Li, Ke-XinGao, XiqiXia, Xiang-Gen2024-05-212024-05-212024-02-16K. -X. Li, X. Gao and X. -G. Xia, "Ergodic Sum Rate Capacity Achieving Transmit Design for Massive MIMO LEO Satellite Uplink Transmission," in IEEE Transactions on Aerospace and Electronic Systems, doi: 10.1109/TAES.2024.33618851557-9603https://udspace.udel.edu/handle/19716/34420This article was originally published in IEEE Transactions on Aerospace and Electronic Systems. The version of record is available at: https://doi.org/10.1109/TAES.2024.3361885. © 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. See https://www.ieee.org/publications/rights/index.html for more information. This article will be embargoed until 02/16/2026.In this paper, we investigate the ergodic sum rate (ESR) capacity achieving uplink (UL) transmit design for massive multiple-input multiple-output (MIMO) low- earth-orbit (LEO) satellite communications with statistical channel state information at the user terminals (UTs). The UL massive MIMO LEO satellite channel model with uniform planar array configurations at the satellite and UTs is presented. We prove that the rank of each UT's optimal transmit covariance matrix does not exceed that of its channel correlation matrix at the UT side, which reveals the maximum number of independent data streams transmitted from each UT to the satellite. We then prove that the transmit covariance matrix design can be transformed into the lower-dimensional matrix design without loss of optimality. We also obtain a necessary and sufficient condition when single data stream transmission from each UT to the satellite can achieve the ESR capacity. A conditional gradient (CG) method is developed to compute the ESR capacity achieving transmit covariance matrices. Furthermore, to avoid the exhaustive sample average, we utilize an asymptotic expression of the ESR and devise a simplified CG method to compute the transmit covariance matrices, which can approximate the ESR capacity. Simulations demonstrate the effectiveness of the proposed approaches.en-USergodic sum rate capacityLEO satellitesmassive MIMOsatellite uplink transmissionArticle