear programming methods

this method is derivative-free

thus requires less computer memory

and the iteration can be implemented by FFT efficiently.