Ultra-Reliable and Low-Latency Communication (URLLC) requires stable transmission under strict latency and high-reliability constraints. Consequently, passive retransmission, which merely waits for bit errors to occur, cannot meet these stringent control and security requirements. This paper proposes an active feedback mechanism, namely the Transmission Prediction Feedback Network (TPFNet). It leverages trajectory-aware modeling and post-decoding statistics to perform risk assessment and guide strategy switching, thereby proactively managing subsequent retransmissions. The TPFNet concept is based on utilizing the historical progression of symbols on the constellation diagram as an initial reference, integrating memory-augmented trajectory-aware modeling. This approach ensures that decision-making is not confined to the instantaneous state received at a single point in time. Initially, it uses the in-phase and quadrature path trajectories of the received sequence to jointly assess instantaneous deviations and temporally cumulative morphological changes. Secondly, it employs residual regression for the calibration of symbol positions, complemented by a concentric constraint loss to mitigate shrinkage bias toward the constellation origin. Finally, it provides a confidence metric for the transceiver link, which facilitates adaptive modulation and coding scheme switching. Simulation results demonstrate that the proposed method significantly enhances transmission fidelity under diverse channel conditions. It markedly improves the block error rate and undetected error rate while enhancing the robustness of symbol decisions at the boundaries.

With advancements in wireless communication and localization technologies, cellular networks are evolving towards integrated sensing and communication (ISAC) capabilities. To address the challenges of sensing-assisted communication, we introduce the digital twin of channel (DToC). Specifically, locations of user terminals (UTs) and their statistical channel state information (sCSI) are treated as physical objects and virtual counterparts in the concept of digital twin (DT), respectively. In this work, we establish a probabilistic model that characterizes sCSI as a location-conditioned distribution. To enable precise sCSI generation, we enhance the latent diffusion model (LDM) and propose an improved latent diffusion model (ILDM) with deterministic sampling. We further propose an accelerated LDM method to speed up the generation process by skipping certain sampling steps. Simulation results demonstrate that the proposed ILDM achieves high accuracy in generating sCSI, while the accelerated LDM delivers significant speedups with minor performance degradation. Our results also validate that the DToC framework can effectively generate sCSI without pilot overhead.

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 propose the precoder design for user-centric network (UCN) massive multiple-input multiple-output (mMIMO) downlink with symplectic optimization. In the UCN mMIMO systems, each user terminal (UT) is served by a subset of base stations (BSs) rather than all BSs, which simplifies the system implementation and reduces the dimension of the precoders to be designed. To address the high complexity of the matrix inversion in traditional linear precoders, we employ symplectic optimization. To better fit the symplectic optimization method, we transform the receive model into the real field. By utilizing the conversion between potential and kinetic energy in physics, we iteratively obtain the precoder vectors directly. Simulation results demonstrate that the proposed method outperforms the weighted minimum mean-squared error (WMMSE) and regularized zero forcing (RZF) precoders, while also exhibiting lower complexity.

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.

With the advancement of communication technology and the improvement of localization accuracy, cellular networks are gradually evolving from communication to perception-integrated networks. Addressing the research challenges of sensing-assisted communication, we propose, for the first time, the concept of Digital Twin of Channel (DToC). Specifically, we regard user terminal (UT) positions as physical objects, and statistical channel state information (CSI) as virtual digital objects. Observing the change trend of UTs’ statistical CSI caused by the changes of UT’s physical position enables predictive analytics for subsequent communication tasks. Then, we establish the relationship between physical and virtual digital objects using a Diffusion Model (DM) to achieve the DToC. Indeed, the DM can generate the desired objects by gradually denoising from noisy data using neural networks. Furthermore, we propose a conditional DM utilizing UTs’ positions, which completes the task of generating the corresponding statistical CSI under known user-specific position conditions, thus mapping UT positions to statistical CSI. Simulation results demonstrate that our DToC framework outperforms previous statistical CSI estimation methods. Without the need of pilots, our method can simultaneously generate statistical CSIs from a large number of UTs’ positions, achieving satisfactory results.

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.

In this paper, we prove the convergence of the simplified information geometry approach (SIGA), which was proposed for massive MIMO-OFDM channel estimation. For a general Bayesian inference problem, we first show that the iteration of the common second-order natural parameter (SONP) is separated from that of the common first-order natural parameter (FONP). Hence, the convergence of the common SONP can be checked independently. We show that with the initialization satisfying a specific but large range, the common SONP is convergent regardless of the value of the damping factor. For the common FONP, we establish a sufficient condition of its convergence and prove that the convergence of the common FONP relies on the spectral radius of a particular matrix related to the damping factor. We give the range of the damping factor that guarantees the convergence in the worst case. Further, we determine the range of the damping factor for massive MIMO-OFDM channel estimation by using the specific properties of the measurement matrices. Simulation results are provided to confirm the theoretical results.

In this paper, we study the coordinated multicast and unicast transmission for cellular-based vehicle-to-vehicle (C-V2V) massive multiple-input multiple-output (MIMO) in the scenario where only imperfect channel state information is available at the base station side and the transmitter in each V2V communication pair. The precoding design problem is a weighted ergodic sum-rate maximization problem with the imperfect CSI including channel mean and variance information known, and the objective function is the weighted sum of the achievable ergodic unicast rate for all the V2V pairs and the achievable ergodic multicast rate for all the cellular users. The minimize-maximize (MM) algorithm and the deterministic equivalent method are utilized to solve the problem and reduce the computational complexity. The simulation results demonstrate the significant improvements of the proposed coordinated communication method in the system spectral efficiency.

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.

Wireless positioning is crucial for Internet of Things (IoT) landscape, enhancing precision and reliability in location-based services. This article addresses the challenges of existing massive multiple-input–multiple-output fingerprint positioning methods, which typically require accurate channel estimation and one-by-one labeled data sets. We propose a semisupervised representation contrastive learning technique that leverages a partially labeled received pilot signal data set readily available from the base station. Our approach employs data augmentation to generate a large number of positive and negative sample pairs, which are then used to pretrain an encoder with a contrastive loss function in the self-supervision way. During pretraining, the encoder learns to encode positive samples close to an anchor, while keeping negative samples far away in the representation space. A fully connected layer is added on top of the encoder for position regression, and the encoder and regression networks are fine-tuned with a small labeled subdataset for the downstream positioning task. Simulation results demonstrate that our pretraining and fine-tuning approach outperforms the previous methods, significantly improving positioning accuracy, avoiding exact channel estimation and achieving labeling efficiency.

In this paper, we investigate the beam domain statistical channel state information (CSI) estimation for the two-dimensional (2D) beam-based statistical channel model (BSCM) in massive multi-input multi-output (MIMO) systems. The problem is to estimate the beam domain channel power matrices (BDCPMs) based on multiple received pilot signals. A received signal model showing the relation between the statistical properties of the received pilot signals and the BDCPMs is derived. On the basis of the received signal model, we formulate an optimization problem with the Kullback-Leibler (KL) divergence. By solving the optimization problem, a novel method to estimate the statistical CSI without the estimates of instantaneous CSI is proposed. We further reduce the complexity of the proposed method by utilizing the circulant structures of particular matrices in the algorithm. We also showed the generality of the proposed method by introducing another application,i.e., estimation of the angle domain channel power matrix. Simulation results show that the proposed method has good convergence and can obtain sparse BDCPMs. Compared with the regularized multiple measurement vector focal underdetermined system solver (RM-FOCUSS) algorithm, the proposed algorithm obtains overall more accurate statistical CSI with much lower complexity and brings significant performance gains when used in channel estimation.

In this paper, we investigate the channel estimation for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. We revisit the information geometry approach (IGA) for massive MIMO-OFDM channel estimation. By using the constant magnitude property of the entries of the measurement matrix and the asymptotic analysis, we find that the second-order natural parameters (SONPs) of the distributions on all the auxiliary manifolds (AMs) are equivalent to each other at each iteration of IGA, and the first-order natural parameters (FONPs) of the distributions on all the AMs are asymptotically equivalent to each other at the fixed point. Motivated by these results, we simplify the iterative process of IGA and propose a simplified IGA for massive MIMO-OFDM channel estimation. It is proved that at the fixed point, the a posteriori mean obtained by the simplified IGA is asymptotically optimal. The simplified IGA allows efficient implementation with fast Fourier transformation (FFT). Simulations confirm that the simplified IGA can achieve near the optimal performance with low complexity in a limited number of iterations.

We propose a cost efficient cross-subcarrier pre-coder design (CSPD) for massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) downlink with imperfect channel state information (CSI). To reduce the high computational complexity caused by individual precoder design for each subcarrier, we design transform domain precoding vectors (TDPVs), from which the precoders for a set of subcarriers can be obtained through a transform. The number of TDPVs is much less than that of subcarriers, and the number of total parameters to be designed can be reduced significantly. The main objective is to maximize an upper bound of the ergodic sum-rate by exploiting the a posteriori beam-based statistical channel model. We provide a concave minorizing function of the upper bound of the ergodic sum-rate and then derive the stationary points of a concave quadratic optimization problem with this minorizing function. To reduce the dimension of the matrix inversion in the stationary points, we propose an algorithm by using block coordinate descent (BCD) method with power allocation.

In this paper, we investigate the downlink robust precoding with imperfect channel state information (CSI) for massive multiple-input-multiple-output (MIMO) communications. With the estimated channel and channel error statistics, the general design of the robust precoder is to maximize the ergodic sum rate subject to the total transmit power constraint. To make the problem more tractable, we find a lower bound of the ergodic sum rate and propose the robust weighted minimum mean-squared-error (WMMSE) precoder to maximize the bound. We characterize the structure of the precoding vectors by low-dimensional parameters, which are learned directly from the available CSI through a neural network. As such, the precoding vectors can be immediately computed without iterations. To extend the deep learning design to multi-antennas users, we present a flexible approach that allows the various antenna configurations at the user side to be handled. Simulation results show that the deep learning design can significantly reduce the computational complexity compared with the existing precoder designs while achieving near optimal performance.

In this paper, we investigate the robust precoding with imperfect channel state information (CSI) for high frequency (HF) skywave massive multiple-input multiple-output (MIMO) communications. Starting with a sparse beam based a posteriori channel model for the available imperfect CSI at the base station (BS), we prove that the robust precoder for ergodic sum-rate maximization can be designed by optimizing the beam domain robust precoder (BDRP) without any loss of optimality. Furthermore, the asymptotic optimal precoder is beam structured for a sufficiently large number of antennas at the BS, involving a low-dimensional BDRP. As a result, the beam structured robust precoding is asymptotic optimal and can be efficiently implemented based on chirp z-transform. We then derive an iterative algorithm to design the BDRP using majorization-minimization (MM). Furthermore, we develop a low-complexity BDRP design with an ergodic sum-rate upper bound, simplifying the MM based design algorithm. Based on our simulation results, the proposed beam structured robust precoding can achieve a near-optimal performance with significantly reduced complexity in various scenarios.

In this paper, we investigate the robust precoding for high frequency skywave massive multiple-input multiple-output communications with imperfect channel state information (CSI). Starting with a sparse beam based a posteriori channel model for the available imperfect CSI at the base station (BS), we prove that the robust precoder for ergodic sum-rate maximization can be designed by optimizing the beam domain robust pre-coder (BDRP) without any loss of optimality. Furthermore, the asymptotic optimal precoder is beam structured for a sufficiently large number of antennas at the BS, involving a low-dimensional BDRP. As a result, the beam structured robust precoding is asymptotic optimal and can be efficiently implemented based on chirp z-transform. We then derive an iterative algorithm to design the BDRP using majorization-minimization. Based on our simulation results, the proposed beam structured robust precoding can achieve a near-optimal performance with significantly reduced complexity in various scenarios.

This paper investigates robust downlink precoding for three-dimensional (3D) massive multi-input multi-output (MIMO) configuration with matrix manifold optimization. Starting with a posteriori channel model, we formulate the robust precoder design to maximize an upper bound of ergodic weighted sum-rate under a total power budget. We derive the generalized eigenvector structure for optimal precoder with matrix manifold optimization. However, since the precoding of multiple users is coupled in the structure, we maximize the objective function for each user in alternation and prove the solution of each individual problem is the generalized eigenvector corresponding to the maximum generalized eigenvalue. In accordance with this, we present an iterative algorithm to design the precoder. Furthermore, we propose a Riemannian conjugate gradient (RCG) method to solve the generalized eigenvalue problem (GEP) for higher efficiency in the precoder design algorithm.

This paper investigates robust downlink precoding for three-dimensional (3D) massive multi-input multi-output (MIMO) configuration with matrix manifold optimization. Starting witha posteriorichannel model, we formulate the robust precoder design to maximize an upper bound of ergodic weighted sum-rate under a total power budget. We derive the generalized eigenvector structure for optimal precoder with matrix manifold optimization. However, since the precoding of multiple users is coupled in the structure, we maximize the objective function for each user in alternation and prove the solution of each individual problem is the generalized eigenvector corresponding to the maximum generalized eigenvalue. In accordance with this, we design an iterative algorithm and present its convergence analysis. Furthermore, we propose a Riemannian conjugate gradient (RCG) method to solve the generalized eigenvalue problem (GEP) for higher efficiency in the precoder design algorithm.

In this paper, we investigate massive multi-input multi-output (MIMO) high frequency (HF) skywave communications. We first introduce a model for HF skywave massive MIMO channels within the orthogonal frequency division multiplexing transmission framework by using the matrix of sampled steering vectors. Considering the large antenna array aperture and increased signal bandwidth, the effect of the propagation delay across the large-scale antenna array cannot be ignored, and thus the steering vectors vary across different subcarriers. Specifically, we derive a wideband beam based channel model and show that the beam domain statistical channel state information (CSI) is frequency-independent. Then, we consider minimum mean-squared error (MMSE) based uplink receiver and downlink precoder with perfect CSI at the base station (BS). With a large number of antennas at the BS, the sum-rate can be asymptotically increased proportionally to the number of user terminals (UTs) while the transmit power per UT is scaled down inverse-proportionally to the number of antennas. In order to reduce the design complexities of the MMSE receiver and precoder, we derive a polynomial expansion based design using a deterministic equivalent. Simulation results demonstrate very significant performance advantages of the proposed HF skywave massive MIMO system.

In this paper, we investigate massive multi-input multi-output (MIMO) high frequency (HF) skywave communications. We first introduce a model for HF skywave massive MIMO channels within the orthogonal frequency division multiplexing transmission framework by using the matrix of sampled steering vectors. The steering vectors vary across different subcarriers due to the effect of the propagation delay across the largescale antenna array. Specifically, we derive a wideband beam based channel model and show that the beam domain statistical channel state information (CSI) is frequency-independent. Then, we consider minimum mean-squared error based uplink receiver and downlink precoder with perfect CSI at the base station (BS). With a large number of antennas at the BS, the sum-rate can be asymptotically increased proportionally to the number of user terminals (UTs) while the transmit power per UT is scaled down inverse-proportionally to the number of antennas. Simulation results demonstrate very significant performance advantages of the proposed HF skywave massive MIMO system.

In this paper, we investigate the massive multi-input multi-output (MIMO) transmission for the satellite communication systems equipped with a uniform rectangular array (URA) and aim to design the precoder with broad coverage radiation power pattern to improve the performance of time and frequency synchronizations. The modified Cramér-Rao vector bounds (MCRVB) are chosen as the benchmark of symbol timing offset and frequency offset estimation problem, which can be viewed as the time and frequency synchronization performance metric for the broad coverage precoder design. By considering the minimax MCRVB criterion and the per-antenna equal power constraint, the precoder design approach is formulated as the non-convex constrained minimax problem over the discrete radiation power pattern. This optimization problem is solved by the smoothing techniques combined with the manifold optimization method. To reduce the calculation complexity, the nonmonotone conjugate gradient method is applied. Simulation results show that the average and the minimum received powers in the coverage area of the proposed scheme are higher than those of the scheme based on fairness criterion. Compared with the existing omnidirectional and broad coverage schemes, the proposed scheme has the best synchronization performance among all the contrast solutions.

In this paper, we investigate broad coverage pre-coder design for 3D massive multi-input multi-output (MIMO) systems. We focus on the synchronization performance in the cell coverage. The log-distance path loss model in the line-of-sight (LoS) scenario is formulated. The synchronization performance can be characterized by the missed detection (MD) probability. By considering the equal MD probability in the cell, we formulate a criterion for the precoder design. Moreover, we consider the equal transmit power constraint on each antenna to efficiently utilize the power amplifier (PA) capacity of the BS. By using the manifold optimization framework, we design the precoder under the aforementioned criterion and constraint. Simulation results show that the fairness among all the users in this cell can be ensured. Compared with the precoders designed by half power beam-width (HPBW), the proposed scheme causes much less inter-cell interference, and has a better synchronization performance.

In this paper, we investigate broad coverage precoder design for 3D massive multi-input multi-output (MIMO) systems, where the base station (BS) is equipped with a uniform rectangular array (URA). We focus on the synchronization performance in the cell coverage. The flat fading channel model is formulated. The synchronization performance can be characterized by the missed detection (MD) probability. By considering the MD probability fairness in the cell, we formulate a criterion for the precoder design. Moreover, we consider the equal transmit power constraint on each antenna to efficiently utilize the power amplifier (PA) capacity of the BS. By using the manifold optimization framework, we design the precoder under the aforementioned criterion and constraint. Simulation results show that the fairness among all the users in this cell can be ensured. Compared with the precoders designed by half power beam-width (HPBW), the proposed scheme causes much less inter-cell interference and has a better synchronization performance.

In this paper, we investigate the omnidirectional precoding for three dimensional (3D) massive multi-input multi-output (MIMO) with uniform planar arrays (UPAs). The omnidirectional precoder is designed for public information transmission, where the channel state information (CSI) is usually not available at the base station (BS) and we would like to guarantee a performance to all users regardless of their angular positions. Thus, the first design objective of the precoding matrices is to satisfy the omnidirectional property, which means that the received mean power is constant at any angle. To ensure the power efficiency of each antenna, the per-antenna constant power constraint is also used in the design. Furthermore, the vectorized precoding matrices need to be mutually orthogonal to guarantee the spectral efficiency. The first two constraints can be satisfied by two dimensional Welti codes or two dimensional Golay arrays, whereas the third constraint is not necessarily satisfied by them. Furthermore, the methods to construct the Welti codes and Golay arrays are only given for certain array sizes. In this paper, we propose a novel and simple array design to construct the precoding matrices that satisfy the three properties. Based on the proposed array design, the design of the precoding matrices reduces to the design of a pair of complementary vectors having special structure, and the design of two sets of complementary orthonormal vectors with their aperiodic cross-correlation being zero. Finally, several examples of the omnidirectional precoding matrices for UPA generated by the proposed method are provided to verify the analytic results.

In this paper, we investigate channel estimation and robust signal detection for uplink massive multi-input multioutput orthogonal frequency division multiplexing systems with in-phase and quadrature-phase imbalances. By processing the real and imaginary parts of the received signal individually, we perform minimum mean square error (MMSE) estimation for the effective channel. Adjustable phase shift pilots (APSPs) are used for reducing the pilot overhead. Motivated by the optimal conditions to achieve the lower bound of the MSE of the effective channel estimation, a pilot scheduling algorithm is provided. We further propose an MMSE criterion based detection scheme which is robust to the channel estimation error. An analytical expression for the asymptotic achievable sum rate of the proposed detection is derived via using operator valued free probability theory. The performance of the channel estimation with APSPs and the robust MMSE detection are demonstrated by numerical results.

In this paper, we design the precoding matrix with broad coverage for massive multi-input multi-output public channels. In order to guarantee the efficient use of power amplifiers and improve the achievable ergodic rate, equal transmit power per-antenna and semi-unitary constraints on the precoding matrix are considered simultaneously. Within the framework of manifold optimization, the precoding matrix design under the above two constraints becomes an optimization problem over the intersection of the oblique manifold and the Stiefel manifold. We propose to use the steepest descent method on the intersection of these two manifolds to obtain the optimal solution. By using the alternating projections method, the search direction of the steepest descent method is derived. Meanwhile, the convergence analysis for the proposed approach is also provided. The proposed approach can be used for both omnidirectional and sector-shaped power pattern design. Simulation results show that the power pattern of our designed precoder has less variation in different spatial directions within the cell coverage compared with the existing Zadoff-Chu scheme.

In this paper, the design of robust linear precoders for the massive multi-input-multi-output (MIMO) downlink with imperfect channel state information (CSI) is investigated. The imperfect CSI for each UE obtained at the BS is modeled as statistical CSI under a jointly correlated channel model with both channel mean and channel variance information, which includes the effects of channel estimation error, channel aging, and spatial correlation. The design objective is to maximize the expected weighted sum-rate. By combining the minorize-maximize (MM) algorithm with the deterministic equivalent method, an algorithm for robust linear precoder design is derived. The proposed algorithm achieves a stationary point of the expected weighted sum-rate maximization problem. To reduce the computational complexity, two low-complexity algorithms are then derived. One for the general case, and the other for the case when all the channel means are zeros. For the later case, it is proved that the beam domain transmission is optimal, and thus the precoder design reduces to the power allocation optimization in the beam domain. Simulation results show that the proposed robust linear precoder designs apply to various mobile scenarios and achieve high spectral efficiency.

In this paper, we design the precoding matrix with broad coverage for massive multi-input multi-output (MIMO) public channels. To sufficiently utilize the power amplifier (PA) capacity of the base station (BS), all the rows of the precoding matrix should have the same 2-norm to guarantee equal transmit power on each antenna. In the meanwhile, the precoding matrix is semi-unitary, which can maximize the achievable ergodic rate for the independent and identically distributed (i.i.d.) channel. Within the framework of manifold optimization, the precoding matrix design under the above two constraints becomes an optimization problem over the intersection of the oblique manifold and the Stiefel manifold. We propose to use the steepest descent method on the intersection of these two manifolds to obtain the optimal solution. By using the alternating projections method, the search direction of the steepest descent method is derived. In the meanwhile, the convergence analysis for the proposed approach is also provided. Simulation results show that the power pattern of our designed precoder has less variation in different spatial directions within the cell compared with the existing schemes.

In this paper, the design of linear precoders for simultaneously wireless information and power transfer (SWIPT) over multi-input multi-output (MIMO) broadcast channels with discrete input signals is investigated. The considered system model consists of one base station (BS), one information receiver (IR) and one energy receiver (ER). The design objective is to maximize the input-output mutual information of the IR subject to the harvested energy requirement for the ER. The structure of the optimal precoder is derived by using the methods of manifold optimization, and an algorithm is proposed to find the optimal precoder. Simulation results show that the proposed algorithm can achieve better performance than the time sharing scheme and the optimal precoder designed for Gaussian inputs.

In this paper, we investigate the design of linear precoders for simultaneously wireless information and power transfer (SWIPT) in a multi-input multi-output (MIMO) broadcasting system with discrete input signals. The considered system model consists of one base station (BS), one information receiver (IR), and one energy receiver (ER). The design objective is to maximize the input-output mutual information of the IR subject to the power constraint and the harvested energy requirement for the ER. We derive the structure of the optimal linear precoder by using manifold optimization, and propose an algorithm to find the optimal precoder. Simulation results show that the proposed algorithm can achieve better performance than the time sharing scheme and the Gaussian optimal precoder when Gaussian inputs are replaced by discrete input signals.

We consider a low complexity polynomial expansion (PE) detector in a massive multiple-input multiple-output (MIMO) uplink channel. In contrast to most massive MIMO systems in the literature, where single antenna user equipments (UEs) are assumed, multiple antenna UEs are employed in this paper. Moreover, the channel between a base station (BS) and a UE is a jointly correlated Rician fading channel. The PE detector reduces the computational complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. The coefficients of the approximate matrix polynomial are computed from the deterministic equivalents of the moments of the channel Gram matrix. We use operator-valued free probability, which is a more general version of free probability, to derive the deterministic equivalents. In particular, we use the operator-valued moment-cumulant formula. The proposed low complexity PE detector is easy to compute. Simulation results show that the proposed detector can achieve performance close to the MMSE detector.

In this paper, a free deterministic equivalent is proposed for the capacity analysis of the multi-input multi-output (MIMO) multiple access channel (MAC) with a more general channel model compared to previous works. In particular, a MIMO MAC with one base station (BS) equipped with several distributed antenna sets is considered. Each link between a user and a BS antenna set forms a jointly correlated Rician fading channel. The analysis is based on operator-valued free probability theory, which broadens the range of applicability of free probability techniques tremendously. By replacing independent Gaussian random matrices with operator-valued random variables satisfying certain operator-valued freeness relations, the free deterministic equivalent of the considered channel Gram matrix is obtained. The Shannon transform of the free deterministic equivalent is derived, which provides an approximate expression for the ergodic input-output mutual information of the channel. The sum-rate capacity achieving input covariance matrices are also derived based on the approximate ergodic input-output mutual information. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.

In this paper, a low complexity polynomial expansion (PE) detector for massive multi-input multi-output (MIMO) uplink transmissions is proposed. In contrast to most massive MIMO systems in the literature, where single-antenna user equipments (UEs) are assumed, multiple-antenna UEs are employed in this paper. Furthermore, each link between a user and the base station forms a jointly correlated Rician fading channel. The PE detector reduces the complexity of the minimum mean square error (MMSE) detector by replacing the matrix inversion with an approximate matrix polynomial. In the design of the low complexity PE detector, the approximations of the moments of the channel Gram matrix are needed. We use operator- valued free probability to derive these approximations. The low complexity PE detector is easy to compute. Simulation results show that it can achieve performance close to the MMSE detector.

In this paper, we propose a free deterministic equivalent for the capacity analysis of multi-input multi-output (MIMO) multiple access channel (MAC) with distributed antenna sets. In the analysis, we use the operator-valued free probability framework, which is much more straightforward than the widely used methods, i.e., the Bai and Silverstein method and the Gaussian method. By replacing independent random Gaussian variables with freely independent circular entries, we obtain the free deterministic equivalent of our channel model. To evaluate the capacity, we use the Shannon transform of the free deterministic equivalent to approximate that of the channel model. The free deterministic equivalent results are easy to compute, and simulation results show that these approximations are numerically accurate and computationally efficient.