Outlier-Robust Three-Element Non-Uniform Linear Arrays Design Strategy for Direction of Arrival Estimation in MIMO Radar

This paper presents a novel design strategy for outlier-robust, three-element non-uniform linear array (NULA) configurations optimized for multiple-input multiple-output (MIMO) radar systems aimed at target direction of arrival (DoA) estimation. The occurrence of outliers, i.e., ambiguous estimates, is a well-known issue in DoA estimation based on the maximum likelihood (ML), which is caused by the local maxima of the likelihood function. Specifically, we study how the positioning of both transmitters and receivers affects both presence of outliers and accuracy of ML DoA estimation. By leveraging a theoretical prediction of the DoA mean squared error (MSE), we propose a design strategy to jointly optimize the positions of NULA array of three transmitting and receiving elements, only inside a subspace which guarantees that the outlier probability remains below a specified threshold. Compared to NULA configurations with a single transmitter, the proposed designs achieve superior estimation accuracy due to two key factors: improved asymptotic performance resulting from a narrower mainlobe, and enhanced robustness against outliers due to reduced sidelobes. Furthermore, the proposed approach is well-suited for practical implementation in low-cost radars using only 3 × 3 or 2 × 3 MIMO configurations, as it also incorporates practical design constraints such as minimum inter-element spacing to account for the physical dimensions of the antennas, and tolerance in the installation accuracy.