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Cramér-Rao Bounds for DoA Estimation of Sparse Bayesian Learning with the Laplace Prior
Hua Bai1, Marco F Duarte1, Ramakrishna Janaswamy1
1Department of Electrical and Computer Engineering, University of Massachusetts, Amherst, MA 01003, USA.
Sensors (Basel, Switzerland)
|January 8, 2023
Summary
This study derives Cramér-Rao lower bounds (CRLB) for direction of arrival (DoA) estimation using sparse Bayesian learning (SBL) with a Laplace prior. The marginalized Bayesian CRLB offers a tighter bound, especially at low signal-to-noise ratios (SNR).
Area of Science:
- Signal Processing
- Statistical Inference
- Array Signal Processing
Background:
- Direction of Arrival (DoA) estimation is crucial in various applications.
- Sparse Bayesian Learning (SBL) and Laplace priors offer robust estimation methods.
- Cramér-Rao Lower Bounds (CRLB) provide a benchmark for estimator performance.
Purpose of the Study:
- Derive and analyze Cramér-Rao Lower Bounds (CRLB) for DoA estimation using SBL with a Laplace prior.
- Investigate different CRLB formulations: hybrid, Bayesian, and marginalized Bayesian.
- Evaluate the impact of hyperparameters and multiple snapshots on CRLB performance.
Main Methods:
- Application of sparse Bayesian learning (SBL) with a Laplace prior for DoA estimation.
- Derivation of hybrid CRLB for mixed deterministic and random parameters.
- Derivation of Bayesian CRLB and marginalized Bayesian CRLB for fully random parameters.
- Analysis of hyperparameter CRLBs and the effect of multiple snapshots.
Main Results:
- The marginalized Bayesian CRLB is shown to be tighter than other CRLBs at low Signal-to-Noise Ratios (SNR).
- The performance gap between different CRLBs diminishes as SNR increases.
- The study explores the relationship between mean squared error of source magnitudes and CRLBs.
Conclusions:
- The derived CRLBs provide theoretical performance limits for SBL-based DoA estimation.
- The marginalized Bayesian CRLB is particularly effective in low SNR regimes.
- Numerical simulations validate the theoretical findings across various antenna configurations and noise conditions.
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