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

## TL;DR

This paper introduces a new performance bound for estimating directions of signals in an L-shaped array, which is tighter than existing methods in certain signal conditions.

## Contribution

The novel contribution is the derivation of a joint azimuth and elevation DOA entropy error bound (AEEEB) for L-shaped arrays.

## Key findings

- The joint a posteriori PDF is derived using Bayesian theorem for DOA estimation.
- The proposed AEEEB provides a tighter performance bound than the Cramér–Rao bound in low- and medium-SNR regions.
- Simulation results confirm the superiority of AEEEB over traditional bounds like CRB.

## Abstract

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 a posteriori 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.