Space-Air-Ground-Integrated Networks: The BER vs. Residual Delay and Doppler Analysis

TL;DR

This work addresses BER performance in Space-Air-Ground Integrated Networks (SAGINs) under non-ideal Doppler compensation and synchronization delays by developing a practical channel model that blends correlated Shadowed-Rician fading, Snell-law path loss, atmospheric absorption, elliptical LEO orbits, and relativistic time effects. It derives a correlation coefficient for the pilot-data pair, and shows the channel can be mimicked by a bi-variate Gamma distribution, enabling a closed-form BER for 16-QAM with least-squares channel estimation. The paper further presents a comprehensive analysis of residual Doppler via Jakes’ model and demonstrates how the residual Doppler, atmospheric shadowing, synchronization errors, and pilot overhead influence BER in L-band SAGINs, with concrete results for a 300 km altitude LEO. The contributions offer practical insights for SAGIN transmitter/receiver design and synchronization strategies under time-varying, relativistic conditions, and establish a tractable BER expression for time-varying SAGIN channels. Overall, the results highlight the importance of accounting for elliptical orbital dynamics and relativity in BER performance and demonstrate feasible closed-form performance predictions for advanced SAGIN deployments.

Abstract

Perfect Doppler compensation and synchronization is nontrivial due to multi-path Doppler effects and Einstein's theory of relativity in the space-air-ground-integrated networks (SAGINs). Hence, by considering the residual Doppler and the synchronization delay, this paper investigates the bit-error-rate (BER) performance attained under time-varying correlated Shadowed-Rician SAGIN channels. First, a practical SAGIN model is harnessed, encompassing correlated Shadowed-Rician channels, the Snell's law-based path loss, atmospheric absorption, the line-of-sight Doppler compensation, elliptical satellite orbits, and Einstein's theory of relativity. Then, a specific correlation coefficient between the pilot and data symbols is derived in the context of correlated Shadowed-Rician Channels. By exploiting this correlation coefficient, the channel distribution is mimicked by a bi-variate Gamma distribution. Then, a closed-form BER formula is derived under employing least-square channel estimation and equalization for 16-QAM. Our analytical results indicate for a 300-km-altitude LEO that 1) the period of realistic elliptical orbits is around 0.8 seconds longer than that of the idealized circular orbits; and 2) the relativistic delay is lower than 1 $μs$ over a full LEO pass (from rise to set). Our numerical results for the L bands quantify the effects of: 1) the residual Doppler; 2) atmospheric shadowing; 3) synchronization errors; and 4) pilot overhead.

Figures (7)

• Figure 1: Illustration of the system model: (a) Channel model and (b) Elliptical orbits & Einstein's theory of relativity.
• Figure 2: The comparison between the circular orbit and elliptical orbit.
• Figure 3: Comparison between Monte Carlo simulations and analytical results for the bi-variate PDF and CDF: Fig. (a)--(d) are the simulated and theoretical joint PDFs and marginal PDFs; Fig. (e)--(h) express the simulated and theoretical joint CDFs and marginal CDFs.
• Figure 4: BER performance versus the receive SNR with different atmospheric shadowing effects ($m= \{2,4,12\}$). (Theorem \ref{['T_Gamma_Correlation']} and Theorem\ref{['T_BER_MQAM']})
• Figure 5: BER performance versus the receive SNR with the different Rician factor ($K= \{2,5,10\}$ dB). (Theorem \ref{['T_Gamma_Correlation']} and Theorem\ref{['T_BER_MQAM']})

Theorems & Definitions (8)

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