Browsing by Author "Gao, Xiqi"
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Item Channel Estimation for Massive MIMO: An Information Geometry Approach(IEEE Transactions on Signal Processing, 2022-10-04) Yang, Jiyuan; Lu, An-An; Chen, Yan; Gao, Xiqi; Xia, Xiang-Gen; Slock, Dirk T. M.In this paper, we investigate the channel estimation for massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Using the sampled steering vectors in the space and frequency domain, we first establish a space-frequency (SF) beam based statistical channel model. The accuracy of the channel model can be guaranteed with sufficient sampling steering vectors. With the channel model, the channel estimation is formulated as obtaining the a posteriori information of the beam domain channel. We solve this problem by calculating an approximation of the a posteriori distribution's marginals within the information geometry framework. Specifically, by viewing the set of Gaussian distributions and the set of the marginals as a manifold and its e -flat submanifold, we turn the calculation of the marginals into an iterative projection process between submanifolds with different constraints. We derive the information geometry approach (IGA) for channel estimation by calculating the solutions of projections. We prove that the mean of the approximate marginals at the equilibrium of IGA is equal to that of the a posteriori distribution. Simulations demonstrate that the proposed IGA can accurately estimate the beam domain channel within limited iterations.Item Ergodic Sum Rate Capacity Achieving Transmit Design for Massive MIMO LEO Satellite Uplink Transmission(IEEE Transactions on Aerospace and Electronic Systems, 2024-02-16) Li, Ke-Xin; Gao, Xiqi; Xia, Xiang-GenIn 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.Item Precoder Design for Massive MIMO Downlink With Matrix Manifold Optimization(IEEE Transactions on Signal Processing, 2024-02-12) Sun, Rui; Wang, Chen; Lu, An-An; Gao, Xiqi; Xia, Xiang-GenWe investigate the weighted sum-rate (WSR) maximization linear precoder design for massive multiple-input multiple-output (MIMO) downlink. We consider a single-cell system with multiple users and propose a unified matrix manifold optimization framework applicable to total power constraint (TPC), per-user power constraint (PUPC) and per-antenna power constraint (PAPC). We prove that the precoders under TPC, PUPC and PAPC are on distinct Riemannian submanifolds, and transform the constrained problems in Euclidean space to unconstrained ones on manifolds. In accordance with this, we derive Riemannian ingredients, including orthogonal projection, Riemannian gradient, Riemannian Hessian, retraction and vector transport, which are needed for precoder design in the matrix manifold framework. Then, Riemannian design methods using Riemannian steepest descent, Riemannian conjugate gradient and Riemannian trust region are provided to design the WSR-maximization precoders under TPC, PUPC or PAPC. Riemannian methods do not involve the inverses of the large dimensional matrices during the iterations, reducing the computational complexities of the algorithms. Complexity analyses and performance simulations demonstrate the advantages of the proposed precoder design.Item Structured Hybrid Message Passing Based Channel Estimation for Massive MIMO-OFDM Systems(IEEE Transactions on Vehicular Technology, 2023-01-26) Liu, Xiaofeng; Wang, Wenjin; Gong, Xinrui; Fu, Xiao; Gao, Xiqi; Xia, Xiang-GenThis paper investigates uplink channel estimation for massive multi-input multi-output orthogonal frequency division multiplexing (MIMO-OFDM) systems with uniform planar array (UPA) antennas at the base station (BS). We first establish a triple beam-based channel model using sampled steering vectors. Based on the presented channel model, we further develop a three-dimensional (3D) Markov random field (MRF) probability model to capture the structured channel sparsity. Then constrained Bethe free energy (BFE) minimization is introduced to provide a systematic theoretical framework for message passing. Under this framework, we derive a structured hybrid message passing (SHMP) algorithm to address the channel estimation problem. The proposed algorithm can significantly improve the estimation accuracy by exploiting the clustered sparse structure of channels with low complexity. Moreover, aiming at the fine factors of the triple beam-based channel model and the coupling parameter of the 3D-MRF sparsity model, we analyze the effect of their different settings in the numerical simulation. Finally, extensive simulation results verify the superiority of the proposed SHMP algorithm.