Joint Waveform and Filter Design for Interference Suppression in Moving Target Environments

Moving targets and digital radio frequency memory (DRFM) interference distort the radar echo due to complex waveform modulation, severely degrading the radar detection performance. In this paper, we propose a joint waveform and filter design scheme with Doppler-tolerant and anti-jamming (JWFDA) for DRFM interference suppression in moving target environments. First, we formulate the moving target auto-correlation peak sidelobe level (M-APSL) model of moving target clusters and the moving jamming cross-correlation peak level (M-JCPL) model of DRFM interference. Second, we establish a JWFDA design scheme to simultaneously minimize M-APSL and M-JCPL while satisfying the moving target loss in processing gain (MT-LPG) constraint of transmit waveform and receive filter, which is a non-convex, non-smooth, and multi-max function optimization problem. To solve it, we smooth the multi-max function by using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{p}$</tex-math></inline-formula> norm. Third, we propose a multi-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{p}$</tex-math></inline-formula> norm balanced penalty majorization-minimization (MLPN-BPMM) algorithm, which approximates the multi-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{p}$</tex-math></inline-formula> norm as a quadratic polynomial and avoids the overfitting of penalty terms. Numerical simulations demonstrate that the proposed method generates the waveforms and the filters with superior performance and effectively suppresses several kinds of DRFM interference in moving target environments.