Joint single-shot ToA and DoA estimation for VAA-based BLE ranging with phase ambiguity: A deep learning-based approach

Conventional direction-of-arrival (DoA) estimation methods rely on multi-antenna arrays, which are costly to implement on size-constrained Bluetooth Low Energy (BLE) devices. Virtual antenna array (VAA) techniques enable DoA estimation with a single antenna, making angle estimation feasible on such devices. However, BLE only provides a single-shot two-way channel frequency response (CFR) with a binary phase ambiguity issue, which hinders the direct application of VAA. To address this challenge, we propose a unified model that combines VAA with BLE two-way CFR, and introduce a neural network based phase recovery framework that employs row / column predictors with a voting mechanism to resolve the ambiguity. The recovered one-way CFR then enables super resolution algorithms such as MUSIC for joint time of arrival (ToA) and DoA estimation. Simulation results demonstrate that the proposed method achieves superior performance under non-uniform VAAs, with mean square errors approaching the Cramer Rao bound at SNR $\geq$ 5 dB.

💡 Research Summary

The paper tackles the long‑standing problem of achieving high‑resolution angle‑of‑arrival (DoA) and time‑of‑arrival (ToA) estimation on Bluetooth Low Energy (BLE) devices, which are severely constrained in size, power, and antenna resources. Classical DoA techniques require multi‑antenna arrays, but BLE hardware typically offers only a single antenna and a single‑shot two‑way channel frequency response (CFR). The authors exploit the concept of a Virtual Antenna Array (VAA), where the motion of the user equipment (UE) creates a set of virtual antenna positions. By stitching together the received signals from N = 16 positions along the UE trajectory and M = 80 sub‑carriers, a non‑uniform spatial sampling grid is formed, enabling array‑processing techniques without any physical array.

A key obstacle is that BLE’s two‑way CFR, obtained by element‑wise Hadamard multiplication of the forward and reverse CFRs, removes the local‑oscillator (LO) phase offsets but also doubles the effective multipath order and reduces the SNR. Recovering a one‑way CFR requires taking an element‑wise square root of the two‑way CFR, which introduces an unknown binary sign (± 1) for each element. This “phase ambiguity” corrupts the phase information needed by super‑resolution algorithms such as MUSIC, leading to large ToA/DoA errors if not correctly resolved.

To solve the binary ambiguity, the authors propose a double‑neural‑network architecture. Two U‑Net models are trained separately: a row‑wise network f_row that processes the phase vector of each spatial row (across sub‑carriers) and a column‑wise network f_col that processes each frequency column (across virtual antenna positions). Both networks output a probability that each element shares the same sign as the first element of its row/column. Training uses supervised data generated from 8 000 simulated VAA channel realizations (60 % training, 20 % validation, 20 % test) with cross‑entropy loss.

After inference, a voting mechanism fuses the two predictions. Because the frequency spacing is fixed, the row‑wise predictor is empirically more reliable; thus the sign of the first element of each row is determined by majority voting over column‑wise candidates, while the rest of the row follows the row‑wise predictions. The resulting binary matrix N is then used to recover the one‑way CFR as eY = √(ĤY) ⊙ N.

With the corrected one‑way CFR, a two‑dimensional MUSIC algorithm is applied. The spatial steering vector a_Θ(θ) captures the phase shift due to the virtual antenna positions, while the frequency steering vector a_F(τ) captures the delay across sub‑carriers. The covariance matrix is formed from the corrected CFR columns, eigen‑decomposed to obtain the noise subspace, and the pseudo‑spectrum P(θ,τ) = 1/(a_Θᴴ(θ) E_n E_nᴴ a_F(τ)) is evaluated. Peaks of P give simultaneous estimates of DoA and ToA for each multipath component.

Simulation results consider a 40 m × 40 m indoor scenario with one line‑of‑sight path and 1–3 non‑line‑of‑sight paths, random UE‑BS distances (20–30 m), and non‑uniform virtual antenna spacings drawn from