⚡ electrical engineering

Amalgamated CHIRP and OFDM for ISAC

This paper proposes a novel ISAC waveform that affinely combines OFDM and chirp signals to simultaneously reduce PAPR, enhance sensing accuracy without sacrificing communication resources, and improve overall range and velocity estimation performance.

Original authors: Pankaj Kumar, Mohammed El-Hajjar, Ibrahim A. Hemadeh, Yasser Mestrah, Suraj Srivastava, Aditya K. Jagannatham, Lajos Hanzo

Published 2026-01-23

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Pankaj Kumar, Mohammed El-Hajjar, Ibrahim A. Hemadeh, Yasser Mestrah, Suraj Srivastava, Aditya K. Jagannatham, Lajos Hanzo

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 send a secret message to a friend while simultaneously using a flashlight to scan the room for obstacles. Traditionally, you would need two separate tools: a radio for the message and a radar for the scanning. This takes up extra space, uses more battery, and requires two different sets of equipment.

This paper proposes a clever new way to do both things at once using a single "super-signal." The authors call this new signal AAC-OFDM.

Here is a breakdown of how it works, using simple analogies:

1. The Problem: The "Traffic Jam" of Signals

In modern wireless systems (like 5G), we use a technology called OFDM to send data. Think of OFDM like a busy highway with many lanes (subcarriers) carrying cars (data). It's great for moving lots of information quickly. However, if you try to use this same highway to "see" objects (sensing/radar), it's not very good at it. It's like trying to spot a deer in the woods by looking at a highway; the signal is too messy, and you can't tell exactly how far away things are or how fast they are moving.

To fix this, engineers usually have to dedicate some lanes of the highway only for radar, which means fewer lanes are left for your actual data. This slows down your internet.

2. The Solution: Mixing the Signal with a "Sweep"

The authors propose mixing the standard data signal with a Chirp.

The Analogy: Imagine the standard data signal is a steady hum. A Chirp is like a siren that smoothly slides from a low pitch to a high pitch.
The Mix: Instead of just sending the hum or just sending the siren, they affinely add them together. Think of it like mixing a steady stream of water (data) with a swirling vortex (chirp). The result is a single, unified stream that has the best of both worlds.

3. Why This is a Big Deal

The paper highlights three main superpowers of this new mix:

No "Pilot" Needed: Usually, to sense things, you need to send out a known "pilot" signal (like a lighthouse beam) so the receiver knows what to look for. This wastes space. The new AAC-OFDM signal is smart enough that the receiver can figure out the distance and speed of an object just by knowing the "shape" of the chirp, even if it doesn't know the secret data message being sent. This is like being able to hear a siren echo off a wall and know how far away the wall is, without needing to know the lyrics of the song playing on the radio.
Smoother Power (Lower PAPR): Standard data signals can have sudden, huge spikes in power (like a car suddenly flooring the gas pedal), which is hard on the equipment. The authors found that adding the chirp smooths out these spikes. It's like adding a shock absorber to a bumpy ride, making the signal more stable and efficient.
Better Accuracy: Because the chirp slides through frequencies, it acts like a very precise ruler. The paper shows that this new mix can measure distance and speed much more accurately than standard signals, especially when you look at a whole "slot" of time (a group of signals) rather than just one single signal.

4. Two Ways to Build It

The paper compares two ways to mix these signals:

CM-OFDM (Multiplicative): This is like painting the data onto the chirp. It works well but requires the receiver to know the exact data message beforehand to decode the sensing info.
AAC-OFDM (Additive): This is like pouring the data and the chirp into the same cup. This is the paper's main innovation. It allows the receiver to sense the environment without needing to know the data message first. This is crucial for "bistatic" sensing, where the person sending the signal and the person receiving it are in different places (like a car talking to a traffic light).

5. The Trade-Off

There is a balance to strike. The authors introduce a "knob" (called $\alpha$ ) that controls how much of the signal is data and how much is the sensing chirp.

If you turn the knob to send more chirp, your sensing gets super accurate, but your data speed might drop slightly.
If you turn it to send more data, your internet is fast, but sensing is less precise.
The paper shows you can find a "sweet spot" where you get excellent sensing without ruining your internet connection.

Summary

In short, this paper presents a new way to build wireless signals that act as both a high-speed internet connection and a precise radar. By mathematically blending a standard data signal with a frequency-sweeping "chirp," they created a system that is more efficient, uses less power, and doesn't need to sacrifice internet speed to "see" the world around it. It's like having a single tool that is both a high-definition camera and a super-fast messenger.

Technical Summary: Amalgamated CHIRP and OFDM for ISAC

Problem Statement
Integrated Sensing and Communication (ISAC) systems aim to unify radar and communication functionalities within a shared infrastructure to address spectrum scarcity and hardware redundancy. However, designing a single waveform that efficiently supports both high-speed data transmission and accurate parameter estimation (range, velocity) remains a challenge. Traditional communication-centric waveforms, such as Orthogonal Frequency Division Multiplexing (OFDM), often suffer from poor autocorrelation properties, leading to high sidelobes that degrade sensing accuracy. Conversely, sensing-centric waveforms like Linear Frequency Modulated (LFM) or Chirp signals offer robust sensing but typically provide lower data rates. Furthermore, existing ISAC implementations often require dedicating specific resources (e.g., pilot subcarriers) for sensing, which inherently reduces communication spectral efficiency. Additionally, traditional OFDM systems face high Peak-to-Average Power Ratio (PAPR), limiting power amplifier efficiency.

Methodology
The paper proposes a novel waveform architecture termed Affine Addition of Chirp and OFDM (AAC-OFDM). This approach combines OFDM and Chirp signals through an affine addition in the time domain, defined as $a(l) = (1 - \alpha)s(l) + \alpha c(l)$ , where $s(l)$ is the OFDM signal, $c(l)$ is the Chirp signal, and $\alpha$ is a power allocation factor.

The study contrasts this with a Chirp-Multiplied OFDM (CM-OFDM) scheme, where the Chirp is multiplicatively combined with the OFDM signal. The authors analyze both waveforms within the context of the 5G New Radio (NR) frame structure. Key methodological steps include:

Waveform Formulation: Defining the discrete-time and continuous-time representations of AAC-OFDM and CM-OFDM, ensuring alignment with OFDM parameters (subcarrier spacing, symbol duration).
Theoretical Analysis: Deriving the Ambiguity Function for both waveforms to evaluate their sensing resolution, Doppler tolerance, and delay-Doppler coupling. The analysis includes a mathematical derivation of the PAPR reduction properties of the affine addition.
Implementation Strategies: Investigating two implementation levels within the 5G NR frame:
- Symbol-level: Applying the Chirp to a single OFDM symbol.
- Slot-level: Applying the Chirp across an entire slot (14 symbols) to increase coherent processing time.
- Hybrid: Combining both approaches within a subframe to balance range and velocity unambiguous windows.
Receiver Design: Proposing a receiver architecture where the Chirp component is removed via a "dechirping" operation prior to standard OFDM demodulation. This allows the extraction of sensing information (range/velocity) without requiring prior knowledge of the transmitted data bits, a critical feature for bistatic scenarios.

Key Contributions
The paper explicitly contrasts its contributions with existing literature (summarized in Table I of the text):

Novel Waveform Design: The proposal of AAC-OFDM, which utilizes affine addition to create a near constant-envelope waveform. This design decouples sensing and communication functionalities, allowing the Chirp to facilitate sensing without consuming dedicated pilot subcarriers.
Theoretical Framework: The derivation of the ambiguity function for AAC-OFDM, establishing a theoretical basis for evaluating its performance in various ISAC scenarios, including bistatic sensing where the receiver lacks prior knowledge of transmitted data.
PAPR Reduction: Demonstration that the affine addition of a Chirp signal to OFDM results in a near constant-envelope waveform, effectively reducing the PAPR compared to standard OFDM and CM-OFDM.
Performance Comparison: A comparative analysis showing that the proposed Chirp-Multiplied OFDM (CM-OFDM) significantly outperforms standard OFDM used as a Position Reference Signal (PRS) in terms of range resolution while maintaining comparable communication performance.
Implementation Insight: A novel comparison of symbol-level versus slot-level Chirp integration. The results indicate that slot-level superposition consistently outperforms symbol-level implementation in terms of Range and Velocity Root Mean Square Error (RMSE) due to noise averaging over a longer coherent processing interval.

Results
Simulation results, based on 5G NR parameters (120 kHz subcarrier spacing, 24 GHz carrier frequency), demonstrate the following:

PAPR: AAC-OFDM exhibits a substantial reduction in PAPR compared to standard OFDM. At a Complementary Cumulative Distribution Function (CCDF) of $10^{-3}$ , AAC-OFDM achieves approximately 9–10.9 dB (depending on $\alpha$ ), whereas standard OFDM and CM-OFDM remain around 11 dB.
Communication Performance: The Bit Error Rate (BER) of AAC-OFDM behaves similarly to conventional OFDM for low values of $\alpha$ (e.g., 0.1). As $\alpha$ increases, BER degrades slightly due to power allocation to the Chirp, but the system remains robust. Crucially, AAC-OFDM achieves higher spectral efficiency (up to 1.7 bits/s/Hz) because it does not require reserving subcarriers for pilots, unlike OFDM and CM-OFDM which lose capacity when dedicating 25% of resources to sensing.
Sensing Performance:
- Ambiguity Function: AAC-OFDM exhibits a sharper "thumbtack" ambiguity function with a tilted shape, offering improved range resolution (approx. 4.20 m for N=128) and Doppler tolerance compared to OFDM (9.89 m) and CM-OFDM (7.50 m).
- RMSE: AAC-OFDM achieves lower RMSE for range and velocity estimation compared to standard OFDM, particularly when implemented at the slot level. While AAC-OFDM without pilots shows a slight performance gap (approx. 5 dB) compared to pilot-heavy schemes at low SNR, it outperforms them in scenarios where pilot resources are limited.
- Velocity Estimation: The velocity RMSE floor for AAC-OFDM is approximately 0.02 m/s, significantly better than the 0.38–0.40 m/s observed for standard OFDM and CM-OFDM, approaching the performance of pure Chirp waveforms.

Significance and Claims
The paper claims that the proposed AAC-OFDM waveform offers a practical and efficient solution for ISAC systems by:

Enabling Pilot-Free Sensing: It allows for accurate sensing without the need for pilot subcarriers or prior knowledge of transmitted data, making it eminently suitable for bistatic and multistatic sensing where the receiver is located at a different base station.
Optimizing Trade-offs: It provides a tunable parameter ( $\alpha$ ) to balance the trade-off between communication reliability (BER) and sensing accuracy (RMSE).
Enhancing Spectral Efficiency: By eliminating the need for dedicated pilot resources for sensing, it preserves communication capacity.
Improving Power Efficiency: The reduction in PAPR allows for more efficient power amplifier operation, a key limitation in traditional OFDM systems.
Flexibility: The slot-level and symbol-level implementation strategies offer a practical way to balance range resolution against unambiguous velocity windows, adapting to specific application needs (e.g., autonomous vehicles vs. environmental monitoring).

The authors conclude that AAC-OFDM represents a significant step forward in waveform design for 6G and future ISAC networks, offering a compatible, high-performance alternative to existing communication-centric and sensing-centric approaches.