Explicit Ziv–Zakai bound for analysis of DOA estimation performance of sparse linear arrays

•Sparse linear arrays provide angular accuracy but are subject to significant ambiguities.•We develop an explicit closed-form expression for the Ziv–Zakai bound on the MSE.•The bound consists of three terms which correspond to the three types of estimation errors.•Small mainlobe errors, errors due to sidelobe ambiguities, and random errors.•The bound is used to analyze the performance of different SLA configurations.

Sparse linear arrays (SLAs) provide similar direction-of-arrival estimation 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 develop an explicit closed-form expression for the Ziv–Zakai bound on the mean square estimation error in order to quantify the degradation in estimation performance due to the sidelobe ambiguities. The bound consists of three terms which correspond to the three types of estimation errors: small mainlobe errors, errors due to sidelobe ambiguities, and random errors. The bound is used to analyze the performance of different SLA configurations. Maximum likelihood estimation 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.