Thermal Noise Modulation (TherMod)

• TherMod is a technique that modulates the variance of equilibrium thermal noise to encode information using precision resistors and statistical detection methods.
• It employs variance estimation and optimized thresholds to achieve low-energy, covert signal transmission with quantifiable BER improvements via increased sample counts.
• Applications span batteryless IoT, SWIPT, and quantum noise engineering, providing reliable, secure communication channels and advanced noise routing in mesoscopic systems.

Thermal Noise Modulation (TherMod) denotes a class of physical-layer technologies, device paradigms, and noise engineering strategies that employ the intrinsic statistical properties of equilibrium thermal (Johnson–Nyquist) noise as a resource for information transmission, modulation, amplification, routing, or quantum-state control. Unlike conventional approaches that treat noise as a deleterious background, ThermMod explicitly encodes, manipulates, or exploits noise characteristics—predominantly the variance—either for communication or for tunable noise flows in mesoscopic, quantum, or classical systems. Implementations span from passive RF wireless links and optomechanical diodes to quantum-coherence modulation and parametric amplifiers. ThermMod is thus not only a foundational method for ultra-low-power and covert communications, but is also a building block for future networks, quantum-limited devices, and engineered thermal environments.

1. Fundamental Principles and Mechanisms

TherMod schemes encode, transmit, or manipulate information by modulating the statistical variance of thermal noise sources, most typically the voltage or power spectral density generated by precision resistors at absolute temperature $T$: $\mathbb{E}[v_R^2(t)] = 4kTR\,\Delta f$ where $k$ is Boltzmann’s constant, $R$ the resistance, and $\Delta f$ the noise bandwidth. In the canonical communication application, two or more resistors ($R_0, R_1$ with $R_1 > R_0$) are switched such that the output noise variance encodes the digital bit value. This process does not require a conventional signal carrier, oscillator, or power amplifier, as the information is contained entirely in the time-varying thermal fluctuation statistics. The received signal is a stochastic process whose second-order statistics (specifically, the sample variance) contain all the information necessary for detection.

In quantum and mesoscopic systems (parametric amplifiers, quantum networks) and cavity-based measurement settings, ThermMod refers also to the modulation, routing, or rectification of thermal noise currents and the engineered transduction of temperature-dependent device parameters (e.g., impedance, frequency, decoherence rates) for amplification or control.

2. System Models and Detection Strategies

Wireless Communication Architectures. The transmitter comprises a pair of precision resistors selected by a low-loss RF (or microwave) switch and, optionally, an up-converter for passband operation. The resistor's inherent noise is radiated via an antenna. No active amplification is required; thus, the transmitter energy budget is set solely by the switching electronics. The receiver includes a low-noise amplifier, down-converter, analog-to-digital converter (ADC), and DSP variance estimator.

Signal Model. The broadcast signal consists of $N$ complex samples per symbol: $$s_n = h\,r_n + w_n,\quad r_n \sim \mathcal{CN}(0, \sigma_b^2),\; w_n \sim \mathcal{CN}(0, \sigma_w^2)$$ with $b \in \{0, 1\}$ for binary modulation; $h$ is the fading coefficient (possibly $h=1$ for AWGN). The key detection statistic is the unbiased sample variance: $\hat\sigma_s^2 = \frac{1}{N} \sum_{n=1}^N |s_n|^2$ A threshold $\gamma$ (typically optimized analytically) splits the received variance into bit hypotheses.

Detection and Performance. The detection process, under Gaussian CLT, yields an explicit BER as a function of resistance ratio ($\alpha = \sigma_1^2/\sigma_0^2$), SNR-analogue ($\delta = \sigma_0^2/\sigma_w^2$), and number of samples ($N$): $$P_e^* = Q\left( \frac{ \sqrt{N} \,\delta\, (\alpha-1) }{ 2 + \delta\, (1 + \alpha ) } \right)$$ Larger $N$ or $\alpha$ rapidly reduce the BER, but at the cost of lower bit-rates ($R_b = f_s / N$).

Variance Modulation in Quantum and Thermal Networks. In quantum optomechanical or cascaded systems, ThermMod realizes unidirectional noise transmission, thermal rectification, or amplification by engineering Hamiltonians or Lindblad evolution to favor noise flows in specific ports. Control is achieved via appropriate detunings, couplings, or bath occupations.

3. Mathematical Formalism for Modulation, Detection, and Routing

The statistical foundation of ThermMod relies on the full Gaussian model: $$p(r_n) = \frac{1}{\pi \sigma_b^2} \exp\left( -\frac{ |r_n|^2 }{ \sigma_b^2 } \right)$$ which, upon transmission and sampling, is combined with channel and receiver noise. Central limit theory ensures that for sufficiently large $N$, the sample variance estimator is approximately normal: $$\hat\sigma_s^2 \sim \mathcal{N}( \tilde\sigma_b^2,\, \tilde\sigma_b^4 / N )$$ where $\tilde\sigma_b^2 = \sigma_{r,b}^2 + \sigma_w^2$ is the total observed variance under bit $b$.

The threshold is optimal when the $Q$-function arguments are balanced. For fading channels, the BER is averaged or conditioned on $|h|^2$: $$P_b(|h|^2) = Q\left( \frac{ \sqrt{N}\, \delta\,(\alpha-1) |h|^2 }{ 2 + \delta\,(\alpha+1)\,|h|^2 } \right)$$

Network and quantum settings formalize noise currents, fluxes, and non-reciprocal behavior via cascaded master equations and thermal Lindblad terms. For instance, in an optomechanical realization: $$\dot\rho = -\frac{i}{\hbar}[H_{\rm sys} + H_{\rm hop}, \rho] + \sum_{i} \mathcal{D}_{\bar N_i,\kappa_i, \hat c_i}[\rho]$$ allowing analytic calculation of noise transfer, isolation, and gain.

4. Implementation and Hardware Considerations

A minimal ThermMod wireless link comprises:

• Two high-precision resistors (for noise variance switching)
• Ultra-low-loss SPDT (or SPST) switch with nanosecond-scale rise/fall
• Antenna or transmission line (for radiative or guided modes)
• Optional upconverter for passband modulation

No local oscillator, active carrier, or linear power amplifier is required. The transmitter quiescent power is dominated by digital control for the switch. The receiver is conventional: LNA, mixer, ADC, and a baseband variance estimator computed over the desired time/frequency window.

Critical design aspects:

• Thermal drift of resistors is compensated via periodic pilot insertion and AGC/threshold re-calibration.
• Bandwidth control is exerted via analog/digital lowpass or root-raised cosine filtering to match the resistor's thermal spectrum.
• Passive surface integration for RIS–linked or distributed noise-based links is feasible by embedding switchable resistances into metasurface elements.
• SWIPT compatibility arises naturally, as a portion of the stochastic power can be harvested while decoding is performed on the variance channel.

For quantum and mesoscopic ThermMod (e.g., SIGIS-based amplifiers, cavity intermodulation noise, optomechanical routers), device-specific engineering targets nonlinear transfer functions (e.g., $R(T)$ for graphene junctions), careful thermal management, bandwidth optimization, and the realization of tunable couplings (optomechanical $G_i$ or photon-hopping $J$).

5. Performance Evaluation and Comparative Analysis

TherMod achieves information transfer at the theoretical minimum energy per bit because the transmitted waveform is locally indistinguishable from background thermal noise—this yields maximal covertness and minimizes probability of detection by unauthorized receivers. Key trade-offs are charted among sample count $N$, resistance ratio $\alpha$, receiver noise figure, achievable bit-rate $R_b$, and required error rate.

Compared with artificial-noise schemes (NoiseMod, NC-NoiseMod, TD-NoiseMod), purely passive ThermMod (i.e., relying strictly on physical resistor noise) achieves the lowest system power and unmatched covertness but the highest BER for given $N$. Schemes involving more than two states (e.g., utilizing four resistors for two bits per symbol) can reduce BER and double rate at the price of multi-level thresholding and higher system complexity.

Monte Carlo and analytical simulations demonstrate quantitative agreement with CLT-based BER predictions. For example, with $\delta=0.1$, $\alpha=10$, and $N$ in the range 100–1000, BER drops exponentially with $N$, reaching $<10^{-3}$ for practical sample sizes. Performance is robust to moderate fading and non-idealities in noise distribution, provided calibration and pilot-based compensation are regularly performed.

In quantum applications, ThermMod architectures can achieve parametric amplification with gains exceeding 18 dB, sub-nanosecond response, and noise temperatures $T_N$ well below 2 K. In optomechanical or cavity-based routing, isolation and rectification of thermal noise flows can be made perfect in the ideal limit, with directionality determined by coupling strengths and detuning.

6. Applications and Future Research Directions

Ultra-Low-Power and Batteryless Communications: ThermMod is uniquely suited to batteryless IoT sensors and autonomous wireless networks, requiring neither active carrier synthesis nor high-power electronics.

Covert and Secure Channels: The statistical indistinguishability of the transmitted signal from ambient noise underpins innate low probability of detection/interception (LPD/LPI), yielding new regimes of physical-layer confidentiality.

Simultaneous Wireless Information and Power Transfer (SWIPT): By leveraging the energy content in the stochastic thermal background, ThermMod enables simultaneous energy harvesting and data decoding, relevant to self-powered networked devices.

Noise Engineering in Quantum Circuits: ThermMod underlies engineered thermal environments for quantum error suppression, coherence preservation via frequency modulation, and hardware-level noise routing in nonreciprocal devices.

RIS and Intelligent Surfaces: Passive integration of switchable thermal noise sources into reconfigurable intelligent surfaces affords new topologies for distributed, low-power, and highly covert links.

Open Directions:

• Development of joint ML/energy detection algorithms that approach traditional SNR-bound performance with minimal hardware overhead.
• Standardization of frame structures, multiuser access protocols, and statistical pilot sequences tailored to ThermMod.
• Extensions to gigahertz-scale bandwidths, exploiting high-frequency thermal noise, advanced resistor materials, and scalable surface-integration.
• Hybridization with quantum-noise sources, jamming-resistant architectures, and cross-domain variants (variance–phase/power “noise constellations”).
• Theoretical development of capacity and optimal coding for variance-modulated noise channels.

Thermal Noise Modulation thus represents both a practical toolset for physical-layer innovation and a paradigm-shift in viewing noise not as a limitation, but as a primary resource for communication, control, and secure information transfer (Silva et al., 6 Nov 2025, Basar, 2022, Basar, 2023, Dallyn et al., 2021, Kapetanovic et al., 2021, Shadfar et al., 19 Oct 2025, Will et al., 21 Aug 2024, Barzanjeh et al., 2017, Xuereb et al., 2018, Slobodianiuk, 2014, Berlin-Udi et al., 2021, Erementchouk et al., 2019, Fedorov et al., 2020).