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Privacy via Modulation Rotation and Inter-Symbol Interference

Morteza Varasteh, Pegah Sharifi

TL;DR

This work investigates user-side differential privacy in wireless links by exploiting deterministic transmitter perturbations, namely modulation rotation and induced ISI, within a BPSK framework. It analyzes three mechanisms—DP via SNR, DP via phase rotation, and DP via deterministic offset—and derives how the privacy budget $\varepsilon$ relates to BER and input distribution, showing that phase rotation reduces decision reliability and ISI introduces symbol-dependent randomness. The key findings are that phase-rotation DP yields privacy that diminishes with angle $\alpha$ and can reach near-perfect privacy as $\alpha\to\frac{\pi}{2}$, while ISI-based DP depends on the input distribution, potentially outperforming phase-rotation for nonuniform inputs (with $p=0.5$ yielding equivalent results). Overall, the results demonstrate that realistic channel imperfections and structured perturbations can serve as private resources, enabling DP without explicit noise and potentially lowering energy and privacy costs in wireless systems.

Abstract

Two physical-layer mechanisms for achieving user-side differential privacy in communication systems are proposed. Focusing on binary phase-shift keying (BPSK) modulation, differential privacy (DP) is first studied under a deterministic phase rotation applied on the BPSK modulation at the transmitter, while the receiver is assumed to be unaware of the rotation angle. In this setting, privacy is achieved through an effective reduction in the decision distance, resulting in a controlled increase in the bit error rate (BER) without explicit noise injection. Next, a BPSK transmission scheme with intentionally induced inter-symbol interference (ISI) is studied, where the receiver is likewise unaware of the deterministic timing offset that generates the ISI. Unlike the rotated BPSK scheme, the DP obtained via ISI is shown to depend explicitly on the input data distribution. In particular, numerical results demonstrate that, for a fixed ISI parameter, the privacy loss is maximized when the binary input symbols are equiprobable. While conventional DP mechanisms rely on artificially added noise, often incurring additional energy or communication costs, it is shown that structured modifications, such as modulation rotation or induced ISI inherent to realistic communication channels can itself provide DP guarantees. While the analysis focuses on deterministic transmitter modifications unknown to the receiver, it is noted that real-world devices naturally introduce unintentional rotations or ISI due to hardware nonidealities and implementation errors. These effects can therefore provide a level of privacy without requiring explicit noise injection. Hence, it is possible to avoid deliberately perturbing the data, instead leveraging inherent device imperfections to achieve privacy guarantees with no additional privacy cost.

Privacy via Modulation Rotation and Inter-Symbol Interference

TL;DR

This work investigates user-side differential privacy in wireless links by exploiting deterministic transmitter perturbations, namely modulation rotation and induced ISI, within a BPSK framework. It analyzes three mechanisms—DP via SNR, DP via phase rotation, and DP via deterministic offset—and derives how the privacy budget relates to BER and input distribution, showing that phase rotation reduces decision reliability and ISI introduces symbol-dependent randomness. The key findings are that phase-rotation DP yields privacy that diminishes with angle and can reach near-perfect privacy as , while ISI-based DP depends on the input distribution, potentially outperforming phase-rotation for nonuniform inputs (with yielding equivalent results). Overall, the results demonstrate that realistic channel imperfections and structured perturbations can serve as private resources, enabling DP without explicit noise and potentially lowering energy and privacy costs in wireless systems.

Abstract

Two physical-layer mechanisms for achieving user-side differential privacy in communication systems are proposed. Focusing on binary phase-shift keying (BPSK) modulation, differential privacy (DP) is first studied under a deterministic phase rotation applied on the BPSK modulation at the transmitter, while the receiver is assumed to be unaware of the rotation angle. In this setting, privacy is achieved through an effective reduction in the decision distance, resulting in a controlled increase in the bit error rate (BER) without explicit noise injection. Next, a BPSK transmission scheme with intentionally induced inter-symbol interference (ISI) is studied, where the receiver is likewise unaware of the deterministic timing offset that generates the ISI. Unlike the rotated BPSK scheme, the DP obtained via ISI is shown to depend explicitly on the input data distribution. In particular, numerical results demonstrate that, for a fixed ISI parameter, the privacy loss is maximized when the binary input symbols are equiprobable. While conventional DP mechanisms rely on artificially added noise, often incurring additional energy or communication costs, it is shown that structured modifications, such as modulation rotation or induced ISI inherent to realistic communication channels can itself provide DP guarantees. While the analysis focuses on deterministic transmitter modifications unknown to the receiver, it is noted that real-world devices naturally introduce unintentional rotations or ISI due to hardware nonidealities and implementation errors. These effects can therefore provide a level of privacy without requiring explicit noise injection. Hence, it is possible to avoid deliberately perturbing the data, instead leveraging inherent device imperfections to achieve privacy guarantees with no additional privacy cost.
Paper Structure (14 sections, 3 theorems, 36 equations, 3 figures)

This paper contains 14 sections, 3 theorems, 36 equations, 3 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Main results
  4. Privacy via SNR
  5. Privacy via a Deterministic Phase Rotation
  6. Privacy via a Deterministic Offset
  7. Numerical Results
  8. Privacy via Phase Rotation
  9. Privacy via ISI
  10. Privacy–BER Tradeoff
  11. Conclusion
  12. Proof of Lemma \ref{['lemma1']}
  13. Proof of Corollary \ref{['cor1']}
  14. Proof of Lemma \ref{['lemma2']}

Key Result

Lemma 1

When sinc function is used as the pulse, i.e., $g(\tau) = \mathop{\mathrm{sinc}}\nolimits(\tau) =\frac{\sin{\pi\tau}}{\pi \tau}$, and $\tau\in(0,1)$ we have

Figures (3)

  • Figure 1: Privacy loss ($\varepsilon$) as a function of the rotation angle ($\alpha$), with $\alpha$ ranging from $0$ to $\pi/2$.
  • Figure 2: Privacy loss ($\varepsilon$) as a function of the ISI offset parameter ($\tau$), with $\tau \in [0,, T=1]$, for different values of the input distribution parameter $p$.
  • Figure 3: Privacy level ($\varepsilon$) as a function of the bit error rate (BER) for both phase rotation and intentional intersymbol interference.

Theorems & Definitions (5)

  • Definition 1: Differential Privacy
  • Remark 1
  • Lemma 1
  • Corollary 1
  • Lemma 2