⚡ electrical engineering

Low-Complexity Learning-Based Beamforming for Ultra-Massive MIMO THz Communications

This paper proposes a novel low-complexity beam training framework for ultra-massive MIMO terahertz communications that utilizes an inception and residual neural network trained on received signal powers to efficiently identify optimal beamforming pairs without requiring constant feedback or exhaustive search.

Original authors: Sourabh Solanki, Abuzar Babikir Mohammad Adam, Chandan Kumar Sheemar, Zaid Abdullah, Eva Lagunas, George C. Alexandropoulos, Symeon Chatzinotas

Published 2026-04-21

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Sourabh Solanki, Abuzar Babikir Mohammad Adam, Chandan Kumar Sheemar, Zaid Abdullah, Eva Lagunas, George C. Alexandropoulos, Symeon Chatzinotas

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

The Big Picture: Finding a Needle in a Haystack at Light Speed

Imagine you are trying to talk to a friend across a massive, noisy stadium using a laser pointer. To make sure your friend sees the dot, you have to aim the laser perfectly. If you miss by even a tiny fraction of a degree, the light hits the wall instead of your friend's eyes.

This is the challenge of Terahertz (THz) communication (the super-fast 6G internet of the future). It uses incredibly high frequencies that carry huge amounts of data, but they are very fragile. They get blocked easily by air molecules and rain. To fix this, engineers use Ultra-Massive MIMO systems—basically, walls covered in thousands of tiny antennas that work together to create a super-tight, powerful laser beam.

The Problem: The "Flashlight Search" is Too Slow

In the past, to find the right direction to aim your laser, you would have to do a systematic search:

Point the laser slightly left.
Ask, "Can you see it?"
Point it slightly right.
Ask again.
Repeat this thousands of times until you find the perfect spot.

In a system with thousands of antennas, this "search" takes too long. By the time you find the right angle, the data you wanted to send has already timed out. It's like trying to find a specific book in a library by checking every single shelf one by one, while the library is on fire.

The Solution: A "Magic Crystal Ball" (The Neural Network)

The authors of this paper propose a clever shortcut. Instead of searching for the perfect narrow beam step-by-step, they built a smart computer brain (an Artificial Neural Network) that acts like a magic crystal ball.

Here is how their new system, called Incept-ResNet, works:

1. The Training Phase (Learning the Map)

Before the system is ever used in the real world, the computer is trained in a simulation.

The Teacher: Imagine a teacher showing the computer a map of the stadium. The computer learns: "If the signal is strong in the 'North-North-West' wide beam, the best narrow laser is likely pointing at 'Seat 42'."
The Data: The computer learns by looking at wide beams (which are easy to find) and predicting where the narrow beams (the precise laser) should be. It doesn't need to know the exact physics of the air or the walls; it just learns the pattern of "Signal Strength = Best Direction."

2. The Inception-ResNet Architecture (The Brain's Structure)

The paper describes a specific type of brain architecture called Incept-ResNet. Think of it like a team of detectives working together:

The "Inception" Team: These detectives look at the problem from different angles at the same time. Some look at the big picture, others zoom in on tiny details. This ensures no clue is missed.
The "Residual" Team: These detectives are the memory keepers. They make sure the team doesn't forget the original clues as they dig deeper into the investigation. This prevents the brain from getting confused or "forgetting" the starting point.
The Fusion: These two teams share their notes instantly to make a final, perfect guess.

3. The Inference Phase (The Magic Trick)

Once the computer is trained, it goes to work in the real world.

Old Way: The transmitter and receiver shout back and forth, testing beam after beam. (High complexity, slow).
New Way: The receiver just measures the signal strength of a few wide, easy-to-find beams. It sends this tiny bit of data to the transmitter.
The Result: The computer brain instantly says, "I know exactly where to point the laser!" without needing to test thousands of other options.

Why This is a Game Changer

No More Shouting: The old methods required a constant "feedback loop" (shouting back and forth) to align the beams. This new method does it almost instantly, saving massive amounts of time and battery power.
Scalability: Whether you have 64 antennas or 2,500 antennas, the computer brain handles it just as easily. It's like having a GPS that works just as well in a small town as it does in a giant city.
Accuracy: The paper proves that this "guessing" method is almost as accurate as the slow, perfect search. It's like a master archer who can hit the bullseye without needing to adjust their aim ten times first.

The Bottom Line

This paper presents a way to make future 6G/7G internet faster and more efficient. Instead of blindly searching for a signal in the dark, we are giving the system a smart map (the neural network) that allows it to instantly know exactly where to point its "laser" to connect with your device, even in a world with thousands of antennas.

In short: They replaced a slow, exhausting "search party" with a smart, instant "GPS" for data beams.

1. Problem Statement

The paper addresses the critical challenge of beam alignment in Ultra-Massive Multiple-Input Multiple-Output (UM-MIMO) systems operating in the Terahertz (THz) frequency band.

Context: THz communications offer vast bandwidth for future 6G networks but suffer from severe propagation losses (molecular absorption and free-space path loss). To mitigate this, UM-MIMO systems use highly directional analog beamforming.
The Bottleneck: Finding the optimal transmit (Tx) and receive (Rx) beam pair (codewords) from a predefined codebook is computationally expensive.
- Exhaustive Search: Tests all possible beam pairs, resulting in complexity proportional to $N^2$ (where $N$ is the number of antennas). This is infeasible for UM-MIMO.
- Hierarchical Search: Uses a multi-stage tree search (wide to narrow beams) to reduce complexity to $O(M \log_M N)$ . However, even this remains high for extremely large antenna arrays and requires iterative feedback between Tx and Rx, increasing latency and overhead.
Goal: Develop a low-complexity beam training method that eliminates the need for continuous feedback and reduces the search space without requiring explicit Channel State Information (CSI).

2. Methodology

The authors propose a novel machine learning-based framework using a custom neural network architecture called Incept-ResNet (Inception-Residual Network).

A. System Model

Setup: Point-to-point outdoor UM-MIMO THz system with single-RF chain analog beamforming at both Tx and Rx.
Channel: Modeled as Line-of-Sight (LoS) dominant with uniform linear arrays.
Codebook: Utilizes a hierarchical binary-tree codebook (based on antenna element deactivation) where codewords are generated in layers, starting from wide beams (Layer 0) to narrow beams.

B. The Proposed Approach: Incept-ResNet

Instead of performing a multi-stage search, the neural network predicts the optimal narrow beam pair directly from power measurements of the initial, widest beams.

Data Generation (Offline Training):
- Training data is generated by simulating the system using the hierarchical codebook.
- The system performs a standard hierarchical search to find the optimal beam pair ( $w^*_T, w^*_R$ ) and the corresponding received power.
- Input Features: The network receives the received power vectors corresponding to the first layer (widest beams) of the Tx and Rx codebooks ( $p^T_1, p^T_2$ and $p^R_1, p^R_2$ ).
- Labels: The optimal codewords ( $w^*_T, w^*_R$ ) and the predicted optimal received power.
Network Architecture:
The Incept-ResNet consists of two parallel processing pipelines that fuse features:
- ConvPath: Integrates Inception modules (applying convolutions of different kernel sizes, e.g., 1x1, 1x3, 3x1, 3x3) to capture spatial features at multiple scales, combined with Residual connections to prevent vanishing gradients in deep networks.
- VecPath: Uses Fully Connected (FC) layers with Batch Normalization to process vectorized inputs.
- Bidirectional Fusion: A mechanism to combine features from the ConvPath and VecPath, enhancing the model's ability to understand the context of the beam alignment.
- Output: The network outputs the indices of the optimal Tx and Rx codewords and the predicted received power.
Inference (Online Operation):
- The Tx and Rx measure the received power using only the widest beams (Layer 0) of the codebook.
- These power measurements are fed into the trained Incept-ResNet.
- The network directly predicts the optimal narrow beam pair ( $w^*_T, w^*_R$ ) without further searching or iterative feedback.

3. Key Contributions

Novel Architecture: Introduction of the Incept-ResNet, specifically designed to map coarse power measurements from wide beams to optimal narrow beam indices.
Elimination of Feedback Overhead: Unlike traditional hierarchical search which requires iterative index exchange between Tx and Rx, the proposed method requires only a single-shot transmission of first-layer power measurements (or a compressed vector) to the transmitter.
CSI-Free Operation: The method relies solely on received signal power measurements, avoiding the complex and expensive channel estimation required for digital/hybrid beamforming in UM-MIMO.
Complexity Reduction: Shifts the computational burden from an online multi-stage search to a single forward pass of a neural network.

4. Numerical Results

The authors evaluated the method against Exhaustive Search and Conventional Hierarchical Search using simulations in PyTorch.

Complexity Comparison:
- Exhaustive Search: $O(N^2)$
- Hierarchical Search: $O(M \log_M N)$ (specifically $2M \log_M N$ for two-sided search)
- Proposed Method: $O(2M)$ (Linear with respect to the number of branches in the first layer, independent of $N$ ).
- Result: The proposed method reduces complexity from logarithmic to constant (relative to antenna count), offering massive gains for large $N$ .
Performance (Received Power):
- Simulations with $N = 64, 128, 256$ antennas showed that the Incept-ResNet achieves average received power comparable to Exhaustive Search and Hierarchical Search.
- The performance remains stable across different distances and antenna sizes.
Robustness (Gain Loss):
- The Cumulative Distribution Function (CDF) of the normalized beamforming gain loss ( $\Delta_{norm}$ ) relative to exhaustive search shows that the proposed method incurs negligible loss.
- The model demonstrates strong generalization, with a small gap between training and testing loss.

5. Significance

This paper presents a paradigm shift for THz communication systems:

Scalability: It solves the "curse of dimensionality" in UM-MIMO beam training. As antenna counts increase (e.g., to thousands), traditional search methods become impractical, whereas the neural network's inference complexity remains low.
Latency Reduction: By eliminating multi-stage feedback loops, the beam alignment time is drastically reduced, which is crucial for high-mobility THz scenarios.
Practical Deployment: The approach is hardware-friendly as it works with low-cost, single-RF chain analog beamforming, making it a realistic solution for future 6G THz devices.

In summary, the authors successfully demonstrate that a learning-based approach can replace complex iterative search algorithms, enabling efficient, low-latency, and high-performance beam alignment for the next generation of wireless networks.