⚡ electrical engineering

Comparison of OTFS and OFDM for RIS-aided Systems in the Presence of Phase Noise

This paper proposes a joint RIS channel and phase noise estimation technique using Wiener filtering to demonstrate that RIS-aided OTFS systems significantly outperform RIS-aided OFDM systems in the presence of oscillator phase noise, achieving up to 3 dB improvement in bit error rate.

Original authors: Stephen McWade, Arman Farhang

Published 2026-02-16

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Stephen McWade, Arman Farhang

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: A High-Speed Mirror Party

Imagine you are trying to send a secret message to a friend across a crowded, noisy room. You can't shout directly because there are walls in the way. So, you use a Reconfigurable Intelligent Surface (RIS). Think of the RIS as a giant wall made of thousands of tiny, smart mirrors. These mirrors can tilt and twist to bounce your signal perfectly to your friend, bypassing the walls and making the connection super strong.

However, there's a problem: the equipment generating the signal (the transmitter) and the equipment listening (the receiver) aren't perfect. They have a slight "wobble" in their timing, known as Phase Noise.

The Analogy: Imagine trying to sing a perfect note while standing on a shaky boat. Even if you know the right note, the boat's rocking makes your voice waver. In wireless terms, this "wobble" scrambles the signal, turning your clear message into static.

This paper asks a simple question: Which way of sending the message handles this "shaky boat" problem better?

OFDM: The current standard (used in 4G and 5G).
OTFS: A new, futuristic waveform designed for high-speed, chaotic environments.

The Two Messengers: OFDM vs. OTFS

1. OFDM: The Stacked Dominoes

How it works: OFDM sends data like a row of dominoes standing side-by-side. Each domino represents a specific frequency. They are packed very tightly together to be efficient.
The Problem: Because the dominoes are so close, if the "shaky boat" (phase noise) wobbles even a little, the dominoes start knocking into each other. This is called Inter-Carrier Interference. The signal gets messy, and the message is lost.
The Paper's Finding: When you add the RIS (the mirror wall) to this shaky setup, the problem gets worse. The mirrors amplify the signal, but they also amplify the chaos caused by the wobble.

2. OTFS: The Spreading Net

How it works: OTFS is different. Instead of sending data in a tight row, it spreads the message out over time and frequency, like casting a wide fishing net. It sends the data in a grid pattern that is very robust against movement and changes.
The Advantage: Because the message is spread out, a little wobble (phase noise) doesn't knock the whole thing over. It's like if one domino falls in the net, the rest of the net holds the message together.
The Paper's Finding: OTFS is naturally much better at handling the "shaky boat" than OFDM.

The Missing Piece: The "Smart Filter"

The authors realized that while OTFS is better, it still needs help. You can't just assume the receiver knows exactly how the signal is wobbling.

The Problem: Existing methods tried to guess the wobble using old tricks (like drawing a smooth line through a few points, called "Spline" or "Basis Expansion"). But phase noise is wild and unpredictable; it's like trying to predict the exact path of a drunk person walking through a crowd. The old methods failed when the wobble got severe.

The Solution: The authors proposed a Joint Estimation Technique using Wiener Filtering.

The Analogy: Imagine you are trying to track a friend running through a foggy park. You know two things:
1. How fast they usually run (the Doppler spread).
2. How the fog usually moves (the statistical nature of phase noise).
Instead of just guessing where they are based on the last time you saw them, you use a "smart filter" that combines your knowledge of their running style and the fog's behavior to predict exactly where they are right now, even if you can't see them clearly.

This technique estimates both the channel (the path the signal takes) and the phase noise (the wobble) at the same time, sample-by-sample, to clean up the signal before decoding it.

The Results: Who Won the Race?

The authors ran thousands of computer simulations to see how this played out. Here is what they found:

OTFS vs. OFDM: In the presence of phase noise, OTFS crushed OFDM.
- The Result: OTFS was up to 100 times (two orders of magnitude) better at getting the message through without errors. It's like comparing a tank driving through a storm to a bicycle; the tank (OTFS) keeps going, while the bike (OFDM) falls over.
The New Filter vs. Old Methods: Their new "Smart Filter" (Wiener approach) was also the winner.
- The Result: It improved the error rate by about 3 dB compared to existing methods. In the world of wireless, a 3 dB gain is huge—it basically means you can double your data speed or double your range without losing quality.

The Takeaway

This paper proves that if we want to use the amazing "smart mirror" technology (RIS) in a real-world environment where equipment isn't perfect (has phase noise), we shouldn't stick with the old standard (OFDM).

Instead, we should switch to OTFS, a more robust waveform, and use this new Smart Filter to clean up the signal. This combination ensures that even with shaky hardware and moving targets, our wireless connections stay fast, clear, and reliable.

1. Problem Statement

The paper addresses a critical gap in the literature regarding Reconfigurable Intelligent Surface (RIS) aided wireless communication systems operating in the presence of oscillator phase noise (PN).

The Context: RIS technology promises significant gains in coverage and spectral efficiency. However, practical RIS systems suffer from RF impairments, specifically phase noise generated by local oscillators at the transmitter and receiver.
The Limitation of OFDM: Orthogonal Frequency Division Multiplexing (OFDM), the standard for current RIS systems, is highly sensitive to phase noise. This sensitivity causes Inter-Carrier Interference (ICI), leading to severe Bit Error Rate (BER) degradation, potentially negating the benefits of RIS.
The Potential of OTFS: Orthogonal Time Frequency Space (OTFS) modulation operates in the delay-Doppler domain and is known for robustness against time-varying channels. While phase noise introduces linear time-variant (LTV) behavior (similar to Doppler spread), existing literature has not fully analyzed the impact of phase noise on OTFS, nor has it proposed estimation techniques for RIS-aided OTFS systems under these conditions.
The Gap: Existing works either assume ideal hardware, assume perfect knowledge of phase noise at the receiver, or fail to consider the specific interaction between RIS, OTFS, and phase noise.

2. Methodology

The authors propose a comprehensive framework involving system modeling, a novel estimation technique, and rigorous numerical analysis.

A. System Modeling

The paper models a generic RIS-aided system where the direct line-of-sight path is blocked. The signal propagates from the transmitter to the RIS, reflects, and travels to the receiver.

Phase Noise Modeling: The system assumes phase noise occurs at the receiver (equivalent to combined Tx/Rx noise). The continuous-time phase noise $\theta(t)$ is modeled as a time-varying process.
Discrete Representation: The received signal is modeled in the delay-time domain, incorporating the RIS reflection coefficients, the cascaded channel (Tx-to-RIS and RIS-to-Rx), and a diagonal phase noise matrix $\Phi_{DT}$ .
Waveform Comparison:
- OTFS: Signals are modulated in the delay-Doppler domain and transformed to time-domain via Inverse Discrete Fourier Transform (IDFT). The phase noise matrix in the delay-Doppler domain ( $\Phi_{DD}$ ) exhibits a block-circulant structure.
- OFDM: Signals are modulated in the frequency domain. The phase noise matrix ( $\Phi_{tf}$ ) is derived similarly but affects the subcarriers differently, causing ICI.

B. Proposed Estimation Technique

The core contribution is a joint RIS channel and phase noise estimation technique using Wiener filtering. The technique operates in two stages:

Stage 1: Partial Channel Estimation (Impulse Pilots):
- Uses known impulse pilot patterns in the delay-time domain (specific to OTFS and OFDM structures).
- Estimates the channel impulse response only at the pilot indices using a threshold-based method.
- Limitation: This leaves gaps in the channel estimate between pilot samples due to the rapid variations caused by phase noise and Doppler spread.
Stage 2: Full Channel Estimation (Wiener Filtering):
- A Wiener filter is designed to interpolate the missing channel samples between pilots.
- Statistical Exploitation: The filter weights are derived based on the statistical properties of two independent processes:
  - Doppler Spread: Modeled using the Jakes model (autocorrelation via Bessel functions).
  - Phase Noise: Modeled as either a Wiener process (for free-running oscillators) or an Ornstein-Uhlenbeck process (for Phase-Locked Loop oscillators).
- The filter minimizes the Mean Squared Error (MSE) between the estimated and actual effective channel.
- Key Advantage: The computation of the filter matrix is performed offline based on statistics and does not scale with the number of RIS elements, making it computationally efficient.

3. Key Contributions

First Analysis of RIS-OTFS under Phase Noise: The paper is the first to analyze the specific effects of phase noise on RIS-aided OTFS systems, highlighting that while OTFS is more robust than OFDM, it is not immune to severe phase noise.
Novel Joint Estimation Algorithm: Proposes a Wiener-filter-based technique that jointly estimates the effective channel (including RIS coefficients, Doppler, and phase noise) without requiring excessive pilot overhead.
Statistical Modeling of Phase Noise: Explicitly derives the autocorrelation matrices for phase noise under two common oscillator types (Free-Running and PLL), allowing for more realistic system modeling.
Comprehensive Performance Comparison: Provides a side-by-side comparison of OTFS and OFDM in RIS scenarios under varying phase noise levels, Doppler spreads, and RIS element counts.

4. Numerical Results

The authors conducted Monte Carlo simulations (averaged over $10^5$ channel instances) using 5G NR TDL-C channel models, 5.9 GHz carrier frequency, and various modulation schemes (4-QAM, 16-QAM).

Estimation Accuracy (NMSE):
- The proposed Wiener filtering technique significantly outperforms existing methods (Basis Expansion Model - BEM and Spline interpolation).
- As phase noise bandwidth increases, BEM performance degrades severely because it cannot capture the sample-to-sample variations of phase noise. The proposed method maintains low Normalized Mean Squared Error (NMSE).
BER Performance (OTFS vs. OFDM):
- Low/Moderate Phase Noise: OTFS significantly outperforms OFDM.
- High Phase Noise: Both systems degrade, but OTFS maintains a distinct advantage.
- RIS Scaling: As the number of RIS elements increases (up to 100), RIS-OTFS provides two orders of magnitude improvement in BER compared to RIS-OFDM.
Gain of Proposed Estimation:
- The proposed estimation technique yields BER gains of up to 3 dB compared to BEM and Spline methods.
- In coded systems (16-QAM with convolutional coding), RIS-OTFS with the proposed method offers an order-of-magnitude improvement over RIS-OFDM.

5. Significance and Conclusion

Validation of OTFS for RIS: The paper confirms that OTFS is a superior waveform for RIS-aided systems in high-mobility or hardware-impaired environments where phase noise is present.
Practical Implementation: The proposed estimation technique bridges the gap between theoretical RIS gains and practical hardware limitations. By effectively mitigating phase noise without increasing pilot overhead, it makes RIS-OTFS systems more viable for real-world deployment.
Future Direction: The work establishes a foundation for designing robust RIS systems that can operate with imperfect hardware, suggesting that future 6G networks may need to adopt OTFS and advanced statistical estimation techniques to fully leverage RIS potential.

In summary, the paper demonstrates that while phase noise is a significant challenge for RIS systems, the combination of OTFS modulation and a statistically-driven Wiener filtering estimation technique can overcome these limitations, offering substantial performance gains over traditional OFDM approaches.