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Capacity Bounds on Doppler OFDM Channels

Pablo Orellana, Zheng Li, Jean-Marc Kelif, Sheng Yang, Shlomo Shamai

TL;DR

This work analyzes the capacity of Doppler-affected OFDM channels in low Earth orbit scenarios by modeling residual Doppler uncertainty as a rank-one channel perturbation $H = F + s G$. It derives both achievable lower bounds via Gaussian signaling and a practical two-layer superposition scheme with subspace alignment, and a capacity upper bound via a duality approach, demonstrating that at most $N-1$ degrees of freedom are available under rank-one uncertainty. The proposed subspace-aligned SN scheme uses a coarse layer as an implicit pilot to enable decoding of a refined layer, achieving near-capacity performance with low receiver complexity, and is validated through Doppler-OFDM NTN simulations. The results provide practical guidelines for robust, high-rate communications in Doppler-rich NTN links and highlight the fundamental limits imposed by Doppler-induced channel uncertainty.

Abstract

Low Earth orbit (LEO) satellite systems experience significant Doppler effects due to high mobility. While Doppler shifts can be largely compensated, residual frequency uncertainty induces a structured form of channel uncertainty that can limit achievable rates. We model this effect using a block-fading channel of the form $ \mathbf{H} = \mathbf{F} + s \mathbf{G} $, where $s$ is an unknown scalar random parameter. We first study this model in a general $N\times N$ MIMO setting. For this channel, we derive achievable rate lower bounds based on explicit transmission schemes and capacity upper bounds using a duality approach. We study Gaussian signaling and propose a practical superposition scheme with subspace alignment (SN) and successive interference cancellation, where a coarse-layer stream serves as an implicit pilot for decoding refined-layer data. We characterize asymptotic capacity in the near-coherent and high-SNR regimes, and show via Doppler-OFDM simulations that the proposed SN scheme achieves near-optimal rates with low complexity.

Capacity Bounds on Doppler OFDM Channels

TL;DR

This work analyzes the capacity of Doppler-affected OFDM channels in low Earth orbit scenarios by modeling residual Doppler uncertainty as a rank-one channel perturbation . It derives both achievable lower bounds via Gaussian signaling and a practical two-layer superposition scheme with subspace alignment, and a capacity upper bound via a duality approach, demonstrating that at most degrees of freedom are available under rank-one uncertainty. The proposed subspace-aligned SN scheme uses a coarse layer as an implicit pilot to enable decoding of a refined layer, achieving near-capacity performance with low receiver complexity, and is validated through Doppler-OFDM NTN simulations. The results provide practical guidelines for robust, high-rate communications in Doppler-rich NTN links and highlight the fundamental limits imposed by Doppler-induced channel uncertainty.

Abstract

Low Earth orbit (LEO) satellite systems experience significant Doppler effects due to high mobility. While Doppler shifts can be largely compensated, residual frequency uncertainty induces a structured form of channel uncertainty that can limit achievable rates. We model this effect using a block-fading channel of the form , where is an unknown scalar random parameter. We first study this model in a general MIMO setting. For this channel, we derive achievable rate lower bounds based on explicit transmission schemes and capacity upper bounds using a duality approach. We study Gaussian signaling and propose a practical superposition scheme with subspace alignment (SN) and successive interference cancellation, where a coarse-layer stream serves as an implicit pilot for decoding refined-layer data. We characterize asymptotic capacity in the near-coherent and high-SNR regimes, and show via Doppler-OFDM simulations that the proposed SN scheme achieves near-optimal rates with low complexity.
Paper Structure (18 sections, 5 theorems, 72 equations, 1 figure, 1 table)

This paper contains 18 sections, 5 theorems, 72 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Notation
  3. System Model and Problem Formulation
  4. Motivating example: OFDM channel with Doppler effects
  5. Abstract channel model
  6. Achievability with Gaussian Signaling
  7. Optimal decoding
  8. Linear receiver and GMI bound
  9. Superposition Coding and Subspace Alignment
  10. Subspace alignment precoding
  11. Coarse layer encoding and decoding
  12. Estimation of $s$ from $\pmb{x}_p$ via orthogonal projection
  13. Conditional LMMSE of $\pmb{w}_d$ given $(\hat{s},\pmb{x}_p)$
  14. Achievable rate
  15. Capacity upper bound
  16. ...and 3 more sections

Key Result

Proposition 1

The channel capacity satisfies where

Figures (1)

  • Figure 1: Comparison of capacity bounds for Doppler-OFDM channel with $1024$ subcarriers. Left: $\sigma=0.1$. Right: $\sigma=0.01$.

Theorems & Definitions (6)

  • Proposition 1: Gaussian signaling with optimal decoding
  • Proposition 2: Gaussian signaling with linear receiver
  • Lemma 1
  • proof
  • Proposition 3: Superposition coding with subspace alignment
  • Proposition 4