Joint Entropy Error Bound of Two-Dimensional Direction-of-Arrival Estimation for L-Shaped Array

Several performance lower bounds have been studied for evaluating the accuracy of direction-of-arrival (DOA) estimation. However, lower bounds for joint estimation have not been fully explored when it comes to DOA estimation. The Cramér-Rao bound (CRB) can guarantee asymptotic tightness in the high-signal-to-noise ratio (SNR) region but cannot provide tight performance bounds for parameter estimators in low- and medium-SNR regions. Consequently, we propose a tight performance bound for the joint estimation of azimuth and elevation DOAs in an L-shaped array. Firstly, the joint conditional probability density function (PDF) is given to establish the mathematical relationship among the receiving signal and the azimuth and elevation DOAs. Then, the joint a posteriori PDF is derived according to the Bayesian theorem. Next, the azimuth and elevation DOA entropy error bound (AEEEB) is derived as a global performance bound using the joint <i>a posteriori</i> entropy. Finally, the CRB and the mean square error (MSE) are provided for comparisons with the proposed performance bound. The simulation results indicate that the AEEEB provides a tighter performance bound compared to the CRB.