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Virtual Polarization Modulation: Enabling CSI-Free DCO-OFDM over Dynamic OWC Channels

Tian Cao, Ping Wang, Tianfeng Wu, Kaile Wang, Jian Song

Abstract

In dynamically varying optical wireless communication (OWC) links, conventional quadrature amplitude modulation (QAM) in optical orthogonal frequency-division multiplexing (OFDM) requires frequent channel estimation and equalization, incurring pilot overhead and processing latency. This paper proposes a virtual polarization modulation (VPM)-based direct-current-biased optical OFDM (DCO-OFDM) scheme that maps each data symbol onto the three-dimensional Stokes space and places its corresponding Jones vector across two adjacent OFDM subcarriers. Using a rotation-based analytical framework, closed-form symbol error rate (SER) expressions are derived for arbitrary spherical constellations, along with upper and lower bounds and high signal-to-noise ratio (SNR) approximations. The framework is further extended to practical OWC scenarios with frequency-selective channels and atmospheric turbulence. Monte Carlo (MC) simulations validate the theoretical results. The results show that under practical OWC impairments, VPM outperforms QAM with least-squares (LS) channel estimation and minimum mean square error (MMSE) equalization. At a target SER of $10^{-5}$, 16-VPM achieves SNR gains of approximately 7.5 dB and 4 dB over equalized 16-QAM and 8-QAM, respectively, in frequency-selective channels, and a 6 dB advantage over equalized 16-QAM under atmospheric turbulence. By eliminating the need for channel state information, the proposed VPM-based DCO-OFDM provides a robust and low-latency solution for dynamic OWC links.

Virtual Polarization Modulation: Enabling CSI-Free DCO-OFDM over Dynamic OWC Channels

Abstract

In dynamically varying optical wireless communication (OWC) links, conventional quadrature amplitude modulation (QAM) in optical orthogonal frequency-division multiplexing (OFDM) requires frequent channel estimation and equalization, incurring pilot overhead and processing latency. This paper proposes a virtual polarization modulation (VPM)-based direct-current-biased optical OFDM (DCO-OFDM) scheme that maps each data symbol onto the three-dimensional Stokes space and places its corresponding Jones vector across two adjacent OFDM subcarriers. Using a rotation-based analytical framework, closed-form symbol error rate (SER) expressions are derived for arbitrary spherical constellations, along with upper and lower bounds and high signal-to-noise ratio (SNR) approximations. The framework is further extended to practical OWC scenarios with frequency-selective channels and atmospheric turbulence. Monte Carlo (MC) simulations validate the theoretical results. The results show that under practical OWC impairments, VPM outperforms QAM with least-squares (LS) channel estimation and minimum mean square error (MMSE) equalization. At a target SER of , 16-VPM achieves SNR gains of approximately 7.5 dB and 4 dB over equalized 16-QAM and 8-QAM, respectively, in frequency-selective channels, and a 6 dB advantage over equalized 16-QAM under atmospheric turbulence. By eliminating the need for channel state information, the proposed VPM-based DCO-OFDM provides a robust and low-latency solution for dynamic OWC links.
Paper Structure (20 sections, 5 theorems, 56 equations, 7 figures)

This paper contains 20 sections, 5 theorems, 56 equations, 7 figures.

Table of Contents

  1. Introduction
  2. System Model and Principle of VPM
  3. VPM-Based Optical OFDM System
  4. VPM Mapping Strategy
  5. CSI-free VPM Demapping in Stokes Space
  6. SER Analysis of VPM-based OFDM over AWGN Channels
  7. SER Derivation and Closed-Form Expression
  8. SER Bounds and High-SNR Approximation
  9. Upper Bound
  10. Lower Bound
  11. SER analysis of VPM-Based OFDM over Optical Wireless Channels
  12. Angular Drift and Average SER under Frequency-Selective Channels
  13. Average SER under Atmospheric Turbulence Channels
  14. Results and Discussions
  15. Conclusion
  16. ...and 5 more sections

Key Result

Lemma 1

Let $\mathbf{E}_i,\mathbf{Y}\in\mathbb{C}^2$ denote the transmitted and received Jones vectors, and let $\mathbf{S}_i,\hat{\mathbf{S}}\in\mathbb{R}^3$ be their corresponding unnormalized Stokes vectors with total powers $E_s=\|\mathbf{E}_i\|^2$ and $\hat{S}_0=\|\mathbf{Y}\|^2$, respectively. Then th where $\mathbf{s}_i=\mathbf{S}_i/E_s$ and $\hat{\mathbf{s}}=\hat{\mathbf{S}}/\hat{S}_0$ are the nor

Figures (7)

  • Figure 1: Block diagram of the VPM-based DCO-OFDM system.
  • Figure 2: Geometric representation of the VPM mapping strategy in the 3D Stokes space. (a) Example of a 16-VPM constellation. (b) Geometric definition of the spherical coordinates $(\theta, \phi)$ corresponding to the Stokes parameters $(S_1, S_2, S_3)$ for the constellation point $\mathbf{S}_i$.
  • Figure 3: Geometric illustration of (a) the received vector $\hat{\mathbf{S}}$ and the transmitted Stokes symbol $\mathbf{S}_i$, and (b) the rotation that aligns $\mathbf{S}_i$ with the north pole of the Poincaré sphere.
  • Figure 4: Average SER comparison between the proposed $M$-VPM and $M$-QAM over AWGN channels with $M \in \{4, 16, 64, 256\}$.
  • Figure 5: Average SER performance of $M$-VPM OFDM with Fibonacci-based and uniformly distributed constellations for $M \in \{4,16,64,128\}$. Theoretical results are validated by MC simulations and compared with the derived upper/lower bounds and the high-SNR approximation.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Theorem 3