⚡ electrical engineering

Optimized Non-Uniform Pilot Pattern for OFDM Sensing

This paper proposes a two-stage framework utilizing a low-complexity hybrid greedy-stochastic cyclic coordinate descent algorithm to design optimized non-uniform pilot patterns for OFDM systems, effectively suppressing delay-domain grating lobes to enhance radar sensing performance without compromising communication reliability.

Original authors: Amir Bouziane, Huseyin Arslan

Published 2026-03-30

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CC0 1.0

Original authors: Amir Bouziane, Huseyin Arslan

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ 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 do two things at once with a single flashlight: talk to a friend across a dark room and detect how far away a wall is by seeing where the light bounces back.

In the world of wireless technology (like 5G and the upcoming 6G), this is exactly what a system called ISAC (Integrated Sensing and Communication) tries to do. It uses the same radio waves to send data (like your text messages) and to act like a radar (to sense cars, people, or obstacles).

The paper you shared tackles a major problem with how we currently design these "flashlights" (specifically, OFDM systems used in Wi-Fi and 5G). Here is the breakdown in simple terms:

1. The Problem: The "Ghost" in the Machine

Currently, these systems use a periodic pilot pattern. Think of this like a lighthouse that flashes its beam at perfectly regular intervals (e.g., every 10 seconds).

For Communication: This is great! It helps the receiver figure out the channel easily.
For Sensing (Radar): This is a disaster. Because the flashes are so regular, the radar gets confused. It sees the real wall, but it also sees "ghost walls" (called grating lobes) appearing at regular intervals. It's like looking in a mirror that creates infinite reflections; you can't tell which one is the real object.

2. The Goal: Break the Pattern

The authors want to change the flashing pattern so it's non-uniform (irregular).

The Catch: You can't just make it random. If you scatter the flashes too wildly, the "friend" (the communication receiver) can't understand the message because they rely on some predictable spots to calibrate the signal.
The Constraint: You must keep a few "anchor" flashes in specific, fixed spots to ensure communication works, but you can move the rest of the flashes around to break the rhythm and kill the ghosts.

3. The Solution: A Two-Step Dance

The paper proposes a clever two-step algorithm to find the perfect irregular pattern:

Step 1: The "Greedy" Builder (Constructive Phase)
Imagine you are placing tiles on a floor. You start by placing your mandatory "anchor" tiles (for communication). Then, you greedily add the remaining tiles one by one, always picking the spot that looks best right now to minimize the "ghosts."
- The Flaw: This is like walking down a hill looking for the lowest point. You might get stuck in a small dip (a local minimum) thinking it's the bottom, when there's actually a much deeper valley nearby. You get stuck because you never look back at your earlier choices.
Step 2: The "Stochastic" Dancer (Refinement Phase)
This is the magic sauce. Once the greedy builder is done, the algorithm starts "dancing." It randomly picks a tile, moves it to a new spot, and checks: "Did this make the ghosts disappear?"
- If yes, it keeps the move.
- If no, it puts it back.
- It repeats this thousands of times. This allows the system to "jump out" of the small dips the greedy builder got stuck in and find the true, deepest valley (the optimal pattern).

4. The Result: Best of Both Worlds

The authors tested this with a computer simulation (using 512 sub-channels, like 512 lanes on a highway).

The Old Way (Uniform/Periodic): The radar performance hit a "ceiling." No matter how much power you added, the "ghosts" got louder, and the distance measurement error (RMSE) stopped improving.
The New Way (Hybrid): By breaking the pattern, the "ghosts" were pushed down so low that they became invisible compared to the natural background noise.
- Radar: The distance measurement became incredibly accurate, with no "ghost" interference.
- Communication: Because they kept the "anchor" tiles fixed, the text messages were received perfectly, with zero loss in quality.

The Big Picture Analogy

Imagine a choir singing a song.

Old Method: Everyone sings the exact same note at the exact same time, perfectly in sync. It's loud, but if you try to listen for a specific echo in a canyon, the perfect harmony creates confusing echoes that drown out the real sound.
New Method: The conductor tells a few singers (the anchors) to stay on beat so the audience can follow the rhythm (communication). But the rest of the choir sings in a slightly irregular, "jittery" rhythm. This irregularity breaks up the confusing echoes, allowing the radar to hear the true sound of the canyon, while the audience still hears a clear song.

In summary: This paper invented a smart, two-step math trick to rearrange radio signals. It kills the "ghost targets" that confuse radar systems, all while keeping the internet connection fast and reliable. It's a win-win for 6G.

1. Problem Statement

The paper addresses a fundamental conflict in Integrated Sensing and Communication (ISAC) systems using Orthogonal Frequency Division Multiplexing (OFDM):

The Sensing Issue: Standard OFDM systems use periodic pilot patterns for channel estimation. In the context of radar sensing, these periodic tones create a frequency-domain "comb" structure. When transformed to the delay domain, this results in strong, regularly spaced grating lobes (ghost targets). These lobes mask weaker reflections, severely degrading range resolution and causing range Root Mean Square Error (RMSE) to saturate at high Signal-to-Noise Ratios (SNR).
The Communication Constraint: Simply randomizing pilot locations to suppress grating lobes often leads to pilot clustering. This violates the Nyquist sampling criterion in the frequency domain, causing the communication receiver to fail at estimating frequency-selective channels, which leads to high Bit Error Rates (BER).
The Challenge: Designing a pilot pattern that minimizes radar sidelobes (grating lobes) while strictly adhering to communication constraints (ensuring sufficient pilot density for channel estimation) is a combinatorial NP-hard problem.

2. Methodology

The authors propose a two-stage hybrid optimization framework to design non-uniform pilot patterns.

A. Theoretical Foundation: Difference Set Representation

The paper establishes that the delay-domain Ambiguity Function (AF), which determines grating lobes, is the Discrete Fourier Transform (DFT) of the cyclic difference multiplicities ( $\lambda(d)$ ) between active pilot tones.

High sidelobes occur when specific cyclic differences between pilot indices are over-represented (constructive interference).
The goal is to distribute these differences as uniformly as possible to flatten the sidelobe profile.

B. The Hybrid Optimization Algorithm (SCCD)

The proposed solution combines a constructive greedy approach with a stochastic refinement step:

Stage 1: Constructive Sidelobe Minimization (CSM) with Anchors:
- Anchor Constraint: A fixed subset of pilots ( $N_{anc}$ ) is scattered across the frequency grid to guarantee wideband channel estimation coverage (satisfying the Nyquist criterion for communication).
- Greedy Selection: The remaining pilots are added iteratively. At each step, the algorithm selects the pilot location that minimizes the Peak Sidelobe Level (PSL) given the current set.
- Limitation: This greedy approach is prone to getting stuck in local minima, especially under strict anchor constraints.
Stage 2: Stochastic Cyclic Coordinate Descent (SCCD):
- To escape local minima, the algorithm performs a stochastic search.
- It randomly selects a pilot from the current set and attempts to swap it with a candidate from the unselected set.
- If the swap reduces the PSL, the change is accepted. This process repeats until convergence.
- This "shatters" the cyclic periodicities that cause deterministic grating lobes.

C. System Model & Metrics

Sensing Model: Monostatic radar using OFDM. The objective is to suppress the deterministic pilot component ( $\Psi_{pp}$ ) of the ambiguity function below the Data-to-Pilot Interference (DPI) noise floor created by the random communication data.
Communication Model: Frequency-selective multipath channel. Performance is measured by BER.
Key Metric: Peak Sidelobe Level (PSL) and Range RMSE.

3. Key Contributions

Mathematical Link: The authors formally link cyclic difference multiplicities to the ambiguity function, providing a mathematical explanation for why periodic pilots cause grating lobes and how non-uniform distributions suppress them.
DPI Noise Floor Integration: The work updates the ISAC model to acknowledge that perfect zero-sidelobe performance is impossible due to the stochastic noise floor generated by communication data. The design goal is shifted to suppressing deterministic lobes beneath this floor.
Hybrid Algorithm: Development of a low-complexity Hybrid Greedy-SCCD algorithm that optimizes discrete pilot placement while strictly enforcing communication anchor constraints.
Trade-off Resolution: Demonstration of a method that improves sensing performance without degrading communication reliability.

4. Results

The framework was validated using an OFDM system with $N=512$ subcarriers, 16-QAM modulation, and various pilot densities ( $K=32, 64, 128$ ).

PSL Suppression: The Hybrid algorithm achieved theoretical PSL suppression gains exceeding 5 dB compared to standard periodic patterns, particularly in sparse pilot configurations.
Range RMSE:
- Standard Periodic Patterns: Showed a "saturation floor" in RMSE at high SNR. Even with more power, ghost targets (grating lobes) prevented further improvement.
- Proposed Hybrid Method: Achieved a monotonically decreasing RMSE curve. By suppressing grating lobes below the DPI noise floor, the system became noise-limited rather than interference-limited, allowing performance to scale with SNR.
Communication BER:
- Crucially, the proposed method maintained a BER curve identical to the standard periodic baseline.
- By enforcing the anchor constraints ( $N_{anc}$ ), the algorithm ensured the channel was sampled sufficiently, proving that sensing enhancement can be decoupled from communication reliability.

5. Significance

This paper provides a practical pathway for 6G ISAC systems to utilize standard OFDM waveforms for high-resolution radar sensing without requiring changes to modulation formats or receiver hardware.

Compatibility: It works within existing 3GPP numerologies and constraints.
Efficiency: It solves a combinatorial NP-hard problem with a low-complexity algorithm suitable for implementation.
Paradigm Shift: It moves the design philosophy from "perfect sequences" (which are often impossible in constrained grids) to "optimal non-uniform patterns" that leverage the inherent noise floor of data transmission to mask residual sensing artifacts.

In summary, the authors successfully demonstrated that by intelligently redistributing pilot tones, one can eliminate the "ghost targets" of OFDM radar while maintaining the integrity of the communication link, effectively resolving the sensing-communication trade-off.