⚡ electrical engineering

Suppressing Beam Squint Effect For Near-Field Wideband Communication Through Movable Antennas

This paper proposes a movable antenna (MA) array-based approach for wideband near-field MISO systems that mitigates the beam squint effect by optimizing antenna positions to maximize the minimum analog beamforming gain across the spectrum, utilizing a slack variable and the smoothed-gradient-descent-ascent (SGDA) method to solve the resulting challenging optimization problem.

Original authors: Yanze Zhu, Qingqing Wu, Yang Liu, Qingjiang Shi, Wen Chen

Published 2026-07-23

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CC0 1.0

Original authors: Yanze Zhu, Qingqing Wu, Yang Liu, Qingjiang Shi, Wen Chen

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the invisible ocean of radio waves that carries our texts, videos, and music. For decades, engineers have tried to catch these waves with antennas that are stuck in place, like lighthouses fixed on a rocky shore. But as we push for faster internet using higher frequencies (like millimeter waves) and wider channels, these fixed antennas start to struggle. They suffer from a glitch called "beam squint." Think of it like trying to shine a flashlight through a prism: the beam splits and bends depending on the color of the light. In a wideband system, different parts of the signal (different colors of radio waves) try to point in slightly different directions, causing the signal to blur and weaken. To fix this, scientists are now experimenting with "movable antennas"—tiny, robotic elements that can slide around on a surface, like dancers rearranging themselves on a stage to catch the perfect spotlight. This paper explores how to choreograph these dancers in a specific, high-tech environment where the waves haven't traveled far yet (the "near-field"), ensuring the signal stays sharp and strong for everyone.

The researchers, Yanze Zhu and their team, tackle the tricky problem of how to move these antennas to stop the "beam squint" from ruining the connection. They set up a scenario where a square grid of movable antennas serves a single user who is relatively close by. In this "near-field" zone, the waves behave differently than they do for distant stars; they curve, and the distance to each antenna matters a lot. The team realized that if they just left the antennas in fixed spots, the signal strength would drop off significantly as the frequency changed across the wide band.

To solve this, they proposed a clever strategy: instead of just making the signal strong at one specific frequency, they wanted to make sure the weakest part of the signal across the entire range was as strong as possible. It's like adjusting a team of runners so that even the slowest runner is still fast enough to win the race. They formulated a mathematical puzzle to find the perfect positions for the antennas to achieve this "max-min" goal. However, solving this puzzle is incredibly hard because the antennas can't overlap, and they have to stay within their square dance floor.

The paper presents two different ways to solve this puzzle. The first method, which they call the "Slack Variable" approach, is like a careful, step-by-step calculator. It breaks the problem down, optimizing one antenna at a time while holding the others steady, and uses advanced math to ensure the solution gets better with every step. The second method uses something called "Smoothed-Gradient-Descent-Ascent" (SGDA). You can think of this as a more agile, high-speed approach. Instead of checking every single frequency one by one (which would be slow if there are thousands of them), this method treats the frequency as a continuous flow and uses a smart, iterative dance to find the best spot quickly.

Through computer simulations, the team tested their ideas. They set up a system with 256 different frequency channels, ranging from 58.92 GHz to 61.08 GHz, with a center frequency of 60 GHz. They used a square array of antennas with a side length of $A = \frac{100c}{f_c}$ (where $c$ is the speed of light) and kept the minimum distance between antennas at $D_{min} = \frac{c}{2f_0}$ . The results showed that their movable antenna setups dramatically improved the signal compared to traditional fixed antennas. Specifically, the SGDA method (Algorithm 2) not only found better antenna positions to keep the signal strong across the whole band but also did so much faster than the first method, especially when the number of frequency channels increased. While the first method's running time exploded as they added more channels, the second method stayed fast and efficient.

The authors are careful to note that these results come from simulations, not real-world field tests. They suggest that while their current work focuses on a single user, the same logic could eventually help in crowded rooms with many users. They also hint that future versions of these antennas might even be able to rotate, not just slide, offering even more control. For now, though, the study proves that giving antennas the freedom to move is a powerful way to keep our high-speed connections steady, even when the signal tries to squint and wander off.

Technical Summary: Suppressing Beam Squint Effect For Near-Field Wideband Communication Through Movable Antennas

Problem Statement
This paper addresses the challenge of the beam squint effect in wideband multiple-input-single-output (MISO) communication systems utilizing Movable Antenna (MA) arrays under a Near-Field (NF) channel model. In wideband systems, particularly those operating at millimeter-wave (mmWave) and terahertz (THz) frequencies, the analog beamforming gain degrades as the subcarrier frequency deviates from the reference central carrier frequency. This phenomenon, known as beam squint, leads to fluctuating performance across the spectrum. While existing literature has explored MAs for improving spectral efficiency and signal-to-noise ratio (SNR) in far-field scenarios, the specific configuration of MA arrays to mitigate beam squint in the near-field regime remains largely uninvestigated. The core difficulty lies in the non-convex nature of optimizing antenna positions to maximize the minimum beamforming gain across the entire wideband spectrum while satisfying physical constraints (feasible dwelling regions and minimum spacing).

Methodology
The authors formulate the problem as a max-min optimization task (Problem P1), aiming to maximize the minimum analog beamforming gain over all subcarriers by adjusting the 2D positions of the MA elements. To solve this challenging non-convex problem, two algorithmic approaches are developed:

Slack Variable (SV) Based Classical Solution (Algorithm 1):
- The max-min problem is transformed into a constrained optimization problem (P2) by introducing a slack variable $\kappa$ .
- A Block Coordinate Descent (BCD) framework is adopted to optimize the position of one antenna at a time.
- For each antenna update, the non-convex constraints are handled using the Majorization-Minimization (MM) method. This involves constructing concave lower bounds for the objective function and the minimum spacing constraint via second-order and first-order Taylor expansions, respectively.
- The resulting sub-problem (P4) is a convex optimization problem solvable by standard numerical solvers (e.g., CVX).
Smoothed-Gradient-Descent-Ascent (SGDA) Based Efficient Solution (Algorithm 2):
- Recognizing that the SV-based method suffers from high computational complexity when the number of subcarriers is large (due to the resulting Second-Order Cone Programming constraints), an efficient SGDA-based approach is proposed.
- The frequency $f$ is treated as a continuous parameter within the band $[f_0, f_L]$ .
- The problem is cast as a min-max game solved via BCD. Within each BCD iteration, the SGDA method is employed to update the antenna position ( $t_m$ ), the frequency ( $f$ ), and an auxiliary variable ( $\alpha_m$ ).
- The updates involve gradient ascent for the antenna position and gradient descent for the frequency and auxiliary variables, incorporating smoothing terms to ensure convergence.
- Projections are applied to ensure updated variables satisfy the feasible region and spacing constraints.

Key Contributions

Novelty: This is the first work to investigate the beam squint effect specifically within a Near-Field wideband MA communication system.
Optimization Criterion: A max-min criterion is proposed to configure MA positions, specifically designed to maximize the minimal analog beamforming gain across the entire wideband spectrum, thereby balancing communication rates across subcarriers.
Algorithmic Development: Two algorithms are developed to resolve the non-convex optimization challenge:
- An SV-based algorithm utilizing MM for tractable solutions.
- An SGDA-based algorithm that offers high efficiency, particularly suitable for systems with a large number of subcarriers.
Performance Verification: Numerical results demonstrate that the proposed algorithms effectively mitigate beam squint, with the SGDA-based solution showing superior convergence values and significantly lower computational complexity compared to the SV-based method and benchmark particle swarm optimization (PSO) techniques.

Simulation Results
Numerical simulations were conducted in a wideband MISO system (58.92 GHz to 61.08 GHz) with a 10m near-field distance.

Convergence: Both proposed algorithms converge monotonically within tens of BCD iterations.
Beamforming Gain: The MA configurations significantly outperform conventional Fixed Position Antenna (FPA) arrays and PSO-based benchmarks in terms of array gain across the frequency band. The SGDA-based algorithm (Alg. 2) achieved higher gain than the SV-based algorithm (Alg. 1).
Complexity: The run-time analysis reveals that while the SV-based method's complexity increases intensively with the number of subcarriers ( $L$ ), the SGDA-based method's run-time per iteration remains nearly insensitive to $L$ and is substantially lower, making it scalable for large bandwidths.

Significance and Claims
The paper claims that deploying MA arrays with the proposed configuration methods offers a viable solution to the beam squint effect in near-field wideband systems, a critical issue for future 5G/6G communications using mmWave and THz bands. The authors emphasize that their SGDA-based solution is particularly significant for its computational efficiency, enabling practical implementation in systems with hundreds or thousands of subcarriers.

The paper modestly notes that while the current study focuses on a single-user scenario, the proposed scheme can be extended to multi-user systems (potentially optimizing spectral efficiency instead of just array gain). Additionally, the authors suggest that future research could explore Six-Dimensional Movable Antennas (6DMA), which offer both position and rotation capabilities, to further enhance beam squint mitigation.

Technical Summary: Suppressing Beam Squint Effect For Near-Field Wideband Communication Through Movable Antennas

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