We investigate a non-orthogonal pilot design for massive multiple-input multiple-output (MIMO) channel estimation with orthogonal frequency division multiplexing (OFDM) modulation. Leveraging two-dimensional (2D) beam based channel model, we formulate a signal model for channel estimation with a comb-type pilot structure. Then, we propose generalized phase shift pilots (GPSPs) and reveal that both GPSPs and their discrete Fourier transform (DFT) have constant modulus, and the DFT of GPSPs also has optimal autocorrelation property and beneficial crosscorrelation property. Subsequently, we prove that the inter-user interference with GPSPs is negligible when the weight sequence length of GPSPs is large enough or when channels can be differentiated in the angle domain, validating the feasibility of GPSPs, especially when the statistical channel state information (CSI) is unavailable. Further, by leveraging the correlation properties of GPSPs, an efficient implementation for GAMP based channel estimation is provided. Simulation results indicate that GPSPs enable low-complexity channel estimation while ensuring satisfactory performance.

In this paper, we investigate the signal detection for user-centric network (UCN) massive multi-input multi-output (mMIMO) system. We consider that the users are divided into multiple user groups (UGs). For each UG, leveraging the interference sparsity, we reveal that the performance of the minimum-mean-square-error (MMSE) detector can be guaranteed in the network mMIMO system by using the matched filtering (MF) outputs of the intra-group and interfering users. Then, with the base station (BS) connection sparsity, we reveal that the detection performance of each UG is primarily determined by a limited number of associated BSs. To facilitate practical application, we propose a straightforward user grouping method and outline the process for determining interfering users and associated BSs for each UG in UCN mMIMO systems. Then, we propose a user-centric detection method that decouples the detection process for each UG into two stages. In the first stage, local MF is performed at each associated BSs using local information. In the second stage, group-wise interference cancellation (IC) is carried out to obtain detection results at the primary serving BS (PSBS) of each UG, with information exchanged from auxiliary serving BSs (ASBSs). Simulation results confirm the effectiveness and computational efficiency of our proposed user-centric detection for the UCN mMIMO system.

In this paper, we propose a low complexity turbo receiver for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) systems. We first introduce the beam based channel model (BBCM) with uniform sampling for directional cosine. By leveraging the BBCM, we reveal the interference sparsity of HF skywave massive MIMO systems, which is defined as the asymptotic sparsity of the channel Gram matrix. Exploiting the interference sparsity, we provide a condition of extracting sufficient observation for signal detection. Motivated by this condition, we construct the interference user terminal (UT) set (IUS) and extract the observation vector from the received signal after matched filtering (MF) for each UT. Then, a low-dimensional interference sparsity-aware detector (ISD) is separately designed for each UT by minimizing the mean-squared error (MSE), and the interference sparsity-aware turbo receiver (ISTR) is subsequently formulated using ISDs. Under a relaxed version of the condition for sufficient observation selection, we prove the optimality of the ISTR. Further, we develop an efficient implementation of the ISTR, involving approximate computation of the ISD, the signal reconstructed by ISD and the channel Gram matrix. Moreover, an efficient construction of IUS using the statistical channel state information (CSI) is also proposed. Simulation results confirm that the proposed ISTR achieves excellent performance with relatively low complexity.

In this paper, we investigate the decoupled designs of precoders and receivers for both downlink (DL) and uplink (UL) in massive multiple-input multiple-output (MIMO) multiple low earth orbit (LEO) satellite communication systems. We first establish the beam based satellite channel model, where the beam matrix is constructed with sampled steering vectors. Then, we propose a decoupled precoder and receiver design for both DL and UL, which allows precoders and receivers to be designed independently at each satellite and user terminal (UT), respectively, with only local statistical channel state information (sCSI). Moreover, with the established beam based channel model, the design of space domain DL precoder and UL receiver can be converted into that of lower-dimensional beam domain vectors with only local sCSI, and the resulting space domain precoder and receiver are beam structured. Furthermore, we propose a low-complexity design and implementation for the beam structured DL precoder and UL receiver by exploiting properties of the beam matrix, significantly reducing the computational complexity. Simulation results validate the proposed approaches.

In this paper, we investigate the precoder design for user-centric network (UCN) massive multiple-input multiple-output (mMIMO) downlink with matrix manifold optimization. In UCN mMIMO systems, each user terminal (UT) is served by a subset of base stations (BSs) instead of all the BSs, facilitating the implementation of the system and lowering the dimension of the precoders to be designed. By proving that the precoder set satisfying the per-BS power constraints forms a Riemannian submanifold of a linear product manifold, we transform the constrained precoder design problem in Euclidean space to an unconstrained one on the Riemannian submanifold. Riemannian ingredients, including orthogonal projection, Riemannian gradient, retraction and vector transport, of the problem on the Riemannian submanifold are further derived, with which the Riemannian conjugate gradient (RCG) design method is proposed for solving the unconstrained problem. The proposed method avoids the inverses of large dimensional matrices, which is beneficial in practice. The complexity analyses show the high computational efficiency of RCG precoder design. Simulation results demonstrate the numerical superiority of the proposed precoder design and the high efficiency of the UCN mMIMO system.

In high-speed railway (HSR) communications, the channel suffers from severe Doppler and channel aging effects caused by the high mobility, making the channel outdated quickly. To address this issue, we investigate the robust precoder design against channel aging and prediction inaccuracy in massive multiple-input multiple-output (MIMO) systems with matrix manifold optimization. First of all, we introduce the concept of the quadruple beams (QBs), and establish a QB based channel model with sampled quadruple steering vectors. Then, the upcoming space domain channel of interest can achieve a higher accuracy by channel prediction with the estimated QB domain channel. To further improve the performance while save the pilot overhead, we predict the forthcoming QB domain channel and integrate the prediction inaccuracy within the a posterior QB domain statistical channel model. Then, we consider the robust precoder design aiming to maximize the upper bound of the ergodic weighted sum-rate (WSR) on the Riemannian submanifold formed by the precoders satisfying the total power constraint (TPC). Riemannian ingredients are derived for matrix manifold optimization, with which the Riemannian conjugate gradient (RCG) method is proposed to solve the unconstrained problem on the manifold. The RCG method mainly involves the matrix multiplication and avoids the need of matrix inversion of the transmit antenna dimension. The simulation results demonstrate the effectiveness of the proposed channel model and the superiority of the RCG method for robust precoder design against channel aging and prediction inaccuracy.

In this paper, we investigate the precoder design for user-centric network (UCN) massive multiple-input multiple-output (mMIMO) downlink with matrix manifold optimization. In UCN mMIMO systems, each user terminal (UT) is served by a subset of the base stations (BSs) instead of all BSs, lowering the dimension of the precoders to be designed. Each BS in the system has a power constraint. By proving that the precoder set satisfying the constraints forms a Riemannian submanifold, we transform the constrained precoder design problem in Euclidean space as an unconstrained one on the Riemannian submanifold. Riemannian ingredients, including orthogonal projection, Riemannian gradient, retraction and vector transport, of the problem on the Riemannian submanifold are further derived, with which the Riemannian conjugate gradient (RCG) design method is proposed for solving the unconstrained problem. The proposed method avoids the inverses of large dimensional matrices. The complexity analyses show the high efficiency of RCG precoder design. Simulation results demonstrate the superiority of the proposed precoder design and the high efficiency of the UCN mMIMO system.

We investigate the weighted sum-rate (WSR) max-imization linear precoder design under total power constraint (TPC) for massive MIMO downlink with matrix manifold optimization. Particularly, we prove that the precoders under TPC are on a Riemannian submanifold, and transform the constrained problem in Euclidean space to the unconstrained one on manifold. In accordance with this, Riemannian design methods using Riemannian steepest descent and Riemannian conjugate gradient are provided to design the WSR-maximization precoders under TPC. Riemannian methods are free of the inverse of large dimensional matrix, posing significant computational savings and potentially allowing to avoid ill numerical behavior in algorithms. Complexity analysis and performance simulations demonstrate the advantages of the proposed precoder design.