⚡ electrical engineering

Ternary Noise Modulation

This paper proposes Ternary Noise Modulation (T-NoiseMod), a novel wireless communication scheme that encodes information into the statistical characteristics of artificial noise by introducing an intentional silence state to achieve higher data rates than binary NoiseMod, while providing an analytical bit error probability derivation and demonstrating a trade-off between reliability and transmission rate.

Original authors: Ata Bilgin, Erkin Yapıcı, Yusuf İslam Tek, Ertuğrul Başar

Published 2026-04-17

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CC BY 4.0

Original authors: Ata Bilgin, Erkin Yapıcı, Yusuf İslam Tek, Ertuğrul Başar

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 across a noisy room. Usually, you'd shout specific words (like "Yes" or "No") or use hand signals. But what if you could send a message just by how much you make noise, or even by staying completely silent?

This paper introduces a new way to communicate called T-NoiseMod (Ternary Noise Modulation). It's a clever trick for wireless devices (like IoT sensors or future 6G networks) to send data using "artificial noise" instead of traditional radio waves.

Here is the breakdown using simple analogies:

1. The Old Way: The "Volume Knob" (Binary NoiseMod)

Imagine your friend is trying to listen to you in a crowded bar.

The Old Method: You have a volume knob.
- Turn it Low: You whisper "0".
- Turn it High: You shout "1".
The Problem: You can only send one bit of information at a time. Also, if the bar gets too loud (interference), it's hard to tell if you whispered or shouted.

2. The New Way: The "Silence, Whisper, Shout" Game (T-NoiseMod)

The authors realized there is a third option they weren't using: Silence.
Instead of just Low and High, they introduced a Silent state.

State L (Low): You whisper.
State H (High): You shout.
State S (Silent): You stop talking entirely.

The Magic Trick:
Sending just one of these states is still slow. So, the new system sends two messages back-to-back as a pair.

If you send (Whisper, Shout), that's one code.
If you send (Silence, Whisper), that's another code.
If you send (Shout, Silence), that's a third.

By pairing them up, you can create 8 different combinations (like a 3-digit binary code: 000, 001, 010, etc.).

Result: Instead of sending 1 bit, you are now sending 3 bits in the same amount of time! It's like upgrading from a single-lane road to a three-lane highway without building any new roads.

3. How the Receiver "Hears" the Message

The receiver (your friend) has to be smart to figure out which combination you sent. They use a Two-Step Detective Process:

Step 1: The "Is Anyone There?" Test (Mean Detection)
The receiver first checks the average sound level.
- If the average sound is near zero, they assume you are Silent.
- If there is sound, they know you are either Whispering or Shouting.
- Analogy: It's like checking if a room is empty. If it's quiet, you know no one is talking.
Step 2: The "How Loud?" Test (Variance Detection)
If the room isn't empty, the receiver checks the variety of the noise.
- Is the noise consistent and low? That's a Whisper.
- Is the noise wild and loud? That's a Shout.
- Analogy: It's like distinguishing between a gentle rain (low variance) and a thunderstorm (high variance).

The Safety Net:
There is one rule: You can't be silent twice in a row (Silent + Silent) because that would look like no one is talking at all, and the message would get lost. If the receiver accidentally thinks you are silent twice, the system has a "safety rule" that forces one of the blocks to be treated as active, ensuring a message is always decoded.

4. Why Do This? (The Trade-Off)

The paper compares this new method to the old "Volume Knob" method.

The Good News: T-NoiseMod is much faster. It sends 50% more data (3 bits vs. 2 bits) in the same time frame. It's also harder for eavesdroppers to catch because "silence" looks just like background noise.
The Bad News: Because there are more options to choose from, it's slightly easier to make a mistake (a "Bit Error"). It's like trying to guess a 3-digit code is harder than guessing a 1-digit code.
The Verdict: The authors show that with the right settings, the speed gain is worth the tiny increase in mistakes.

Summary

Think of T-NoiseMod as a new language for machines. Instead of just saying "Yes" or "No," they can say "Yes," "No," or "Shhh." By combining these three options in pairs, they can speak a much richer, faster language that is hard for others to intercept and doesn't require complex equipment to understand. It's a smarter way to use the "static" in the air to carry our digital lives.

1. Problem Statement

Noise-based communication is an emerging paradigm for low-complexity, secure, and energy-efficient wireless systems (e.g., IoT, covert communications). Unlike traditional schemes that encode data onto deterministic waveforms, noise-based systems embed information into the statistical properties (mean, variance) of artificial noise.

However, existing noise modulation techniques, such as Binary NoiseMod, rely on two-level statistical signaling (e.g., low variance vs. high variance). This binary approach fundamentally limits the spectral efficiency, typically transmitting only one bit per signaling block. To increase data rates, these systems often require longer observation windows or bandwidth expansion, which increases latency and energy consumption. Furthermore, existing schemes treat "silence" (non-transmission) merely as an idle state rather than an active information-bearing symbol. The paper addresses the need for a higher-order signaling scheme that improves information rates without sacrificing the inherent advantages of noise-based communication (low complexity, robustness, and covertness).

2. Methodology: Ternary Noise Modulation (T-NoiseMod)

The authors propose T-NoiseMod, a signaling framework that introduces a ternary state space to noise modulation.

Signaling States: Instead of binary (Low/High variance), the system utilizes three states for each transmission block:
1. Low Variance (L): Gaussian noise with variance $\sigma^2_L$ .
2. High Variance (H): Gaussian noise with variance $\sigma^2_H$ .
3. Silent (S): Intentional non-transmission (zero vector), acting as a deliberate signaling state.
Block Pairing Strategy: To transmit 3 bits per signaling interval, the system pairs two consecutive noise blocks ( $x_1, x_2$ $x_{1}, x_{2}$ ).
- The combination of two ternary states creates $3^2 = 9$ possible pairs.
- The pair $(S, S)$ is invalid (as at least one block must be active to convey information), leaving 8 valid combinations.
- This allows the mapping of 3 information bits ( $b_1, b_2, b_3$ ) to one signaling interval (two blocks).
Receiver Architecture (Two-Stage Detection):
1. Stage 1: Mean-Based Silent Detection: The receiver calculates the sample mean of the received block. If the mean is close to zero (below a threshold relative to the reference mean $\mu$ ), the block is classified as Silent (S). Otherwise, it is deemed active.
2. Stage 2: Variance-Based Classification: For blocks classified as active, the receiver estimates the empirical variance. A Likelihood Ratio Test (LRT) threshold distinguishes between Low (L) and High (H) variance.
3. Consistency Refinement: A specific logic step handles the rare case where the detector erroneously classifies both blocks as Silent ( $S, S$ ). In this event, the block with the "stronger" silent metric is re-evaluated as active to ensure a valid decision is made.

3. Key Contributions

Novel Signaling Scheme: Introduction of the first ternary noise modulation scheme that explicitly exploits intentional silence as an information-bearing state, expanding the signaling alphabet without increasing bandwidth.
Increased Spectral Efficiency: By pairing two blocks, the scheme transmits 3 bits per interval, compared to the 2 bits transmitted by a binary NoiseMod scheme over the same duration (assuming equal energy constraints).
Theoretical Analysis: Derivation of a closed-form expression for the Bit Error Probability (BEP) under Rayleigh fading channels. This includes:
- Statistical modeling of sample means and variances.
- Analysis of the two-stage detection error probabilities (False Alarm, Miss Detection, and Variance confusion).
- Incorporation of the "consistency refinement" logic into the final BEP calculation.
Receiver Design: Development of a non-coherent, low-complexity receiver that relies on statistical detection (mean and variance) rather than phase/frequency synchronization.

4. Results

The authors validated their theoretical analysis through computer simulations under Rayleigh fading conditions:

Analytical vs. Simulation: The derived theoretical BEP curves closely matched the simulation results, validating the accuracy of the statistical approximations used.
Impact of Parameters:
- Reference Mean ( $\mu$ ): Increasing the reference mean value improves the reliability of the silent-state detection, thereby reducing the overall BEP.
- Block Length ( $N$ ): Increasing the number of samples ( $N$ ) in each block improves estimation accuracy for both mean and variance, leading to a monotonic decrease in BEP.
Performance Trade-off:
- Reliability vs. Rate: Binary NoiseMod achieves a slightly lower BEP (higher reliability) for a given $N$ because it has fewer decision levels.
- Throughput: Despite the slight increase in BEP, T-NoiseMod offers a higher information rate. For the same number of transmitted blocks, T-NoiseMod delivers 50% more data (3 bits vs. 2 bits) compared to binary NoiseMod.
- Energy Efficiency: The scheme maintains competitive performance while consuming the same average transmit energy as the binary baseline (by scaling the variance of the binary scheme to match the average energy of the ternary scheme over two blocks).

5. Significance

This work represents a significant step forward in noise-based communication by breaking the binary limitation of the field.

Spectral Efficiency: It demonstrates that noise-based systems can achieve higher data rates without the complexity of traditional high-order modulation (like QAM) or the need for strict synchronization.
Covert & Low-Power Applications: The inclusion of the "Silent" state not only boosts data rates but also enhances covertness (making transmission harder to distinguish from background noise) and reduces average transmit energy, making it ideal for energy-constrained IoT and secure military communications.
Future Framework: The paper establishes a theoretical foundation for higher-order noise modulation, suggesting potential for further optimization in multi-user scenarios (NOMA) and imperfect channel state information (CSI) environments.