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 microsecond 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.

翻译：由于空天地一体化网络（SAGINs）中存在的多径多普勒效应及爱因斯坦相对论，理想的多普勒补偿与同步并非易事。因此，本文通过考虑残余多普勒效应与同步时延，研究了时变相关阴影莱斯SAGIN信道下的误码率（BER）性能。首先，构建了一个实用的SAGIN模型，涵盖相关阴影莱斯信道、基于斯涅尔定律的路径损耗、大气吸收、视距多普勒补偿、椭圆卫星轨道及爱因斯坦相对论。随后，在相关阴影莱斯信道背景下，推导了导频符号与数据符号间的特定相关系数。利用该相关系数，信道分布被模拟为二元伽马分布。进而，针对采用最小二乘信道估计与均衡的16-QAM调制，推导出闭合形式的误码率公式。分析结果表明，对于高度300千米的低轨卫星（LEO）：1）实际椭圆轨道周期比理想圆轨道周期长约0.8秒；2）在完整LEO过境期间（从升起至降落），相对论时延小于1微秒。针对L波段的数值结果量化了以下因素影响：1）残余多普勒效应；2）大气阴影效应；3）同步误差；4）导频开销。