⚡ electrical engineering

Low-PAPR Joint Channel Estimation and Data Detection in ZP-OTFS System

This paper proposes a two-step joint channel estimation and data detection method for Zero-Pad OTFS (ZP-OTFS) systems that strategically utilizes zero bins for pilot insertion to reduce pilot overhead and peak-to-average power ratio, achieving superior normalized mean square error and bit error rate performance compared to traditional embedded pilot schemes at high signal-to-noise ratios.

Original authors: Omid Abbassi Aghda, Mohammad Javad Omidi, Hamid Saeedi-Sourck

Published 2026-02-18

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CC BY 4.0

Original authors: Omid Abbassi Aghda, Mohammad Javad Omidi, Hamid Saeedi-Sourck

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 with a friend while riding on a very fast, bumpy train. The train represents a high-speed wireless connection (like 6G), and the bumps represent the "noise" and interference that mess up your voice.

In the world of wireless technology, there's a new way of talking called OTFS (Orthogonal Time Frequency Space). Think of OTFS as a special language designed specifically for fast-moving trains. It's great at keeping your message clear even when the train is shaking violently.

However, this new language has two big problems:

The "Pilot" Problem: To understand the train's movement, the system needs to send out "test signals" (called pilots) to check the channel. In older systems, these test signals were like shouting a single, incredibly loud scream to be heard over the noise. This was inefficient (wasting energy) and caused a "Peak-to-Average Power Ratio" (PAPR) issue—imagine your radio transmitter trying to scream so loud it almost breaks its own speakers.
The "Overhead" Problem: To make sure the test signal doesn't get mixed up with your actual conversation, you have to leave big empty gaps (guard symbols) between them. This is like having to pause your conversation for a long time just to shout a test word, which wastes a lot of time and space.

The Solution: The "ZP-OTFS" System with a Two-Step Trick

The authors of this paper propose a clever new way to fix these problems using a system called ZP-OTFS (Zero-Pad OTFS).

The Setup: The Empty Seats
Imagine the train car has rows of seats. In this new system, the last few rows of seats are left completely empty (zeroed out) by design.

Old Way: You shout your test signal in the middle of the crowd, and you need empty space around it so no one interrupts.
New Way: You have a whole row of empty seats at the back. You place your test signals there. Because the seats are empty, your test signals don't get interrupted by passengers (data) sitting in the front rows.

The Two-Step Detective Game

The paper proposes a two-step process to figure out what the train is doing and then listen to your friend clearly.

Step 1: The Quick Glance (Coarse Estimation)

The Analogy: Imagine you look at the empty back row of seats. Since no one is sitting there, you can easily see the "wind" (the channel) blowing through those specific seats.
What happens: The system looks only at the pilot signals in those empty rows. It quickly guesses what the channel looks like. It's not perfect yet, but it's a good start.
The Result: Because we used the empty seats, we didn't need to shout as loudly (lower PAPR), and we didn't need to leave as many empty gaps between conversations (lower overhead).

Step 2: The Deep Dive (Refinement)

The Analogy: Now that you have a rough idea of the wind from Step 1, you listen to the entire train car. You use your rough guess to "cancel out" the wind noise from the passengers' voices. Once the noise is gone, you can hear the passengers much more clearly.
What happens: The system takes the rough guess from Step 1, uses it to clean up the signal, and then looks at everything (both the empty seats and the occupied seats) to get a super-accurate picture of the channel.
The Result: This second look is so accurate that the system can now use a very simple, fast, and efficient way to decode the message (called the MRC detector).

Why is this a Big Deal?

It's Quieter (Low PAPR): Instead of one loud scream, the test signals are spread out like a gentle whisper across the empty seats. This saves power and protects the equipment.
It's Faster (Low Overhead): Because the test signals fit neatly into the "empty seats," we don't need to waste as much space with guard gaps. We can fit more actual conversation in the same amount of time.
It's Smarter (Better Accuracy): By using a "two-step" approach (guess, then refine), the system gets a clearer picture of the channel than older methods, especially when the signal is strong.

In a Nutshell:
The authors figured out how to turn the "wasted space" in a high-speed communication system into a useful tool. By filling the empty seats with smart test signals and using a two-step detective process, they made the system faster, more efficient, and less likely to break its own equipment, all while keeping the conversation crystal clear on a bumpy train ride.

1. Problem Statement

Orthogonal Time Frequency Space (OTFS) modulation is a promising technology for 6G high-mobility communications, as it maps information to the Delay-Doppler (DD) domain to combat high Doppler shifts. However, OTFS systems face two critical challenges:

Channel Estimation Overhead and PAPR: Accurate Channel State Information (CSI) is vital for detection. Traditional Embedded Pilot (EP) methods suffer from high Peak-to-Average Power Ratio (PAPR) due to high-power pilot impulses and high pilot overhead caused by the need for guard symbols to separate pilots from data.
Detection Complexity: Optimal detection methods (e.g., MMSE, Zero-Forcing) are computationally prohibitive. While Message Passing (MP) and Linear MMSE (LMMSE) reduce complexity, they remain demanding.
The ZP-OTFS Trade-off: Zero-Pad OTFS (ZP-OTFS) enables the use of a low-complexity Maximal Ratio Combining (MRC) detector by setting specific delay-axis rows to zero. However, this introduces significant system overhead and traditionally requires complex pilot designs that exacerbate PAPR issues.

2. Methodology

The authors propose a two-step joint channel estimation and data detection scheme specifically designed for ZP-OTFS systems. The core innovation lies in a novel pilot design that utilizes the "zero" bins of the ZP-OTFS structure.

A. System Design & Pilot Insertion

ZP-OTFS Structure: The system sets $l_{ZP}$ rows along the delay axis to zero, where $l_{ZP} = l_{max} + 1$ (based on the maximum channel delay spread).
Pilot Placement: Instead of placing pilots in data bins (which causes interference) or using high-power impulses, the authors insert Zadoff-Chu pilot sequences into the $l_{ZP}$ zero rows of the DD domain.
Time-Domain Transformation: Due to the Inverse Discrete Fourier Transform (IDFT) applied along the Doppler axis, these zero rows in the DD domain translate to the last $l_{ZP}$ samples of every OTFS sub-symbol in the time domain.
Result: This arrangement ensures that specific time-domain samples are free from data interference, allowing for initial channel estimation without guard symbols.

B. Two-Step Algorithm

The process operates in the Time Domain, avoiding the computational cost of transforming received signals back to the DD domain for estimation.

Step 1: Preliminary Estimation & Data Detection
- Channel Estimation: The receiver extracts the last $l_{ZP}$ samples of each sub-symbol (which contain only pilot sequences, free of data interference).
- Sparse Recovery: The Orthogonal Matching Pursuit (OMP) algorithm is applied to these time-domain samples to estimate the channel vector $\hat{h}$ . This leverages the sparsity of the DD channel.
- Interference Cancellation: The estimated channel effect of the pilots is subtracted from the received signal.
- Data Detection: The MRC detector is applied to the remaining signal to detect information symbols.
Step 2: Refined Estimation & Final Detection
- Joint Pilot Construction: The detected data symbols from Step 1 (treated as known pilots) are combined with the original pilot sequences to form a "joint pilot" matrix.
- Refined Estimation: The OMP algorithm is run again on the entire received signal (including data-interfered parts) using this joint pilot matrix to refine the channel estimate ( $\hat{h}$ ).
- Final Detection: The MRC detector is applied again using the refined channel estimate to achieve lower Bit Error Rates (BER).

3. Key Contributions

Low-PAPR Pilot Design: By spreading pilot sequences across the zero-bins (Zadoff-Chu sequences) rather than using a single high-power impulse, the method maintains a low and constant PAPR regardless of the number of subcarriers.
Reduced Overhead: The method eliminates the need for guard symbols between pilots and data. The overhead is strictly limited to the zero-padding rows ( $l_{max} + 1$ ), which is significantly lower than EP and Pilot with Cyclic Prefix (PCP) schemes.
Time-Domain Estimation: The algorithm estimates CSI directly from time-domain samples, eliminating the need for computationally expensive transformations to the DD domain for channel estimation.
Compatibility with Low-Complexity Detection: The design enables the use of the MRC detector, which offers significantly lower computational complexity compared to MP or LMMSE detectors while improving SNR.
No Prior Knowledge Required: Unlike some superimposed pilot methods, this approach does not assume prior knowledge of delay/Doppler taps or the CSI covariance matrix at the receiver.

4. Simulation Results

The authors evaluated the system using the EVA channel model with $M=N=64$ and 4-QAM modulation.

Channel Estimation Accuracy (NMSE):
- At low SNR, the first step performs slightly worse than the EP scheme due to estimation errors.
- At high SNR (>11 dB), the second step outperforms the EP scheme, achieving lower Normalized Mean Square Error (NMSE).
Bit Error Rate (BER):
- The second step achieves BER performance comparable to the EP scheme and systems with Known CSI.
- The crossover point where the proposed method surpasses EP occurs around 11 dB SNR.
PAPR Performance:
- The proposed method exhibits significantly lower PAPR than the EP scheme.
- Unlike EP, where PAPR increases with system size ( $M, N$ ), the proposed method's PAPR remains low and stable.
- It achieves PAPR levels similar to the PCP method but with much lower overhead.
Overhead Efficiency:
- The number of pilot overhead bins is substantially lower than both EP and PCP schemes, particularly as the Doppler dimension ( $N$ ) increases.

5. Significance

This paper presents a practical solution to the "trilemma" of OTFS implementation: Overhead, PAPR, and Complexity.

It enables the use of the highly efficient MRC detector without the traditional penalty of high system overhead.
It solves the PAPR issue inherent in sparse pilot designs for OTFS, making the system more suitable for power-constrained hardware.
By performing estimation in the time domain using sparse recovery, it offers a computationally efficient path for 6G receivers to handle high-mobility channels with high spectral efficiency.

In conclusion, the proposed two-step joint estimation and detection method offers a superior trade-off for ZP-OTFS systems, delivering high accuracy and low complexity while maintaining low PAPR and minimal pilot overhead.