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

Electrical Engineering and Systems Science > Signal Processing [Submitted on 12 Dec 2024 (v1), last revised 16 Jun 2026 (this version, v2)] Title:Fully Bayesian Wideband Direction-of-Arrival Estimation and Detection via RJMCMC View PDFAbstract:Consider an array receiving unknown wideband signals from an unknown number of sources $k$. Wideband signals can occupy arbitrarily wide bandwidths, rendering demodulation-based approaches inapplicable, a common situation in settings involving acoustic signals. Here, we aim to determine $k$ given $N$ noisy array-valued measurements, a task known as the "detection problem," for which Bayesian model comparison is a common approach. To render Bayesian inference tractable, it is typically necessary to marginalize the source signals. Unfortunately, for wideband signals, naive marginalization has an unaffordable time complexity of $\mathcal{O}(N^3 k^3)$. As a result, fully Bayesian signal detection has yet to be demonstrated in wideband settings. In this work, we propose a wideband signal model that allows for computationally tractable marginalization of the source signals. We begin from the canonical model of linear time-invariant (LTI) signal propagation, which is then augmented into a circular convolution, all without loss of generality. This allows for efficient computation in the frequency domain, where the resulting linear system admits a decomposition into a sparse matrix we refer to as a \textit{stripe matrix decomposition}. Exploiting this sparsity pattern reduces the time complexity of computing the marginal likelihood to $\mathcal{O}(N k^3)$. These computational improvements enable efficient posterior inference via reversible-jump Markov chain Monte Carlo (RJMCMC). In this work, we use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than RJMCMC. Detection of the latent source signals can then be performed in a fully Bayesian manner using samples drawn by NRJMCMC. We evaluate our procedure by comparing it against generalized likelihood ratio testing (GLRT) and information criteria. Submission history From: Kyurae Kim [view email][v1] Thu, 12 Dec 2024 03:15:08 UTC (2,674 KB) [v2] Tue, 16 Jun 2026 12:23:26 UTC (2,478 KB) Current browse context: eess.SP References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.