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.

翻译：在空天地一体化网络中，由于多径多普勒效应及爱因斯坦相对论的影响，实现完美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与同步延迟，研究了时变相关阴影莱斯信道下空天地一体化网络所能达到的误码率性能。首先，构建了一个实用的空天地一体化网络模型，该模型涵盖了相关阴影莱斯信道、基于斯涅尔定律的路径损耗、大气吸收、视距多普勒补偿、椭圆卫星轨道以及爱因斯坦相对论。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之间的特定相关系数。利用该相关系数，通过双变量伽马分布对信道分布进行了近似。进而，针对采用最小二乘信道估计与均衡的16-QAM系统，推导了误码率的闭式表达式。我们的分析结果表明，对于高度为300公里的低地球轨道卫星：1）实际椭圆轨道的周期比理想化圆轨道长约0.8秒；2）在一次完整的低地球轨道卫星过境期间（从升起到落下），相对论延迟低于1微秒。我们在L波段的数值结果量化了以下因素的影响：1）残余多普勒；2）大气阴影效应；3）同步误差；4）导频开销。