Waveform design with low range sidelobe and high Doppler tolerance for cognitive radar

The unimodular LFM-Syn waveform is formulated by a combination of random noise waveform and conventional LFM, where the phase-scaling factor makes it come true.To achieve low range sidelobes and high Doppler tolerance, a novel template-optimizing function is established with constraints on quadratic phase and random phase.Relaxed Alternating Projection Phase Control method, incorporating spectrum approximation and quadratic phase amendment, is proposed.The LFM-Syn waveform optimized by RAPPC has Doppler tolerance, LPI capability and low range sidelobes. This paper considers the unimodular Linear-FM Synthesized (LFM-Syn) waveform design for cognitive radar.Firstly, the synthesized waveform is formulated by a given phase-scaling factor which combines the random noise waveform and the conventional LFM waveform. Secondly, to achieve low range sidelobes and high Doppler tolerance of LFM-Syn waveforms, a novel template-optimizing objective function is established and then transformed into a two-variable non-convex optimization case with constraints on quadratic phase and random phase. Meanwhile, a Relaxed Alternating Projection Phase Control method (RAPPC) incorporating spectrum approximation relaxed alternating projection and quadratic phase amendment is proposed via an iterative way. RAPPC not only enhances local exploiting for desired waveforms but also keeps high Doppler tolerance and low range sidelobes. Lastly, simulations have provided evidences that the LFM-Syn waveform optimized by RAPPC 1) has high Doppler tolerance similar to conventional LFM, 2) has Low Probability of Intercept (LPI) similar to random noise waveform, and 3) has low range sidelobe levels for prescribed requirement. Additionally, simulations also highlight the superior performance of our proposed algorithms over several existing techniques.