Analysis of DOA estimation performance of sparse linear arrays using the Ziv-Zakai bound

Sparse linear arrays (SLAs) provide similar performance to filled linear arrays in terms of angular accuracy and resolution with reduced size, weight, power consumption, and cost. However, they are subject to significant ambiguities due to high sidelobes in the array beampattern, which give rise to large estimation errors. In this paper, we study the direction-of-arrival (DOA) estimation performance of various SLA configurations using the Ziv-Zakai bound (ZZB) and simulation of the maximum likelihood estimator (MLE). The ZZB consists of three terms which correspond to the three types of estimation errors: small mainlobe errors, errors due to sidelobe ambiguities, and random errors. MLE simulations confirm the contribution of the different types of estimation errors predicted by the bound. The analysis shows that much of the performance degradation due to ambiguities are from random errors that cannot be controlled by array design, while additional degradation due to sidelobe errors depends strongly on the array configuration. Isolating the contributions of the three types of errors provides greater understanding of the behavior of sparse arrays, allowing for more effective system design and analysis.