Precoding Matrices Research Articles

Performance evaluation of precoding system for massive multiple-input multiple-output

Low latency, high data speeds, and a higher degree of perceived service quality for consumers and base station capacity are only some of the advantages of fifth generation (5G) mobile communications. This paper focuses on the design of a precoding system for downlink transmission of multi-user multiple-input multiple-output (MU-MIMO). For MU-MIMO systems, the traditional precoding techniques investigated are difficult since the transmitter precoding matrices created by singular value decomposition (SVD) are calculated twice. This paper implements different techniques of precoding with channel coding. Two advanced precoding, zero forcing (ZF) and maximum ratio transmitter (MRT) systems will be evaluated to find the best between them. Three different coding channels (turbo, low-density parity-check (LDPC), and polar) are used in this paper. The results indicate that the ZF-MU-MIMO with turbo coding outperforms MRT precoding, and more spatial diversity gain may be gained, in terms of throughput, number of users supported, and lower error rate in downlink and uplink massive MIMO.

Deep Reinforcement Learning for RIS-Aided Multiuser MISO System with Hardware Impairments

In this paper, we study a reconfigurable intelligent surface (RIS)-aided multiuser MISO system with imperfect hardware, where the transceiver design is based on the statistical channel state information (CSI). Considering the transceiver hardware impairments (HWI), we aim to maximize the minimum average user data rate, where the precoding matrices at the base station (BS) and the reflecting phase shifts at the RIS are jointly optimized. Since the problem is nonconvex and the objective function cannot be derived in closed form, we adopt the deep deterministic policy gradient (DDPG) algorithm to deal with this challenging optimization problem, where we generate a set of CSI vectors in an offline way, and then these data sets are used to train the neural networks. The simulation results demonstrate the rapid convergence speed of the adopted DDPG algorithm and also emphasize that it is crucial to consider the HWI when optimizing the transceiver.

Sum-Rate-Optimal Statistical Precoding for FDD Massive MIMO Downlink With Deterministic Equivalents

Statisticalprecoding is considered as a promising technique to release the channel state information (CSI) acquisition overhead. This article investigates a linear precoder design for frequency-division duplexing (FDD) massive MIMO downlink with only statistical CSI. We use a beam-based statistical channel model to capture the spatial correlation characteristics of the channels. The objective of the precoder design is to maximize the ergodic sum-rate under total power constraint. Based on the minorize-maximize (MM) algorithm, a stationary solution of the ergodic sum-rate maximization problem can be obtained. The stationary solution is shown to be the same as the optimal solution to a stochastic weighted minimum mean square error (SWMMSE) problem. Further, we establish the approximations for rate expressions with deterministic equivalent. The deterministic equivalents of ergodic rates are only related to the precoding matrices and statistical CSI. According to these closed-form rate expressions, we propose a linear precoder design algorithm and obtain tractable expressions for precoding matrices. Numerical comparisons with the existing precoding approach demonstrate the significant advantages of the developed algorithm.

Constructions of 2-D Golay Complementary Array Sets for MIMO Omnidirectional Transmission

Two-dimensional (2-D) Golay complementary array sets (GCASs) have found important applications in massive multiple-input multiple-output (MIMO) systems equipped with a uniform rectangular array (URA), which are employed as precoding matrices to produce omnidirectional transmission. In this letter, new constructions of 2-D GCASs based on 2-D multivariable functions are presented. Compared with the existing constructions in the literature, the proposed constructions can be represented by explicit function forms that are more convenient to use in practical applications. Furthermore, 2-D GCASs with new parameters are obtained. Finally, numerical results show that the proposed 2-D GCASs are useful in massive MIMO systems.

On The Optimization of Weighted Sum Rate for Mimo Broascast Channels

n this paper, we study the problem of optimizing the weighted total system rate (WSR) for a downlink broadcast communication system using multiple input-multiple output (MIMO) antenna technology, wherein a Base station (BS) transmits multiple data streams simultaneously to K multi-antenna MIMO mobile stations (MSs). Upon the power constraint, the optimal solution is to find the pre-coding matrices at the BS and the decoding matrices at the MSs. However, this type of optimization problem is usually nonlinear and non-convex, so it is relatively difficult to solve by analytical methods. To tackle the problem, we propose a novel algorithm to optimize the WSR of the system based on the Harris Hawking Optimization (HHO) algorithm using the linear least squares mean error (MMSE) filter at the MSs. Numerical results have been used to demonstrate the outperformance of the proposed algorithm, comparing with existing methods such as Block Diagonalism with Waterfilling algorithm and Particle Swarm Optimization, particularly at the low signal-to-noise (SNR) range. In the end, we may propose an adaptive method that combines the advantages of different algorithms at various SNR domains to maximize the system performance.

Transceiver Optimization for Two-Hop AF MIMO Relay Systems With DFE Receiver and Direct Link

In this paper, we consider precoding and receiving matrices optimization for a two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with a decision feedback equalizer (DFE) at the destination node in the presence of the direct source-destination link. By adopting the minimum mean-squared error (MMSE) criterion, we develop two new transceiver design algorithms for such a system. The first one employs an iterative procedure to design the source, relay, feed-forward, and feedback matrices. The second algorithm is a non-iterative suboptimal approach which decomposes the optimization problem into two tractable subproblems and obtains the source and relay precoding matrices by solving the two subproblems sequentially. Simulation results validate the better MSE and bit-error-rate (BER) performance of the proposed algorithms and show that the non-iterative suboptimal method has a negligible performance loss when the ratio of the source node transmission power to the relay node transmission power is small. In addition, the computational complexity analysis suggests that the second algorithm and one iteration of the first algorithm have the same order of complexity. As the first algorithm typically converges within a few iterations, both proposed algorithms exhibit a low complexity order.

Joint LED Selection and Precoding Optimization for Multiple-User Multiple-Cell VLC Systems

This paper proposes a hybrid dimming scheme based on joint LED selection and precoding design (TASP-HD) for multiple-user (MU) multiple-cell (MC) visible light communications (VLC) systems. In TASP-HD, both the LED selection and the precoding of each cell can be dynamically adjusted to reduce the intra- and inter-cell interferences while satisfying illumination constraints. First, a MU-MC-VLC system model is established, and then a sum-rate maximization problem under dimming level and illumination uniformity constraints is formulated. In this studied problem, the indices of activated LEDs and precoding matrices are optimized, which result in a complex non-convex mixed integer problem. To solve this problem, the original problem is separated into two subproblems. The first subproblem, which maximizes the sum-rate of users via optimizing the LED selection with a given precoding matrix, is a mixed integer problem solved by the penalty method. With the optimized LED selection matrix, the second subproblem which focuses on the maximization of the sum-rate via optimizing the precoding matrix is solved by the Lagrangian dual method. Finally, these two subproblems are iteratively solved to obtain a convergent solution. Simulation results verify that in a typical indoor scenario under a dimming level of 70%, the mean bandwidth efficiency of TASP-HD is 4.8 bit/s/Hz and 7.13 bit/s/Hz greater than AD and DD, respectively.

Weighted Sum Rate Maximization of the mmWave Cell-Free MIMO Downlink Relying on Hybrid Precoding

The cell-free MIMO concept relying on hybrid precoding constitutes an innovative technique capable of dramatically increasing the network capacity of millimeter-wave (mmWave) communication systems. It dispenses with the cell boundary of conventional multi-cell MIMO systems, while drastically reducing the power consumption by limiting the number of radio frequency (RF) chains at the access points (APs). In this paper, we aim for maximizing the weighted sum rate (WSR) of mmWave cell-free MIMO systems by conceiving a low-complexity hybrid precoding algorithm. We formulate the WSR optimization problem subject to the transmit power constraint for each AP and the constant-modulus constraint for the phase shifters of the analog precoders. A block coordinate descent (BCD) algorithm is proposed for iteratively solving the problem. In each iteration, the classic Lagrangian multiplier method and the penalty dual decomposition (PDD) method are combined for obtaining near-optimal hybrid analog/digital precoding matrices. Furthermore, we extend our proposed algorithm for deriving closed-form expressions for the precoders of fully digital cell-free MIMO systems. Moreover, we present the convergency analysis and complexity analysis of our proposed method. Finally, our simulation results demonstrate the superiority of the algorithms proposed for both fully digital and hybrid precoding matrices.

HP‐SPC algorithm with dynamic partially connected structure for mmWave MIMO systems

AbstractThis article proposes a low complexity hybrid precoding algorithm for the switch network‐based dynamic partially connected (SPC) structure, that is, named as HP‐SPC algorithm. First, via a new defined effective optimal precoding matrix, the analog switch precoding matrix optimization problem is transformed into a sparse representation problem. Thus, invoking that the key characteristic of only one nonzero entry in each row of the analog dynamic switch precoding matrix, the analog dynamic switch precoding matrix can be accurately and effectively solved. Second, the digital precoding matrix optimization problem is modeled as a dictionary update problem by the defined effective optimal precoding matrix and the combining matrix. Further, the digital precoding matrix is easily optimized based on the defined effective optimal precoding matrix, since the measurement vectors are sparsely represented by a single dictionary atom. Third, the analog phase shifter precoding matrix is given by the phase rotation method. Finally, the precoding matrices are alternant updated until convergence, a near optimal solution of the precoding matrix is obtained. Compared with the previous works, the proposed HP‐SPC algorithm provides better hybrid precoding performance, for examples: (1) it avoids complexity computation such as matrix inversion and singular value decomposition, so that it presents a low computational complexity; (2) it has a favorable property of convergence since a stable point can be reached with about 10 loop iterations. Based on the simulation results, the effectiveness of HP‐SPC algorithm is further demonstrated.

Weighted Sum Rate Optimization for STAR-RIS-Assisted MIMO System

In this work, we study a simultaneous transmitting and reflecting reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output network. For the system under consideration, we maximize the weighted sum rate, mainly based on the energy splitting (ES) scheme. To tackle this optimization problem, a sub-optimal block coordinate descent (BCD) algorithm is proposed to design the precoding matrices and the transmitting and reflecting coefficients (TRCs) in an alternate manner. Specifically, the precoding matrices are solved using the Lagrange dual method, while the TRCs are obtained using the constrained concave-convex procedure (CCCP). The simulation results reveal that: 1) Simultaneous transmitting and reflecting RIS (STAR-RIS) can achieve better performance than conventional reflecting/transmiting-only RIS; 2) In unicast communication, time switching (TS) scheme outperforms the ES and mode selection (MS) schemes, while in broadcast communication, ES scheme outperforms the TS and MS schemes.

Double Intelligent Reflecting Surface-Assisted Multi-User MIMO Mmwave Systems With Hybrid Precoding

This work investigates the effect of double intelligent reflecting surface (IRS) in improving the spectrum efficient of multi-user multiple-input multiple-output (MIMO) network operating in the millimeter wave (mmWave) band. Specifically, we aim to solve a weighted sum rate maximization problem by jointly optimizing the digital precoding at the transmitter and the analog phase shifters at the IRS, subject to the minimum achievable rate constraint. To facilitate the design of an efficient solution, we first reformulate the original problem into a tractable one by exploiting the majorization-minimization (MM) method. Then, a block coordinate descent (BCD) method is proposed to obtain a suboptimal solution, where the precoding matrices and the phase shifters are alternately optimized. Specifically, the digital precoding matrix design problem is solved by the quadratically constrained quadratic programming (QCQP), while the analog phase shift optimization is solved by the Riemannian manifold optimization (RMO). The convergence and computational complexity are analyzed. Finally, simulation results are provided to verify the performance of the proposed design, as well as the effectiveness of double-IRS in improving the spectral efficiency.

Joint Altitude and Hybrid Beamspace Precoding Optimization for UAV-Enabled Multiuser mmWave MIMO System

The combination of unmanned aerial vehicles (UAVs) and millimeter wave (mmWave) multiple-input multiple-out (MIMO) system is regarded as a key enabling technology for beyond 5G networks, as it provides high data rate aerial links. However, establishing UAV-enabled mmWave MIMO communication is quite challenging due to the high hardware cost in terms of radio frequency (RF) chains. As a cost-effective alternative, a beamspace precoding with discrete lens arrays (DLA) architecture has received considerable attention. However, the underlying optimal design in beamspace precoding has not been fully exploited in UAV-enabled communication scenario. In this paper, the joint design of the UAV’s altitude and hybrid beamspace precoding is proposed for the UAV-enabled multiuser MIMO system, in which the DLA is exploited to reduce the number of the RF chain. In the proposed scheme, the optimization problem is formulated as a minimum weighted mean squared error (MWMSE) method. Then an efficient algorithm with the penalty dual decomposition (PDD) is proposed that aims to jointly optimize the altitude of UAV, beam selection and digital precoding matrices. Simulation results confirm the comparable performance of the proposed scheme and perform close to full-digital beamforming in terms of achievable spectral efficiency.

Hybrid Precoding for mmWave MIMO Systems With Overlapped Subarray Architecture

Traditional precoding is incompatible with millimetre wave (mmWave) multiple input multiple output (MIMO) systems due to hardware costs and power consumption. As a result, hybrid precoding is being considered as a promising technology for balancing hardware complexity and system performance. This paper proposes a hybrid precoding technique for overlapped subarrays (OSA) architecture in mmWave MIMO systems. It exploits the OSA’s structure to decompose the hybrid precoding problem into a series of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_tN_s</i> /2 subproblems and then solves them iteratively, where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L_t</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N_s</i> are the numbers of RF chains and transmitted data streams, respectively. First, the proposed scheme determines the analog and digital precoding submatrices of each OSA iteratively and then constructs the analog and digital precoding matrices of the whole OSA architecture. The digital precoding submatrix of each OSA is determined from each vector in the OSA submatrix. The results show that the proposed hybrid precoding for the OSA architecture outperforms the successive interference cancellation (SIC)-based hybrid precoding for non-overlapped SA (NOSA) and provides performance close to the fully-connected (FC) spatially sparse hybrid precoding, despite requiring less hardware and computational complexities.

Multiuser Uplink MIMO Communications Assisted by Multiple Reconfigurable Intelligent Surfaces

This letter focuses on the design of multiuser uplink multiple-input multiple-output (MIMO) communications assisted by multiple reconfigurable intelligent surfaces (RISs), where we consider both linear minimal mean-squared error (MMSE) and nonlinear MMSE-decision feedback equalization (DFE) receivers. The RISs, consisting of massive low-cost passive elements, can reflect the incident signals with either continuous or discrete phase shifts. Adopting the sum mean-squared error (MSE) minimization criterion, we jointly optimize the RIS phase shifts, the linear or nonlinear receiving matrices, and the source precoding matrices in iterative manner. Simulation results show that, when the signals in direct user-access point (AP) links suffer severe attenuation, the introduction of indirect user-RIS-AP links can significantly improve the system performance.

Iterative Generalized Eigenvector Precoder With Deterministic Equivalents for 3D Massive MIMO

In this paper, we propose an iterative generalized eigenvector (GE) precoder design for three dimensional (3D) massive multi-input multi-output (MIMO) downlink with uniform planar array (UPA) and imperfect channel state information (CSI). We use a posterior beam based statistical channel model which includes the channel aging and the spatial correlation. We consider the problem of maximizing the expected sum-rate under a total power constraint. By replacing the expected sum-rate with their deterministic equivalents, we obtain the structure of the optimal linear precoders. The columns of the optimal precoding matrices are the generalized eigen-vectors of two matrices. One of the two matrices is related to the transmitted signal of the intended user, and the other is related to the power constraint and the leakage to other users. Furthermore, the two matrices are also functions of the precoders, thus iterative updates of the precoder are needed. Then, we investigate the power allocation and the computation of the Lagrangian multiplier, and propose an iterative algorithm based on the structure of the optimal precoders. Simulation results show that the proposed precoders can achieve significantly performance gain than the widely used regularized zero forcing (RZF) precoder and signal to leakage plus noise ratio (SLNR) precoder.

Millimeter Wave MIMO out Door Channel Estimation and Precoding

Millimeter wave (mm Wave) communications is one of the technologies for 5G cellular systems. In the mm Wave communication, there is a lot of path loss can be reduced by Precoding. The channel state information (CSI) should be known at the transmitting station, in the design of precoding matrices and to get good accuracy in estimating sparse channels a Compressive sensing (CS) based recovery algorithms was used. Not only for good accuracy the algorithm is also used for mm Wave channel estimation for exploiting the mm Wave channel’s sparse in multi-path construction. Hence, in this paper, for mm Wave outdoor channel estimation, the CS recovery methods orthogonal matching pursuit (OMP) and compressive sampling matching pursuit (CoSaMP) are used. The singular value decomposition (SVD) precoding is developed using the estimated channel. By (MSE) mean square error and spectral efficiency which were the performance metrics in channel estimation and precoding were done by using MATLAB simulations to get the efficacy of the OMP and CoSaMP algorithm.

Low Spatial Peak-to-Average Power Ratio Transmission for Improved Energy Efficiency in Massive MIMO Systems.

A significant portion of the operating power of a base station is consumed by power amplifiers (PAs). Much of this power is dissipated in the form of heat, as the overall efficiency of currently deployed PAs is typically very low. This is because the structure of conventional precoding techniques typically results in a relatively high variation in output power at different antennas in the array, and many PAs are operated well below saturation to avoid distortion of the transmitted signals. In this work, we use a realistic model for power consumption in PAs and study the impact of power variation across antennas in the array on the energy efficiency of a massive MIMO downlink system. We introduce a family of linear precoding matrices that allow us to control the spatial peak-to-average power ratio by projecting a fraction of the transmitted power onto the null space of the channel. These precoding matrices preserve the structure of conventional precoders; e.g., they suppress multiuser interference when used together with zeroforcing precoding and bring advantages over these precoders by operating PAs in a more power-efficient region and reducing the total radiated distortion. Our numerical results show that by controlling the power variations between antennas in the array and incorporating the nonlinearity properties of PA into the precoder optimization, significant gains in energy efficiency can be achieved over conventional precoding techniques.

Joint Deep Reinforcement Learning and Unfolding: Beam Selection and Precoding for mmWave Multiuser MIMO With Lens Arrays

The millimeter wave (mmWave) multiuser multiple-input multiple-output (MU-MIMO) systems with discrete lens arrays (DLA) have received great attention due to their simple hardware implementation and excellent performance. In this work, we investigate the joint design of beam selection and digital precoding matrices for mmWave MU-MIMO systems with DLA to maximize the sum-rate subject to the transmit power constraint and the constraints of the selection matrix structure. The investigated non-convex problem with discrete variables and coupled constraints is challenging to solve and an efficient framework of joint neural network (NN) design is proposed to tackle it. Specifically, the proposed framework consists of a deep reinforcement learning (DRL)-based NN and a deep-unfolding NN, which are employed to optimize the beam selection and digital precoding matrices, respectively. As for the DRL-based NN, we formulate the beam selection problem as a Markov decision process and a double deep Q-network algorithm is developed to solve it. The base station is considered to be an agent, where the state, action, and reward function are carefully designed. Regarding the design of the digital precoding matrix, we develop an iterative weighted minimum mean-square error algorithm induced deep-unfolding NN, which unfolds this algorithm into a layer-wise structure with introduced trainable parameters. Simulation results verify that this jointly trained NN remarkably outperforms the existing iterative algorithms with reduced complexity and stronger robustness.

Broad Coverage Precoding for 3D Massive MIMO with Huge Uniform Planar Arrays.

In this paper, we propose a novel broad coverage precoder design for three-dimensional (3D) massive multi-input multi-output (MIMO) equipped with huge uniform planar arrays (UPAs). The desired two-dimensional (2D) angle power spectrum is assumed to be separable. We use the per-antenna constant power constraint and the semi-unitary constraint which are widely used in the literature. For normal broad coverage precoder design, the dimension of the optimization space is the product of the number of antennas at the base station (BS) and the number of transmit streams. With the proposed method, the design of the high-dimensional precoding matrices is reduced to that of a set of low-dimensional orthonormal vectors, and of a pair of low-dimensional vectors. The dimensions of the vectors in the set and the pair are the number of antennas per column and per row of the UPA, respectively. We then use optimization methods to generate the set of orthonormal vectors and the pair of vectors, respectively. Finally, simulation results show that the proposed broad coverage precoding matrices achieve nearly the same performance as the normal broad coverage precoder with much lower computational complexity.

Diversity-Achieving Quadrature Space-Frequency Index Modulation

Quadrature space-frequency index modulation (QSF-IM) is a recently developed space-frequency transmission scheme which generalizes the idea of quadrature spatial modulation into both spatial and frequency domains. However, QSF-IM lacks of transmit diversity. In this letter, by combining QSF-IM and space-frequency code designing, a novel diversity-achieving QSF-IM (DA-QSFIM) scheme which can achieve the second-order transmit diversity is proposed. In the proposed scheme, the real and imaginary parts of a symbol vector are respectively multiplied by two different precoding matrices and then they are placed into space-frequency resource block in diagonal or anti-diagonal form for transmission. Theoretical performance analysis and simulation results are presented to validate the superiority of DA-QSFIM over other existing schemes in terms of bit error rate (BER) performance under both Rayleigh and Rician channels.