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Maximum Spectral Efficiency With Adaptive MQAM Transmissions Over Terrestrial Coherent FSO Links

Himani Verma, Kamal Singh, Ranjan K. Mallik

TL;DR

This work provides a rigorous theoretical framework for adaptive MQAM in terrestrial coherent FSO links under gamma-gamma turbulence with pointing errors by deriving an exact average spectral-efficiency (ASE) limit for unconstrained MQAM. It demonstrates that a small, finite set of square MQAM constellations can nearly achieve this limit, enabling near-optimal performance with low complexity. The findings show significant SNR/power savings and substantial ASE gains over fixed-constellation systems, offering practical design guidelines for high-rate FSO fronthaul/backhaul links. The results also quantify how pointing errors and turbulence affect the high-SNR ASE, highlighting the value of adaptive modulation in challenging atmospheric conditions.

Abstract

Coherent free-space optical (FSO) communication is recognized as a key enabler for ultra-high-capacity fronthaul and backhaul links in next-generation wireless networks. Spectrally efficient $M$-ary quadrature amplitude modulation (MQAM) formats are well-suited for these links. However, theoretical analyses of adaptive MQAM transmissions over terrestrial FSO channels remain limited. In this letter, we first derive the spectral efficiency limit of adaptive unconstrained MQAM over gamma-gamma turbulence with pointing error. We then show that adaptive transmissions using only six square MQAM constellations performs close to the theoretical limit (within $0.10$-$0.12$ bits/s/Hz) across a wide range of signal-to-noise ratios and channel conditions.

Maximum Spectral Efficiency With Adaptive MQAM Transmissions Over Terrestrial Coherent FSO Links

TL;DR

This work provides a rigorous theoretical framework for adaptive MQAM in terrestrial coherent FSO links under gamma-gamma turbulence with pointing errors by deriving an exact average spectral-efficiency (ASE) limit for unconstrained MQAM. It demonstrates that a small, finite set of square MQAM constellations can nearly achieve this limit, enabling near-optimal performance with low complexity. The findings show significant SNR/power savings and substantial ASE gains over fixed-constellation systems, offering practical design guidelines for high-rate FSO fronthaul/backhaul links. The results also quantify how pointing errors and turbulence affect the high-SNR ASE, highlighting the value of adaptive modulation in challenging atmospheric conditions.

Abstract

Coherent free-space optical (FSO) communication is recognized as a key enabler for ultra-high-capacity fronthaul and backhaul links in next-generation wireless networks. Spectrally efficient -ary quadrature amplitude modulation (MQAM) formats are well-suited for these links. However, theoretical analyses of adaptive MQAM transmissions over terrestrial FSO channels remain limited. In this letter, we first derive the spectral efficiency limit of adaptive unconstrained MQAM over gamma-gamma turbulence with pointing error. We then show that adaptive transmissions using only six square MQAM constellations performs close to the theoretical limit (within - bits/s/Hz) across a wide range of signal-to-noise ratios and channel conditions.

Paper Structure

This paper contains 6 sections, 4 theorems, 31 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. FSO System and Channel Models
  3. Maximum Spectral Efficiency with Adaptive Unconstrained MQAM Constellations
  4. Average Spectral Efficiency With Finite Square MQAM Constellations Set
  5. Numerical Results and Discussion
  6. Conclusion

Key Result

Theorem 1

The maximum ASE achievable by the adaptive unconstrained MQAM transmissions over the GG turbulence channel with pointing errors described in eq:PEPdf, is given by where $\alpha$, $\beta$, $A_\mathrm{ 0}$, $\xi^2$, and $S_k(x,\bar{x},\xi^2)$ coefficients are defined in eq:GG_alpha, eq:GG_beta, eq:redefined_A0, eq:redefined_xi, and eq:sKcoeff, respectively, $\psi(\cdot)$ is the Digamma function, an

Figures (3)

  • Figure 1: Numerical verification of the ASE limits for adaptive MQAM transmissions in Theorems \ref{['eq:thm1']} and \ref{['eq:thm2']} via Monte Carlo simulations ($4 \times 10^{4}$ realizations).
  • Figure 2: Average spectral efficiency of adaptive QAM transmissions over weak gamma-gamma turbulence channel with and without pointing errors.
  • Figure 3: Average spectral efficiency of adaptive QAM transmissions over strong gamma-gamma turbulence channel with and without pointing errors.

Theorems & Definitions (6)

  • Definition
  • Theorem 1
  • Theorem 2
  • Corollary 3
  • Corollary 4
  • Remark