🔢 mathematics

Transformer-Based Hybrid Beamforming with Reconfigurable Pixel Antenna for HAPS Communications

This paper proposes a Transformer-based hybrid beamforming framework called PR-HBFNet for HAPS communications, which utilizes a Transformer encoder to optimize radiation patterns and model-driven residual learning to compute precoders, achieving near-optimal spectral efficiency with significantly reduced computational complexity.

Original authors: Ruiqi Wang, Ziwei Wan, Keke Ying, Zhen Gao

Published 2026-05-19

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Ruiqi Wang, Ziwei Wan, Keke Ying, Zhen Gao

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ 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 a high-tech airship floating in the stratosphere, about 12 miles above the Earth. This is a HAPS (High-Altitude Platform Station), acting like a super-powerful cell tower in the sky. Its job is to beam internet and data down to thousands of people on the ground.

To do this effectively, the airship uses a massive array of antennas. However, there's a problem: the airship has strict limits on how much power and weight it can carry. It can't afford the expensive, power-hungry equipment needed for a "fully digital" system where every single antenna has its own dedicated computer brain.

So, engineers use a "hybrid" approach: a few powerful computer brains (digital) control many simple, passive antennas (analog). But there's a catch. Traditional antennas are like flashlights with a fixed beam. Once you build them, the shape of the light they shine is permanent. If the wind blows the airship slightly, or if the users on the ground move, that fixed beam might miss the target or waste energy shining into empty space.

The Innovation: "Shape-Shifting" Antennas

This paper introduces a new kind of antenna called a Reconfigurable Pixel Antenna (RPA). Think of these not as static flashlights, but as smart, shape-shifting spotlights.

Inside each antenna, there are tiny electronic switches (like microscopic light switches). By flipping these switches on and off in different combinations, the antenna can instantly change the shape and direction of its signal beam. It can choose from a "menu" of four different beam shapes (patterns) to best match where the users are standing.

The Problem: Too Many Choices

The challenge is that if you have 32 of these shape-shifting antennas, and each can choose from 4 patterns, the number of possible combinations is astronomical. Trying to find the perfect combination of shapes and signal directions using traditional math is like trying to find a specific needle in a haystack the size of a mountain. It takes too long and requires too much computing power, which the airship doesn't have.

The Solution: The "Transformer" Brain

The authors propose a new AI system called PR-HBFNet (Pattern Reconfigurable Hybrid Beamforming Network) to solve this instantly. They use a type of AI architecture called a Transformer (the same kind of technology behind advanced chatbots and translation tools).

Here is how their system works, using a simple analogy:

The Pattern Reconfigurable Network (The "Eye"):
Imagine a scout looking at the ground. This part of the AI looks at the "channel state information" (a map of how the radio waves are traveling). Instead of guessing, the Transformer analyzes the whole picture at once. It decides, "Okay, Antenna 1 should use Pattern A, Antenna 2 should use Pattern B," and so on. It picks the best "shape" for every single antenna in a split second.
The Hybrid Beamforming Network (The "Hand"):
Once the shapes are picked, the second part of the AI acts like a conductor. It fine-tunes the volume and timing of the signals from the digital computers to the analog antennas.
- The Trick: Instead of starting from scratch, this AI uses a "residual learning" strategy. It starts with a smart guess (like a standard mathematical formula) and then uses the AI to learn the tiny corrections needed to make it perfect. This is like a student who knows the basic math but uses a tutor to learn the specific shortcuts for a tricky test.

The Results: Fast and Accurate

The researchers tested their system in a computer simulation:

Performance: The new AI system performed almost exactly as well as the "Greedy" method. The "Greedy" method is like a super-slow, super-smart robot that tries every single combination to find the absolute best one. The new AI got within 1.1% of that perfect score.
Speed: This is the big win. The "Greedy" method took 4 to 8 seconds to make a decision. The new AI system took only 26 to 38 milliseconds (less than a blink of an eye).
Efficiency: It uses significantly less computing power (math operations) to achieve this speed.

The Bottom Line

This paper shows that by combining shape-shifting antennas with a smart Transformer AI, we can make high-altitude internet towers much more efficient. The system can instantly reconfigure its "flashlights" to follow the users on the ground, delivering faster data speeds without needing heavy, power-hungry equipment. It turns a slow, complex math problem into a fast, instant decision.

Technical Summary: Transformer-Based Hybrid Beamforming with Reconfigurable Pixel Antenna for HAPS Communications

Problem Statement
High-altitude platform stations (HAPS) operating in the stratosphere are envisioned as critical components of 6G space-air-ground networks, offering wide coverage and strong line-of-sight (LoS) connectivity. To meet stringent data-rate requirements while compensating for free-space path loss, massive multiple-input multiple-output (MIMO) is essential. However, fully digital beamforming is impractical for HAPS payloads due to excessive hardware costs and power consumption associated with dedicated radio-frequency (RF) chains per antenna. Hybrid beamforming (HBF) offers a solution by reducing RF chains, yet conventional HBF architectures rely on fixed-pattern antenna elements. In HAPS channels, which are often dominated by LoS or near-LoS components with limited angular spread, static radiation patterns restrict the array's ability to concentrate energy toward dominant spatial directions, leaving potential array and channel gains underexploited.

While Reconfigurable Pixel Antennas (RPAs) introduce an additional degree of freedom by allowing dynamic selection of radiation patterns, jointly optimizing the discrete pattern selection, analog beamforming, and digital precoding creates a highly complex mixed-integer nonlinear programming (MINLP) problem. The search space grows exponentially with the number of antennas and radiation modes. Existing iterative algorithms, such as greedy pattern selection combined with HBF optimization, suffer from substantial computational complexity and inference latency, making them unsuitable for the real-time scheduling requirements of practical HAPS systems.

Methodology
To address these challenges, the authors propose PR-HBFNet, a Transformer-based end-to-end deep learning framework designed to solve the joint pattern–analog–digital beamforming problem. The system model considers a HAPS equipped with a uniform planar array (UPA) of $N_t$ RPA elements, partitioned into $N_{RF}$ subarrays (sub-connected architecture) to comply with payload constraints. The channel is modeled as a wideband 3D geometry-based stochastic model with Rician fading.

The proposed PR-HBFNet is a cascaded neural network comprising two primary modules:

Pattern Reconfigurable Network (PRN):
- Input: An electromagnetic channel state information (CSI) tensor $\hat{H}$ containing responses for all candidate radiation patterns.
- Mechanism: The input is processed by a Transformer Encoder to capture long-range dependencies among antennas, users, and candidate patterns.
- Output: A fully connected layer followed by a Softmax activation generates probabilities for each candidate mode per antenna. An Argmax operation (approximated during training via a Straight-Through Estimator) selects the optimal discrete pattern vector $c$ .
Hybrid Beamforming Network (HBN):
- Input: The equivalent channel derived from the selected pattern vector.
- Strategy: The network employs model-driven residual learning to preserve physical constraints and improve convergence.
- Analog Branch: A Transformer Encoder learns a residual correction over an initial analog beamformer derived from subarray-wise Singular Value Decomposition (SVD). The output is projected onto the feasible set to ensure a block-diagonal structure with constant-modulus entries (satisfying passive phase shifter constraints).
- Digital Branch: Similarly, a Transformer Encoder predicts a residual refinement over an SVD-based initial digital precoder to suppress multi-user interference. The final digital precoders are rescaled across all subcarriers to satisfy the total transmit-power constraint.

The entire network is trained in an unsupervised manner by directly maximizing the system's average downlink sum spectral efficiency, eliminating the need for labeled optimal solutions from conventional solvers.

Key Results
Simulation results, conducted using a 3D wideband channel model (QuaDRiGa) with $N_t=32$ antennas, $N_{RF}=8$ RF chains, and a pattern codebook of size $M=4$ , demonstrate the following:

Spectral Efficiency (SE): The proposed PR-HBFNet closely approaches the performance of a greedy benchmark (Greedy+HBFNet). At a transmit power of 50 dBm, PR-HBFNet achieves an SE of approximately 30.87 bits/s/Hz, which is within 1.1% of the benchmark value (31.23 bits/s/Hz). Both reconfigurable schemes significantly outperform systems using fixed radiation patterns or random pattern selection.
Scalability: The performance advantage of the proposed method over fixed-pattern massive MIMO becomes more pronounced as the number of users ( $K$ ) increases, indicating effective adaptation to multi-user interference and channel geometry.
Computational Complexity: The proposed method offers a dramatic reduction in inference latency and computational load.
- Latency: PR-HBFNet operates in the millisecond range (26.83–38.30 ms), whereas the greedy benchmark requires seconds (4.2–8.2 seconds).
- FLOPs: The proposed network requires 0.96–1.25 G FLOPs, compared to 7.79–47.23 G FLOPs for the benchmark.
- Parameters: While the proposed network has a moderate increase in trainable parameters compared to the benchmark, the gain in computational efficiency is substantial.

Significance and Claims
The paper claims that PR-HBFNet successfully bridges the gap between the high performance of iterative optimization methods and the low-latency requirements of practical HAPS systems. By explicitly incorporating hardware constraints (sub-connected architecture, constant modulus, and total power constraints) into the learning framework, the method ensures consistency with the underlying physical model. The authors conclude that the framework is suitable for real-time HAPS communications, offering a low-complexity solution that effectively approaches the spectral efficiency of greedy pattern-selection schemes while reducing inference latency from seconds to milliseconds.