Computationally efficient MUSIC based DOA estimation algorithm for FMCW radar

This paper proposes low-cost yet high-accuracy direction of arrival (DOA) estimation for the automotive frequency-modulated continuous-wave (FMCW) radar. The existing subspace-based DOA estimation algorithms suffer from either high-computational costs or low accuracy. We aim to solve such contradictory relation between complexity and accuracy by using randomized matrix approximation. Specifically, we apply an easily-interpretable randomized low-rank approximation to the covariance matrix (CM) and approximately compute its subspaces. That is, we first approximate CM $R$ $\in {ℂ}^{M\times M}$ through three sketch matrices, in the form of $R\approx QB{Q}^H$, here the matrix $Q\in {ℂ}^{M\times z}$ contains the orthonormal basis for the range of the sketch matrix $C\in {ℂ}^{M\times z}$ which is extracted from $R$ using randomized uniform column sampling and $B\in {ℂ}^{z\times z}$ is a weight-matrix reducing the approximation error. Relying on such approximation, we are able to accelerate the subspace computation by the orders of the magnitude without compromising estimation accuracy. Furthermore, we drive a theoretical error bound for the suggested scheme to ensure the accuracy of the approximation. As validated by the simulation results, the DOA estimation accuracy of the proposed algorithm, efficient multiple signal classification (E-MUSIC), is high, closely tracks standard MUSIC, and outperforms the well-known algorithms with tremendously reduced time complexity. Thus, the devised method can realize high-resolution real-time target detection in the emerging multiple input and multiple output (MIMO) automotive radar systems.