Bi-Level <i>l</i> <sub>1</sub> Optimization-Based Interference Reduction for Millimeter Wave Radars
Zhihuo Xu
Abstract
With the increasing number of radar-equipped vehicles in dense traffic situations, millimeter wave radars are suffering from serious interference problems. Therefore, this article presents a novel bi-level <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> optimization based approach for reducing interferences between automotive radars for range, velocity and angle measurement. Firstly, sparse difference analysis between the interfering signal and the target signal is investigated. According to the analysis results, one bi-level based signal optimization model is further derived by using <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> -norm penalized least squares. This bi-level optimization enables a trade-off between suppressing interference and preserving radar targets. Specifically, in the first <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> level, the interfering signal is first optimized as the “desired signal”, while the target is considered as “noise”. Meanwhile, sparse optimization is applied on the target signals in the frequency domain at the second <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> level. Finally, the iterated soft-thresholding algorithm is used to optimize the proposed model. In real road interference suppression experiments, the proposed method improves the signal to interference plus noise ratio (SINR) for the target from 5.06 dB to 19.26 dB in the range-Doppler domain and from 6.86 dB to 22.10 dB in the azimuth spatial domain.