Polarization based direction of arrival estimation using a radio interferometric array

TL;DR

The paper tackles DOA estimation using radio interferometric arrays that are optimized for imaging rather than direct DOA sensing. It introduces a distributed pipeline that performs polarized ESPRIT on per-baseline visibilities, unwraps phases across almost-linear sub-arrays with phase difference projection, and then refines the 2D DOA with a transformer neural network trained on simulated data. Simulations on AARTFAAC and SKA0 layouts demonstrate DOA estimates with a few-degree accuracy across a wide bandwidth, while achieving online operation and favorable computational cost compared to MUSIC. The work enables fast RFI localization and transient detection using existing array infrastructure, with future work extending to multiple DOAs and near-field scenarios.

Abstract

Direction of arrival (DOA) estimation is mostly performed using specialized arrays that have carefully designed receiver spacing and layouts to match the operating frequency range. In contrast, radio interferometric arrays are designed to optimally sample the Fourier space data for making high quality images of the sky. Therefore, using existing radio interferometric arrays (with arbitrary geometry and wide frequency variation) for DOA estimation is practically infeasible except by using images made by such interferometers. In this paper, we focus on low cost DOA estimation without imaging, using a subset of a radio interferometric array, using a fraction of the data collected by the full array, and, enabling early determination of DOAs. The proposed method is suitable for transient and low duty cycle source detection. Moreover, the proposed method is an ideal follow-up step to online radio frequency interference (RFI) mitigation, enabling the early estimation of the DOA of the detected RFI.

Figures (12)

• Figure 1: Radiation from a source at distance $R$ and angle $\theta,\phi$ is received by a 3D array of arbitrarily placed dual polarized receivers (blue crosses x). The coordinates of the $p$-th receiver are given by ${\bf x}_p$. The baseline $pq$ is formed by correlating the digitized and channelized data received by receivers $p$ and $q$. The distance to the source from the $p$-th receiver is given by $d_p$. The baseline length is $b_{pq}$. The angle between the baseline $pq$ and the source DOA is $\alpha_{pq}$.
• Figure 2: The transformer deep neural network architecture with input encoding (${\bf W}_1$,${\bf W}_2$) and output encoding (${\bf W}_3$), one cross attention block and 6 self attention blocks.
• Figure 3: A fraction of the LOFAR AARTFAAC array receiver locations and the linear sub-arrays ($N_l$) are denoted by the various colours. Each sub-array has $N_r$ receivers.
• Figure 4: The layout of the receivers of a SKA-Low station. The receivers lie on a plane at random positions. Subsets of receivers are selected to form $N_l$ almost linear sub-arrays denoted by the various colours. Each sub-array has $N_r$ receivers.
• Figure 5: Cost function (\ref{['fcost']}) evaluated on a $N_g\times N_g$ grid of elevation $\theta$ and azimuth $\phi$ for the AARTFAAC array example. The ground truth DOA is shown by the red circle o. The DOA corresponding to the minimum value of the cost function is shown by the green cross x. The output of the transformer deep neural network is shown by the blue cross x.