Explicit Performance Limit for Joint Range and Direction of Arrival Estimation in Phased-Array Radar Sensors

For radar sensors in vehicle safety systems, it is of importance to establish a fundamental performance limit for the estimation accuracy of targets. Bayesian bounds, such as the ZivZakai bound (ZZB), can provide an accurate prediction for the performance limit under all signal-to-noise ratio (SNR) conditions. However, Bayesian bounds for the joint estimation of multiple parameters in radar systems have not been sufficiently studied and the explicit expression is still unavailable. 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 phased-array 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 the theoretical RDEE is derived. The explicit theoretical RDEE is comprehensive and captures the effect of the SNR, the number of elements, and the ratio of the signal bandwidth to the carrier frequency. The explicit theoretical RDEE is compared with the Cramér-Rao bound and the ZZB by a numerical simulation and the result shows that the theoretical RDEE can provide a more accurate performance prediction for the joint range-DOA estimation in phased-array radar.