Super-resolution range estimation in FMCW radar system

Abstract

This paper presents a new algorithm to estimate the ranges of multiple targets with super-resolution in Frequency Modulated Continuous Wave (FMCW) radar systems. The proposed algorithm is based on the monopulse estimation technique. The estimation of multiple ranges is equivalent to finding multiple frequencies from noisy discrete-time observations. In multiple frequency estimation, the frequencies are estimated as follows. First, we initialize the frequencies from FFT or CFAR detection technique. Then, we estimate each of frequencies by considering the rest of the frequencies as the interference plus noise term, where the interference plus noise term is the sum of the components of the rest of the frequencies and noise. From estimated frequency, rank-one matrix is updated, respectively. The covariance matrix of the interference plus noise term is updated since it is the sum of rank-one matrices and noise covariance matrix. Because the covariance matrix of the interference plus noise term gets close to true one over iterations, the estimated frequency gets close to true value. Each of the multiple frequencies converges to the true value through a few of iterations. The complexity of this algorithm is reduced to O(N2) by Sherman-Morrison formula even though MLE requires the complexity of O(N3) because of the inverse form of covariance matrix. The simulation demonstrates the relationship between SNR and Root Mean Square Errors (RMSE) of estimated frequencies. We confirmed that RMSE of each frequency estimated from the proposed algorithm approaches to Cramer-Rao Bound (CRB). The proposed algorithm is also applicable to multiple AOAs finding problems.