Fast 3D Joint Superresolution Algorithm for Millimeter Wave FMCW Radars

This article formulates a novel fast three-dimensional joint superresolution algorithm for millimeter wave (mmWave) imaging. The existing three-dimensional superresolution techniques for joint estimation are inherently slow. Firstly, the size of the correlation matrix, used for the subspace-based superresolution algorithms such as MUltiple SIgnal Classification (MUSIC), increases with a dimension. This escalates the computational cost of singular value decomposition (SVD) or eigenvalue decomposition (EVD) required for the subspace estimation. Secondly, the existing approaches involve an exhaustive joint search over the entire grid of multiple dimensions. To reduce these cost complexities for the joint 3D estimation problem, we propose a two-stage imaging algorithm based on the Fourier transform and beamspace MUSIC to jointly estimate the range, azimuth, and elevation of the targets. Due to the reduced implementation complexity, the proposed algorithm becomes an attractive option for the silicon implementation of superresolution techniques. Our novel 3D imaging algorithm is explained with a detailed mathematical framework by utilizing the mmWave frequency modulated continuous wave (FMCW) radar, which is popular in the automotive industry. In addition, we derive the asymptotic analytical expressions for analyzing the statistical performance of the proposed method in terms of mean square error (MSE). The performance of the proposed approach is verified through various simulations and a real radio-frequency (RF) experiment using a 60 GHz FMCW radar.