Explicit bounds for joint range and direction-of-arrival estimation in MIMO radar

Abstract

Bayesian bounds, such as the Ziv–Zakai bound (ZZB), can provide a tight baseline for the performance of estimators or an accurate prediction for the performance limit of radar systems under all signal-to-noise ratio (SNR) conditions. However, there exists very limited literature that deals with the explicit bound for joint estimation of multi-parameters in radar systems. In this paper, we employ the thought of Shannon’s information theory to propose a tight bound with closed-form expression for joint range and direction-of-arrival (DOA) estimation in multiple-input multiple-output radar. Based on the joint a posteriori probability density function, we define range-DOA entropy error (RDEE) as the entropy power of range and DOA. With normalized a posteriori entropies in low and high SNRs, the closed-form approximation for RDEE is derived. The explicit RDEE is comprehensive and captures the effect of the SNR, the number of array elements, and the ratio of the signal bandwidth to the carrier frequency. RDEE is compared with the ZZB by a numerical simulation and the result shows RDEE and ZZB are almost identical in low and high SNRs.