Two-Stage Rotation-Based Joint ToA-AoA Estimation for Spatial Wideband Systems

arXiv:2503.18111 · eess.SP · Submitted 2025-03-23 · Read on arXiv

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Introduction to the show: ident: Electrical Engineering. The day in electrical engineering: signals, systems and the hardware that carries them.

Rosa: We're looking at the paper: "Two-Stage Rotation-Based Joint ToA-AoA Estimation for Spatial Wideband Systems".

Dev: Here's the gist of the paper. Spatial and temporal delays in a wireless multiantenna system, paired with an orthogonal frequency division multiplexing (OFDM) waveform, can be utilized to estimate the Angle of Arrival (AoA) and Time of Arrival (ToA) of scatterers in the radio channel through spectral estimation techniques.

Rosa: However, in millimeter-wave (mmWave) and TeraHertz (THz) systems, the spatial delays across the aperture of massive array elements are comparable to the inverse of the signal bandwidth.

Dev: As a result, these delays cannot be approximated solely by phase terms, necessitating consideration of the Spatial Wideband Effect (SWE).

Rosa: The SWE in the mmWave/THz system causes migration of the actual AoA-ToA coarse bins.

Paper summary: Rosa: So this paper by Chandrashekhar Rai and Debarati Sen is looking at how you can estimate the Angle of Arrival and Time of Arrival of scatterers in a wireless channel using spectral estimation techniques, especially with OFDM waveforms. It points out that in millimeter-wave or terahertz systems, the spatial delays across a massive antenna array are comparable to the inverse of the signal bandwidth.

Dev: That means those spatial delays can't be just approximated by phase terms anymore because of this Spatial Wideband Effect, which causes a migration of the actual Angle of Arrival and Time of Arrival coarse bins. And they also noted that using a finite grid measurement on continuous frequencies can cause spectral leakage if there's a grid mismatch.

Taro: So the main idea here seems to be addressing those limitations in high-frequency systems where the spatial delays are spread out by the bandwidth, which makes estimating those coarse AoA-ToA bins tricky because they migrate.

Rosa: Exactly, and they suggest using the inverse Discrete Fourier Transform for an initial two-dimensional spectrum estimation of the channel response because it's computationally efficient and practical. Then they propose a two-stage rotation-based algorithm for fine-tuning those signatures in spatial wideband systems with uniform linear arrays.

Dev: The core contribution, as you put it, is this novel two-stage efficient rotation method for estimating super-resolution signatures in spatial wideband systems. This algorithm first identifies the correct coarse bin and then performs fine-tuning around that corrected bin to get the continuous AoA-ToA signature.

Taro: So it’s about taking a rough guess at where the signal is coming from, correcting that guess using a rotation around a peak, and then refining it to get a really precise continuous signature.

Rosa: Right, so we're dealing with these super-resolution signatures in wideband systems. This technique should be useful for things like handling beam squint effect in near-field communications or for wideband MIMO radar in 6G and beyond.

Conclusion: Dev: Thinking about the paper "Two-Stage Rotation-Based Joint ToA-AoA Estimation for Spatial Wideband Systems" and its authors, Rai and Sen, the big picture here is how you can get a more accurate AoA-ToA estimate when you're dealing with wideband signals in massive antenna arrays.

Rosa: Basically, they tackle the problem that spatial delays get mixed up by the signal bandwidth in mmWave and THz systems. Their solution is a two-stage rotation method that first finds the right coarse bin and then fine-tunes it for a continuous signature.

Taro: What this means practically is that you can use this to handle beam squint effect, which comes up in applications like 6G MIMO radar or near-field communications where those spatial delays become significant.

Dev: The implication is that we can move beyond just looking at the coarse bins and get a better continuous AoA-ToA signature by using this rotation approach. They showed how to compensate for the wideband effect up to integer values during the first stage of rotation.

Rosa: But they also pointed out a limitation, which is that their method relies on using neighborhood points as Mnbr and Nnbr, which means the performance depends heavily on how you set those neighborhood sizes.

Taro: So for someone listening just for what this paper does, it's about getting super-resolution signatures in spatial wideband systems by correcting coarse bins with a rotation around a peak.

Dev: That’s the gist of the work, moving from rough bin identification to fine-tuning the signature. It shows a path toward more accurate localization and channel estimation in these challenging high-frequency environments.

Indian Institute of Technology Kharagpur

eess.SP

Submitted: 2025-03-23

Updated: 2026-10-28

Comments: 13 pages, 12 figures, 2 tables

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 75/100

The gist: Spatial and temporal delays in a wireless multiantenna system, paired with an orthogonal frequency division multiplexing (OFDM) waveform, can be utilized to estimate the Angle of Arrival (AoA) and

Key concepts

Spatial Wideband Effect (SWE): In mmWave/THz systems with massive arrays, spatial delays across elements are comparable to signal bandwidth. This effect causes the actual AoA-ToA coarse bins to migrate during estimation, meaning simple phase approximations are insufficient for accurate localization.
Channel Impulse Response (CIR) Model: This model describes how a signal travels through a spatial wideband system with Uniform Linear Array (ULA) antennas. It frames the localization task as a 2-D frequency estimation problem on a grid, showing how high bandwidth and large antenna size cause coupled spreading effects.
Two-Stage Rotation Algorithm: This proposed method estimates super-resolution signatures by first rotating around path cluster maxima to find the correct coarse bin. Then, it fine-tunes this corrected bin to obtain the continuous AoA-ToA signature, compensating for the wideband effect up to integer values.
Inverse Discrete Fourier Transform (DFT): The DFT is used efficiently for initial 2-D spectrum estimation of the channel response. It is chosen because it offers computational efficiency and broad practical applicability in spectral analysis tasks.

Terminology

Spatial Wideband Effect — 13× in this paper
Fine-Tuning — 12× in this paper · explained in 5 episodes
Localization — 10× in this paper · explained in 2 episodes
Discrete Fourier Transform — 8× in this paper
Angle of Arrival — 6× in this paper
Time of Arrival — 6× in this paper
Uniform Linear Array — 6× in this paper
Channel Impulse Response — 2× in this paper
Clustering — 2× in this paper · explained in 2 episodes
Computational Efficiency — 2× in this paper · explained in 2 episodes
Core — 2× in this paper · explained in 2 episodes
Multiple Input Multiple Output — 2× in this paper
Compressive Sensing — 1× in this paper
Decoupling — 1× in this paper · explained in 2 episodes
Fast Fourier Transform — 1× in this paper
Geometric Progression — 1× in this paper
Machine Learning (ML) — 1× in this paper · explained in 2 episodes
Receiver Station — 1× in this paper
Root Mean Squared Error — 1× in this paper
Signal-to-Noise Ratio — 1× in this paper
Signal-to-Noise Ratio (SNR) — 1× in this paper · explained in 6 episodes

Summary

Spatial and temporal delays in a wireless multiantenna system, paired with an orthogonal frequency division multiplexing (OFDM) waveform, can be utilized to estimate the Angle of Arrival (AoA) and Time of Arrival (ToA) of scatterers in the radio channel through spectral estimation techniques. However, in millimeter-wave (mmWave) and TeraHertz (THz) systems, the spatial delays across the aperture of massive array elements are comparable to the inverse of the signal bandwidth. As a result, these delays cannot be approximated solely by phase terms, necessitating consideration of the Spatial Wideband Effect (SWE). The SWE in the mmWave/THz system causes migration of the actual AoA-ToA coarse bins. Moreover, a finite grid measurement of complex sinusoidal signals of continuous frequencies results in spectral leakage whenever there is a grid mismatch. In this work, given the Discrete Fourier Transform’s computational efficiency and broad practical applicability, we propose utilizing the inverse Discrete Fourier Transform (DFT) for the initial 2-D spectrum estimation of the channel response. Further, in this paper, we propose a two-stage efficient rotation-based algorithm for fine-tuned signature estimation of spatial wideband systems with uniform linear arrays. The proposed technique in this work can be used for handling beam squint effect in different applications like near-filed communications, wideband Multiple Input Multiple Output (MIMO) radar, channel estimation in Extremely Large (XL)-MIMO for 6G and beyond systems etc.

The core contribution of this research is a novel two-stage efficient rotation method for estimating super-resolution signatures in spatial wideband systems. This algorithm first identifies the correct coarse bin and then performs fine-tuning around that corrected bin to obtain the continuous AoA-ToA signature.

System Modeling and Wideband Effects

The paper establishes a Channel Impulse Response (CIR) measurement model for a spatial wideband system with a ULA antenna configuration where localizing a scatterer is formulated as a 2-D frequency estimation problem measured on a finite-size spatio-temporal grid. The authors derive the theoretical spreading limits of the proposed spatial wideband system in closed form and demonstrate the coupled spreading effect arising from the use of a high BW signal with a massive antenna size. The normalized space-frequency channel response is defined as Hm(n) = X I−1 i=0 β˜ie−j2πnτ˜i e−j2πmϕ˜i e−j2πα N mnϕ˜i [z] W ideband−T erm + wm(n). This model shows that for α → 0, the wideband term vanishes to unity, and the conventional temporal-only wideband system can be shown as a special case of the spatialtemporal wideband system.

The Two-Stage Rotation Algorithm

The proposed two-stage rotation method is introduced for estimating super-resolution signatures in spatial wideband systems. The process involves two main stages:

** First Stage Rotation:**

**) In the first stage, we rotate around the maximum of each path cluster to get the correct coarse bin. This is done by setting neighborhood points as Mnbr, Nnbr = ⌈αM⌉ and searching for the maximum among these neighborhood points while simultaneously removing the wideband effect by conjugation with angle corresponding to the peak itself. The resulting corrected coarse bin is then chosen by finding the maximum of Grem(k, l) around the neighborhood. This procedure yields the estimate of fractional parts i.e., ϕc˜Fi = ∆ˆϕ˜i and τ˜cFi = ∆ˆτ˜i. The mathematical procedure for this is described in Algorithm 1. This stage aims to find the correct coarse bin by minimizing the spread when approaching the correct bin. The number of bins spread for an i-th path is ⌈αMϕ˜i⌉. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1. This stage can compensate for the wideband effect up to the integer values as shown in Figs. 5(b) and 6(b). The resulting corrected coarse bin is denoted as (ˆˆki, ˆˆli). The mathematical procedure for this is described in Algorithm 1.

Improvements for AI systems

Spatial Wideband Signature Estimation for 6G/THz Systems: The proposed two-stage rotation-based algorithm can be integrated into AI systems for high-resolution sensing by accurately estimating Angle of Arrival (AoA) and Time of Arrival (ToA) in mmWave and THz environments, overcoming the limitations imposed by the Spatial Wideband Effect.
Beam Squint Handling: The technique can be applied to correct beam squint effects in near-field communications or wideband MIMO radar systems by utilizing the derived rotation matrices to compensate for frequency-dependent phase shifts.
Enhanced Target Detection and Localization: AI systems employing this method can achieve superior scatter detection performance, reaching hit rates as high as 0.98 at high Signal-to-Noise Ratios, leading to more reliable localization in massive MIMO scenarios compared to traditional methods like 2D-MUSIC or 2D-OMP.
Complex Path Coefficient Estimation: The algorithm provides a method for estimating complex path coefficients, which is valuable for advanced channel modeling in AI systems requiring detailed knowledge of the radio environment.