Designing Interference-Immune Doppler-Tolerant Waveforms for Radar Systems

Abstract

Dynamic target detection using LFM waveform is challenging in the presence of interference for different radar applications. Degradation in SNR is irreparable and interference is difficult to mitigate in time and frequency domain. In this paper, a waveform design problem is addressed using the Majorization-Minimization (MM) framework by considering PSL/ISL cost functions, resulting in a code sequence with Doppler-tolerance characteristics of an LFM waveform and interference immune characteristics of a tailored polyphase sequence (unique phase code + minimal ISL/PSL). The optimal design sequences possess polynomial phase behavior of degree <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> amongst its sub-sequences and obtain optimal ISL and PSL solutions with guaranteed convergence. By tuning the optimization parameters such as degree <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$Q$</tex-math></inline-formula> of the polynomial phase behavior, sub-sequence length <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> and the total number of sub-sequences <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L$</tex-math></inline-formula> , the optimized sequences can be as Doppler tolerant as LFM waveform in one end, and they can possess small cross-correlation values similar to random-phase sequences in polyphase sequence on the other end. The numerical results indicate that the proposed method is capable to computationally design chirplike sequences which prior to this work, were obtained by mimicking phase variations of LFM waveform. An application of the proposed method for the automotive scenario is also illustrated in the numerical results.