The sophisticated scenarios always challenge MIMO(Mutiple-Input Mlitiple-Output) radar.A relaxed iterative spectrum approximation alternating projection method (RISAAP) is proposed to design phase-coded waveforms

for suppressing high range sidelobes of strong scatters

electromagnetic interference in specified frequencies and cross-interference from different signals.This method is based on power spectral density (PSD) approximation and alternating projection with extended accelerating factor.Firstly

the correlation fitting is transformed into PSD approximation via FFT between the aperiodic correlation function and PSD.Secondly

the desired spectrum constraint is formulated and the projection space is expanded by its relaxed mechanism.Finally

the iterative optimization is conducted via FFT and accelerated alternating projection.Simulations demonstrate that this method could obtain efficient performance and avoid local stagnation which seems more convenient for waveform design on-the-fly than some prevalent algorithms.