Explicit Ziv-Zakai bound for DOA estimation with sparse linear arrays

Sparse linear arrays 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 develop an explicit closed-form expression for the Ziv-Zakai bound (ZZB) 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 explicit bound is shown to be nearly identical to the exact numerically evaluated ZZB and to closely characterize the performance of the maximum likelihood (ML) estimator.