⚡ electrical engineering

LSTM-Based Power Delay Profile Predictions for Intra-Bus Wireless Propagation

This paper proposes a simple Long Short-Term Memory (LSTM) model to predict the channel transfer function for 60 GHz intra-bus wireless propagation, achieving a power delay profile prediction error of less than 10% compared to ground truth.

Original authors: Rajeev Shukla, Atharva Verma, Aniruddha Chandra, Ondrej Zeleny, Radek Zavorka, Jiri Blumenstein, Ales Prokes, Jaroslaw Wojtun, Jan M. Kelner, Cezary Ziolkowski, Domenico Ciuonzo

Published 2026-03-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Rajeev Shukla, Atharva Verma, Aniruddha Chandra, Ondrej Zeleny, Radek Zavorka, Jiri Blumenstein, Ales Prokes, Jaroslaw Wojtun, Jan M. Kelner, Cezary Ziolkowski, Domenico Ciuonzo

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 you are trying to have a conversation inside a crowded, metal bus. The walls are shiny, the seats are cluttered, and the air is full of echoes. If you shout a message, it bounces off the metal ceiling, the windows, and the passengers before reaching the person across the aisle. Sometimes the message arrives clearly; other times, it gets garbled by the echoes.

In the world of wireless technology (like your phone or Wi-Fi), this is called a wireless channel. Engineers need to understand exactly how these "echoes" behave to make sure your data gets through without errors.

This paper is about teaching a computer to predict how these signals will behave inside a bus, specifically using high-speed 60 GHz internet (the kind used for super-fast connections).

Here is the breakdown of what the researchers did, using some everyday analogies:

1. The Problem: The Bus is a "Hall of Mirrors"

Inside a bus, the metal surfaces act like a hall of mirrors for radio waves. When a signal is sent, it doesn't just travel in a straight line; it splits into dozens of tiny paths, hitting different things and arriving at slightly different times. This is called multipath.

The Old Way: Traditionally, engineers tried to map this out using math formulas or by physically measuring the bus over and over again. But the bus changes! If a passenger stands up, sits down, or walks by, the "echoes" change instantly. Old math models are like a static map of a city that doesn't account for traffic jams or road closures—they can't adapt fast enough.
The Goal: The researchers wanted a system that could look at a few measurements and then guess what the signal would look like at a spot they hadn't measured yet.

2. The Solution: The "Super-Student" (LSTM)

To solve this, the team used a type of Artificial Intelligence called LSTM (Long Short-Term Memory).

The Analogy: Think of an LSTM not as a calculator, but as a super-observant student.
- If you show this student a few pages of a story (the signal measurements at certain distances), they don't just memorize the words. They learn the pattern of the story.
- Once they understand the pattern, you can ask them, "What happens in the next chapter?" or "What would happen if the main character was standing in a different seat?"
- Because LSTMs are designed to remember sequences (like a sentence or a melody), they are perfect for tracking how a radio signal changes as it bounces around over time and distance.

3. How They Trained the Student

The researchers went to a bus in Brno, Czech Republic, and set up a "test track."

They placed a transmitter (the shout) and a receiver (the listener) at various distances (from 1 meter to almost 10 meters).
They recorded how the signal behaved at the 60 GHz frequency band (which is great for speed but struggles to go through walls).
They fed this data into the LSTM "student." They taught it: "When the distance is X and the frequency is Y, the signal looks like Z."

4. The Magic Trick: Predicting the Unseen

Once the student was trained, they tested it on distances they had never shown it before (like 3.7 meters and 9.75 meters).

The Result: The AI didn't just guess randomly. It successfully predicted the "Power Delay Profile" (PDP).
- What is PDP? Imagine a graph showing how loud the echoes are and when they arrive. The AI drew a curve that looked almost exactly like the real measurements.
- The Accuracy: The AI's prediction was off by less than 10%. That's like guessing the weight of a person within a few pounds just by looking at their height and build.

5. Why This Matters

The researchers checked if this prediction was good enough to actually send data. They simulated sending digital messages (calculating the Bit Error Rate, or BER).

The Finding: The AI-predicted model worked almost as well as the real, physical measurements.
The Benefit: This means that in the future, we might not need to physically measure every single bus, train, or car to design its Wi-Fi. We can just feed the AI a few data points, and it can imagine the rest.

The Bottom Line

This paper is about teaching a computer to be a crystal ball for radio waves inside a bus.

Instead of needing a massive team of engineers with expensive equipment to measure every inch of a vehicle, we can use a smart algorithm (LSTM) to learn the "rules of the road" for radio signals. Once it learns the rules, it can predict how the signal will behave anywhere inside the bus, helping us build faster, more reliable 60 GHz internet for our future autonomous vehicles and public transport.

In short: They taught a computer to listen to the echoes in a bus, learn the pattern, and then accurately predict what the echoes would sound like in a spot it had never visited before.

1. Problem Statement

The paper addresses the challenges of characterizing wireless channels within complex, cluttered environments, specifically inside public transport vehicles like buses.

Environmental Complexity: Buses contain highly reflective metal surfaces and a cluttered physical environment, leading to significant multipath effects, signal fading, and delay spread.
Limitations of Existing Models: Traditional empirical and deterministic models (e.g., ray-tracing) often fail to capture the dynamic nature of these channels. They struggle to generalize across different transmitter-receiver (TX-RX) distances and cannot easily adapt to physical changes or interpolate/extrapolate beyond measured datasets.
The 60 GHz Challenge: While the 60 GHz millimeter-wave (mmWave) band (55–65 GHz) offers high bandwidth and is ideal for in-vehicle connectivity (due to limited penetration preventing external interference), its propagation is highly dispersive and frequency-dependent, making accurate modeling difficult with standard analytical methods.

2. Methodology

The authors propose a Deep Learning approach using Long Short-Term Memory (LSTM) networks to predict the Channel Transfer Function (CTF) and subsequently the Power Delay Profile (PDP) for intra-bus scenarios.

Data Source: The model utilizes measurement data collected during a campaign at Brno University of Technology, Czech Republic, covering the 55–65 GHz frequency band.
Input Parameters: The LSTM model is designed with a simplified input structure using only two physical parameters:
1. Frequency: 55–65 GHz with a 10 MHz step size (sequential data).
2. Distance: Various TX-RX distances ranging from 1.18m to 9.72m.
Model Architecture:
- Structure: A 2-layer LSTM network followed by a dense output layer.
- Configuration:
  - Layer 1: 100 LSTM cells (returns sequences).
  - Layer 2: 9 LSTM cells (returns single output per cell).
  - Output: Dense layer with 1 unit.
- Training: Uses the Adam optimizer with Mean Squared Error (MSE) loss.
- Hyperparameter Tuning: An exhaustive search (Algorithm 1) was conducted to optimize the number of neurons in both layers (tested 20–100 for layer 1, 2–9 for layer 2) and the number of epochs. The optimal configuration selected was 100/9 neurons with 94 epochs and a batch size of 20.
Validation Strategy: The model was trained on a specific dataset and tested on unseen TX-RX distances (3.7m and 9.75m) to evaluate its ability to interpolate and extrapolate channel characteristics for new locations.

3. Key Contributions

Novel Application: This is one of the first studies to apply LSTM models specifically for predicting CTFs and PDPs in the 60 GHz mmWave band within a bus environment.
Simplified Input: Unlike complex models requiring extensive environmental mapping, this approach uses only frequency and distance as inputs, demonstrating that deep learning can learn complex propagation patterns from minimal physical parameters.
Generalization Capability: The study successfully demonstrates that the LSTM model can predict channel behavior for TX-RX pairs that were not present in the training data, effectively bridging gaps in measurement coverage.
Comprehensive Evaluation: The paper validates the model not just on raw CTFs, but through a full chain of analysis: CTF $\rightarrow$ Channel Impulse Response (CIR) $\rightarrow$ Power Delay Profile (PDP) $\rightarrow$ Tapped Delay Line (TDL) model $\rightarrow$ Bit Error Rate (BER).

4. Results

The performance of the LSTM model was evaluated against ground truth measurement data:

CTF Prediction: The model successfully captured the general trend of the measured CTFs, particularly in lower frequency regions. It effectively smoothed out high-frequency fluctuations caused by small-scale fading and measurement noise while preserving the overall multipath decay behavior.
PDP Accuracy: The predicted PDPs retained the power distribution trends of the measured data.
Error Metrics:
- The average error of the derived PDP taps compared to the ground truth was less than 10%.
- RMSE Analysis (Table I):
  - At 3.7m: RMSE between measured and predicted was 7.96 ( $R^2$ = 0.47).
  - At 9.75m: RMSE between measured and predicted was 3.04 ( $R^2$ = 0.78).
- The model performed better at longer distances (9.75m) in terms of RMSE, likely due to the averaging effect over more multipath components.
BER Performance: The Bit Error Rate (BER) calculated using the LSTM-predicted TDL model closely matched the measured BER for shorter distances. At longer distances, the model showed slightly higher deviations due to severe fading and deep fades, but the overall trend remained consistent.

5. Significance and Conclusion

Practical Utility: The proposed LSTM model offers a dynamic, AI-driven alternative to static empirical models. It is particularly valuable for scenarios where measurement equipment is unavailable or when rapid channel modeling is needed for new vehicle layouts.
Interpolation/Extrapolation: The study proves that deep learning can generalize channel characteristics to unmeasured TX-RX locations, which is critical for the deployment of autonomous vehicles and intelligent transportation systems (ITS).
Future Outlook: While the model performs well, the authors note that performance degrades in severe fading conditions. They suggest that incorporating more training datasets and additional features could further enhance accuracy.
Overall Impact: This work validates the use of simple, sequential deep learning models to solve complex wireless propagation problems in the 60 GHz band, paving the way for more robust and adaptive in-vehicle communication systems.