Fully Bayesian Wideband Direction-of-Arrival Estimation and Detection via RJMCMC

TL;DR

This paper introduces a fully Bayesian method for wideband DoA estimation and detection using NRJMCMC, modeling signals in the time domain and exploiting system structure for computational efficiency.

Contribution

It presents a novel Bayesian framework with closed-form marginalization and a computationally efficient RJMCMC approach for wideband DoA estimation and detection.

Findings

Achieves lower autocorrelation and faster convergence with NRJMCMC

Reduces likelihood computation complexity from O(N^3 k^3) to O(N k^3)

Demonstrates competitive detection performance against GLRT and information criteria

Abstract

We propose a fully Bayesian approach to wideband, or broadband, direction-of-arrival (DoA) estimation and signal detection. Unlike previous works in wideband DoA estimation and detection, where the signals were modeled in the time-frequency domain, we directly model the time-domain representation and treat the non-causal part of the source signal as latent variables. Furthermore, our Bayesian model allows for closed-form marginalization of the latent source signals by leveraging conjugacy. To further speed up computation, we exploit the sparse ``stripe matrix structure'' of the considered system, which stems from the circulant matrix representation of linear time-invariant (LTI) systems. This drastically reduces the time complexity of computing the likelihood from $\mathcal{O}(N^3 k^3)$ to $\mathcal{O}(N k^3)$, where $N$ is the number of samples received by the array and $k$ is the number of sources. These computational improvements allow for efficient posterior inference through reversible jump Markov chain Monte Carlo (RJMCMC). We use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than the conventional reversible variant. Detection, estimation, and reconstruction of the latent source signals can then all be performed in a fully Bayesian manner through the samples drawn using NRJMCMC. We evaluate the detection performance of the procedure by comparing against generalized likelihood ratio testing (GLRT) and information criteria.