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Symbol-Aware Precoder Design for Physical-Layer Anonymous Communications

Yu Li, Milad Tatar Mamaghani, Xiangyun Zhou, Nan Yang

TL;DR

This paper considers an anonymous communication problem where the receiver should reliably decode the signal from the transmitter but should not make use of the signal to infer the transmitter's identity, and proposes an anonymous symbol-level precoding strategy that preserves reliable communication under spatial multiplexing while preventing transmitter identification.

Abstract

Physical-layer characteristics, such as channel state information (CSI) and transmitter noise induced by hardware impairments, are often uniquely associated with a transmitter. This paper investigates transmitter anonymity at the physical layer from a signal design perspective. We consider an anonymous communication problem where the receiver should reliably decode the signal from the transmitter but should not make use of the signal to infer the transmitter's identity.Transmitter anonymity is quantified using a Kullback-Leibler divergence (KLD)-based metric, which enables the formulation of explicit anonymity constraints in the precoder design.We then propose an anonymous symbol-level precoding strategy that preserves reliable communication under spatial multiplexing while preventing transmitter identification. The proposed framework employs a partitioned equal-gain combining (P-EGC) scheme that leverages receiver diversity without requiring transmitter-specific CSI. Simulation results demonstrate anonymity-reliability tradeoffs across different signal-to-noise ratios (SNRs) and numbers of data streams. Moreover, the results reveal opposite trends of anonymity with respect to transmitter-dependent noise variations in the low-SNR and high-SNR regimes.

Symbol-Aware Precoder Design for Physical-Layer Anonymous Communications

TL;DR

This paper considers an anonymous communication problem where the receiver should reliably decode the signal from the transmitter but should not make use of the signal to infer the transmitter's identity, and proposes an anonymous symbol-level precoding strategy that preserves reliable communication under spatial multiplexing while preventing transmitter identification.

Abstract

Physical-layer characteristics, such as channel state information (CSI) and transmitter noise induced by hardware impairments, are often uniquely associated with a transmitter. This paper investigates transmitter anonymity at the physical layer from a signal design perspective. We consider an anonymous communication problem where the receiver should reliably decode the signal from the transmitter but should not make use of the signal to infer the transmitter's identity.Transmitter anonymity is quantified using a Kullback-Leibler divergence (KLD)-based metric, which enables the formulation of explicit anonymity constraints in the precoder design.We then propose an anonymous symbol-level precoding strategy that preserves reliable communication under spatial multiplexing while preventing transmitter identification. The proposed framework employs a partitioned equal-gain combining (P-EGC) scheme that leverages receiver diversity without requiring transmitter-specific CSI. Simulation results demonstrate anonymity-reliability tradeoffs across different signal-to-noise ratios (SNRs) and numbers of data streams. Moreover, the results reveal opposite trends of anonymity with respect to transmitter-dependent noise variations in the low-SNR and high-SNR regimes.
Paper Structure (19 sections, 1 theorem, 44 equations, 7 figures, 1 algorithm)

This paper contains 19 sections, 1 theorem, 44 equations, 7 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. Our Contributions
  4. Organization and Notation
  5. System Model
  6. Signal Representation
  7. Transmitter Detection Strategy
  8. Anonymity Metric: Detection Error Rate
  9. Anonymity Metric: Information-theoretic Metric
  10. Transmitter Anonymity Constraint
  11. Anonymous Communication Design
  12. Constructive Interference Precoder
  13. Partitioned Equal-Gain Combiner
  14. Anonymous Precoding Requirements
  15. Design Problem and Solution
  16. ...and 4 more sections

Key Result

Lemma 1

The KLD between the distributions $p_k$ and $p_i$, defined in KLdef, admits the following closed-form expression:

Figures (7)

  • Figure 1: Illustration of CI precoding for QPSK modulation. The green area represents the constructive decision region and the black points denote the reference constellation symbols. The parameter $\gamma$ indicates the minimum in-phase distance from the origin. The blue point corresponds to a received symbol $x_m^{\ell}$ on stream $m$ at timeslot $\ell$, with $s_m^{\ell}$ denoting the corresponding target constellation symbol. After rotating the point by the negative phase of the first-quadrant reference symbol, the rotated point lies in the constructive region if the ratio between its imaginary and real components remains within the $\pm\tan \theta$ boundaries, where $\theta = 45^\circ$ for QPSK.
  • Figure 2: DER vs. SNR under different anonymity relaxations $\epsilon$.
  • Figure 3: Average symbol error rate (SER) vs. SNR with different $\epsilon$.
  • Figure 4: SER-DER tradeoff under different transmit SNRs and $\epsilon$.
  • Figure 5: SER-DER tradeoff under different number of data streams $N_s$ and $\epsilon$. The SNR is set to $20$ dB.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Remark 1
  • Remark 2
  • Lemma 1
  • proof
  • Remark 3