⚡ electrical engineering

Phase-Shifted Pilot Design for NOMA-Empowered Uplink ISAC Systems

This paper proposes a phase-shifted pilot design with a novel nulling variant and adapted interference cancellation techniques to enable efficient integration of communication transmitters in NOMA-empowered uplink ISAC systems, achieving improved spectral efficiency and sensing integrity while significantly reducing receiver computational complexity compared to conventional interleaved baselines.

Original authors: Ahmet Sacid Sümer, Ebubekir Memişoğlu, Hüseyin Arslan

Published 2026-04-03

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ahmet Sacid Sümer, Ebubekir Memişoğlu, Hüseyin Arslan

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 a busy highway where two types of vehicles are trying to travel at the same time: Delivery Trucks (carrying communication data like your text messages and videos) and Surveillance Drones (sending out radar-like signals to sense the environment, like detecting cars or people).

In the old way of doing things (called "Orthogonal Allocation"), the highway was split into separate lanes. Trucks used the left lanes, and drones used the right lanes. This was safe, but it wasted half the road. If a truck had no cargo, that left lane sat empty, and if a drone had nothing to sense, the right lane sat empty.

The Problem:
As the Internet of Things (IoT) grows, we have thousands of these trucks and drones. If we keep splitting the road, we run out of space. We need them to share the same lanes at the same time. This is called NOMA (Non-Orthogonal Multiple Access).

But here's the catch: If a truck and a drone drive in the exact same spot, they crash into each other (interference). The truck can't hear the drone, and the drone can't see the road.

The Paper's Solution:
This paper proposes a clever new way to let them share the road without crashing, using a concept called Phase-Shifted Pilots.

Here is the breakdown using simple analogies:

1. The "Ghost" vs. The "Solid" Truck (The Pilot Design)

To understand the road, the drones need to send out a "pilot" signal (like a lighthouse beam).

The Old Way (Interleaved): Imagine the drones only send their lighthouse beams on specific, sparse days. This creates gaps in the data, making it hard to see far away or see small details (low resolution).
The New Way (Phase-Shifted): The paper suggests the drones send their beams every single day (full bandwidth), but they change the color or phase of their light slightly.
- Analogy: Imagine 4 drones are all shining white flashlights at the same time. To the receiver, it looks like one giant, blinding mess. But, if Drone A shines a light that is slightly "red-shifted," Drone B is "blue-shifted," and Drone C is "green-shifted," the receiver can use a special filter to separate them instantly.
- The Benefit: The receiver gets a full, high-resolution picture of the road (sensing) without needing to wait for different days.

2. The "Traffic Cop" Strategy (Iterative Interference Cancellation)

Even with the color-coded lights, the trucks (communication data) are still getting in the way of the drones. The paper introduces a "Traffic Cop" (the Receiver) that uses a two-step cleaning process:

Step A: The "Joint" Cop (For most scenarios):
The cop looks at the traffic, guesses what the trucks are saying, subtracts that guess from the noise, and then looks at what's left to see the drones. Then, it looks at the drones, subtracts them, and refines the guess for the trucks. It does this over and over (iteratively) until the traffic is perfectly sorted.
- Metaphor: It's like trying to hear a friend's voice in a crowded room. You guess what they said, subtract the background noise you think you heard, and listen again. You repeat this until you clearly hear your friend.
Step B: The "Sequential" Cop (For the "Nulling" variant):
Sometimes, the trucks are so loud they drown out the drones completely. The paper suggests a "Spectral Nulling" trick: The drones intentionally turn off their lights exactly where the trucks are shouting their most important instructions (the pilots).
- The Strategy: The cop first locks onto the trucks' clear instructions (because the drones aren't shouting there). Once the trucks are understood, the cop uses that knowledge to clean up the rest of the noise and finally hear the drones. This is faster and requires less brainpower (computational complexity).

3. The Result: A Smarter, Faster Highway

The paper proves that this new system is a win-win:

Better Sensing: Because the drones use the full road (not just sparse lanes), they can see further and more clearly.
Better Communication: The trucks can send more data because they aren't waiting for their own dedicated lanes.
Less Brainpower: The most exciting part is that the receiver (the Traffic Cop) doesn't have to work as hard.
- The Math: The old system required the cop to run a complex calculation for every single drone separately. The new system lets the cop run one single calculation for the whole group, then just sort the colors.
- The Savings: This reduces the computer work by about 19% to 21%. In the world of battery-powered IoT devices, saving 20% of your battery life is a massive deal.

Summary

This paper is about teaching a crowded highway of sensors and phones to share the same space efficiently. Instead of building more lanes (which is expensive and wasteful), they taught the vehicles to drive in the same lane but wear different colored uniforms (Phase-Shifted Pilots). They also gave the traffic police a smarter, faster way to sort the traffic (Iterative Interference Cancellation), allowing the whole system to run faster, see further, and use less battery power.

1. Problem Statement

The paper addresses the critical challenge of integrating Integrated Sensing and Communication (ISAC) in dense Internet of Things (IoT) networks, specifically within Uplink (UL) scenarios involving multiple transmitters (TXs).

The Conflict: In dense networks, communication signals (from Communication TXs, or CTXs) and sensing signals (from Sensing TXs, or STXs) collide, causing severe mutual interference.
Limitations of Current Solutions:
- Orthogonal Allocation: Traditional time/frequency division is inefficient and reduces spectral efficiency (SE).
- Interleaved Pilots (CI): While Non-Orthogonal Multiple Access (NOMA) with interleaved pilots improves SE, it creates spectral sparsity. This sparsity degrades sensing resolution (specifically the maximum unambiguous range) and imposes a high computational burden on the receiver (RX) because it requires a separate Inverse Fast Fourier Transform (IFFT) for every scheduled STX.
- Nulling Extensions (CIN): Existing attempts to "null" sensing signals at pilot locations to protect communication estimates inherit the structural trade-offs of interleaved designs.

2. Methodology

The authors propose a novel framework combining Phase-Shifted (PS) Pilot Design with NOMA, supported by two specialized Iterative Interference Cancellation (IIC) receiver architectures.

A. System Model

Scenario: A single-antenna CTX and $U$ single-antenna STXs transmit simultaneously over shared time-frequency resources to a single ISAC receiver.
Signal Structure:
- CTX: Transmits a payload with data and pilot tones.
- STXs: Transmit a common reference probing sequence. To ensure separability, each STX applies a STX-specific cyclic phase shift in the frequency domain.
- Phase Shift Mechanism: The phase shift $\theta_{u,k}$ for the $k$ -th subcarrier of the $u$ -th STX is defined as $\theta_{u,k} = -2\pi k \frac{n_u}{N}$ . This shifts the Channel Impulse Response (CIR) of each STX into a distinct, non-overlapping window in the time domain (delay domain), allowing separation without frequency-domain interleaving.

B. Proposed Pilot Variants

PS-ISAC-NOMA: Full-bandwidth phase-shifted sensing pilots overlaid on communication signals.
PSN-ISAC-NOMA (Phase-Shifted Nulling): A variant that strategically punctures (nulls) the sensing signal at the specific subcarriers used for CTX pilots. This preserves the integrity of the initial communication channel estimates without sacrificing time-domain separability.

C. Receiver Architectures (IIC)

To resolve the dense multi-TX interference, two iterative receiver strategies are adapted:

Joint IIC: Used for non-nulling configurations (PS and CI). It concurrently updates communication and sensing channel estimates in every iteration. It is robust but computationally heavier.
Sequential IIC: Specifically designed for nulling variants (PSN and CIN).
- Phase 1 ( $q \le Q_1$ ): The communication channel estimate is frozen (fixed) based on the initial pilot estimate. The receiver only updates sensing channels and data symbols. This accelerates convergence and reduces complexity.
- Phase 2 ( $q > Q_1$ ): Once sensing interference is suppressed, the communication channel is "unfrozen" and refined using Decision-Directed (DD) techniques.

3. Key Contributions

Novel Pilot Design: Introduction of the PS-ISAC-NOMA framework, which overlays high-rate communication data onto full-bandwidth phase-shifted sensing pilots. This maintains optimal sensing resolution (unlike interleaved designs) while enabling NOMA.
Spectral Nulling Variant (PSN): Proposal of the PSN scheme, which punctures sensing signals at communication pilot locations. This protects initial channel estimates, enabling dense data overlay while maintaining separability.
Adaptive Receiver Algorithms: Development and evaluation of Joint IIC (for non-nulling) and Sequential IIC (for nulling) architectures. The Sequential IIC significantly reduces computational load by freezing the communication channel during early iterations.
Complexity Reduction: Demonstration that shifting multi-STX separation to the time domain (via phase shifts) eliminates the need for multiple IFFTs per STX, drastically reducing receiver hardware complexity.

4. Simulation Results

The framework was evaluated against baselines (CI-ISAC-NOMA and CIN-ISAC-NOMA) across varying STX densities ( $U$ ) and modulation orders ( $M$ ).

Sensing Performance:
- The PS and PSN frameworks maintain sensing integrity (Normalized Mean Square Error - NMSE) comparable to orthogonal sensing-only benchmarks.
- Unlike interleaved designs, they do not suffer from spectral sparsity, preserving the maximum unambiguous range.
Communication Performance:
- PSN variants show superior robustness in high-density scenarios ( $U=16$ ) and high-order modulation ( $M=16$ ). The spectral nulling protects the CTX channel estimate, preventing error propagation.
- At moderate densities ( $U \le 4$ ), all NOMA schemes approach theoretical lower bounds for communication NMSE and Bit Error Rate (BER).
Spectral Efficiency (SE):
- NOMA frameworks significantly outperform orthogonal TDM baselines.
- While $M=16$ offers the highest theoretical throughput, it suffers from error floors due to interference; however, PSN variants retain higher SE than non-nulling counterparts under these conditions.
Computational Complexity:
- Receiver Savings: The proposed phase-shifted architectures reduce receiver-side computational complexity by 18.8% (PS vs. CI) and 21.0% (PSN vs. CIN) in terms of real multiplications.
- Mechanism: This is achieved by replacing $U$ separate IFFTs (required for interleaved designs) with a single composite IFFT followed by time-domain windowing.

5. Significance

This paper provides a scalable solution for 6G and massive IoT deployments where communication and sensing must coexist efficiently.

Hardware Efficiency: By reducing the computational burden on the receiver, the proposed schemes are highly suitable for energy-constrained edge devices and dense networks.
Performance Balance: It successfully resolves the trade-off between sensing resolution and spectral efficiency, a common bottleneck in current ISAC systems.
Scalability: The Sequential IIC architecture allows the system to scale to high user densities without a linear explosion in processing power, making it a viable candidate for next-generation wireless networks.

In conclusion, the Phase-Shifted Nulling (PSN) architecture is identified as the optimal solution for computational efficiency, while the Phase-Shifted (PS) architecture serves as a robust secondary option, both outperforming traditional interleaved NOMA approaches in dense ISAC environments.