Weighted Gauss-Seidel Precoder for Downlink Massive MIMO Systems

In this paper, a novel precoding scheme based on the Gauss-Seidel (GS) method is proposed for downlink massive multiple-input multiple-output (MIMO) systems. The GS method iteratively approximates the matrix inversion and reduces the overall complexity of the precoding process. In addition, the GS method shows a fast convergence rate to the Zero-forcing (ZF) method that requires an exact invertible matrix. However, to satisfy demanded error performance and converge to the error performance of the ZF method in the practical condition such as spatially correlated channels, more iterations are necessary for the GS method and increase the overall complexity. For efficient approximation with fewer iterations, this paper proposes a weighted GS (WGS) method to improve the approximation accuracy of the GS method. The optimal weights that accelerate the convergence rate by improved accuracy are computed by the least square (LS) method. After the computation of weights, the different weights are applied for each iteration of the GS method. In addition, an efficient method of weight computation is proposed to reduce the complexity of the LS method. The simulation results show that bit error rate (BER) performance for the proposed scheme with fewer iterations is better than the GS method in spatially correlated channels.     

Efficient Gauss-Seidel Precoding with Parallel Calculation in Massive MIMO Systems

A number of requirements for 5G mobile communication are satisfied by adopting multiple input multiple output (MIMO) systems. The inter user interference (IUI) which is an inevitable problem in MIMO systems becomes controllable when the precoding scheme is used. In this paper, the horizontal Gauss-Seidel (HGS) method is proposed as precoding scheme in massive MIMO systems. In massive MIMO systems, the exact inversion of channel matrix is impractical due to the severe computational complexity. Therefore, the conventional Gauss-Seidel (GS) method is used to approximate the inversion of channel matrix. The GS has good performance by using previous calculation results as feedback. However, the required time for obtaining the precoding symbols is too long due to the sequential process of GS. Therefore, the HGS with parallel calculation is proposed in this paper to reduce the required time. The rows of channel matrix are eliminated for parallel calculation in HGS method. In addition, HGS uses the ordered channel matrix to prevent performance degradation which is occurred by parallel calculation. The HGS with proper number of parallelly computed symbols has better performance and reduced required time compared to the traditional GS.     

Optimization of Channel Estimation Using ELMx-based in Massive MIMO

In communication channel estimation, the Least Square (LS) technique has long been a widely accepted and commonly used principle. This is because the simple calculation method is compared with other channel estimation methods. The Minimum Mean Squares Error (MMSE), which is developed later, is devised as the next step because the goal is to reduce the error rate in the communication system from the conventional LS technique which still has a higher error rate. These channel estimations are very important to modern communication systems, especially massive MIMO. Evaluating the massive MIMO channel is one of the most researched and debated topics today. This is essential in technology to overcome traditional performance barriers. The better the channel estimation, the more accurate it is. This paper investigated machine learning (ML) for channel estimation. ML channel estimations based on the Extreme Learning Machine (ELMx) group are also implemented. These estimations, known as the ELMx group, include Regularized Extreme Learning Machine (RELM) and Outlier Robust Extreme Learning Machine (ORELM). Then, it was compared with LS and MMSE. The simulation results reveal that the ELMx group outperforms LS and MMSE in channel capacity and bit error rate. Additionally, this paper has proven complexity for verified computational times. The RELM method is less time consuming and has low complexity which is suitable for future use in large MIMO systems.     

Hybrid detectors for wireless orthogonal frequency division multiplexing with code division multiplexing systems based on reliability information

Orthogonal frequency division multiplexing with code division multiplexing (OFDM-CDM) is attractive for the next generation high-speed wireless systems due to the fact that the performance of OFDM-CDM systems can be considerably improved by employing a joint detection scheme such as the maximum likelihood (ML) detector. However, the complexity of the ML detector increases rapidly as the number of orthogonal spreading codes and/or the number of bits per modulation symbol increase. In this study, the authors introduce a unified detection model and propose two hybrid detectors, which combine zero forcing (ZF) with successive interference cancellation (SIC) and sphere detection (SD) algorithms, respectively. After obtaining the initial solution from the front-end ZF receiver, the proposed back-end algorithms are adopted to extend the potential solution list and search for the final result. The objective is to utilise the combination of a simplified linear equaliser and a comprehensive detection scheme to achieve enhanced performance and offer alternatives to the more complex and channel-estimation-sensitive minimum mean squared error (MMSE) scheme. The results show that the proposed hybrid detectors are able to achieve superior performance compared to the MMSE scheme and provides a significant performance improvement compared to the conventional OFDM counterpart.     

Tomlinson-Harashima precoding with imperfect channel state information

Nonlinear Tomlinson-Harashima precoding (THP) is an attractive solution for a scenario where the transmission system employs multiple antennas at transmitter and multiple users with a single antenna at the receiver, so that the cooperation among the receive antennas are impossible (downlink scenario). THP solution based on zero forcing (ZF) and minimum mean square error (MMSE) criteria is one of the important techniques to achieve near multiple input multiple output channels capacity with reasonable complexity. In this paper, the effect of channel imperfection on THP is considered. At first, the achievable rate of THP with respect to ZF criterion in an imperfect channel state information (CSI) scenario is calculated. Moreover, based on MMSE criterion, a new robust solution is derived which provides a significant improvement with respect to the conventional optimisation method. Then, the effect of channel estimation error on THP is considered as an improved optimisation where THP filters are optimised together with a channel estimator. Spatial power loading is found to be important to the THP performance. This loading for robust/joint optimisation of MMSE THP is developed by minimum average symbol error rate sense. Simulation results show the capacity loss, the performance advantage attained by the robust/joint optimisation and the power loading in an imperfect CSI scenario.     

Error performance of ultrawideband spatial multiplexing systems

In this paper, a number of ultrawideband (UWB)multiple-input multiple-output (MIMO) spatialmultiplexing systems are presented and their error performance is analysed. For both model-based and measured UWB channels, the performance of various MIMO detectors is evaluated under the multiband orthogonal frequency division multiplexing (MB-OFDM) regime. Contrary to expectation, the results demonstrate that significant spatial diversity can be extracted, in addition to linear data-rate scaling, despite the large frequency diversity inherent in the UWB channel. It is shown that nonlinear detection schemes with reasonable complexity can provide considerable diversity gain, in contrast to well-known linear receivers. Thus, the proposed UWB spatial multiplexing schemes not only increase the data rate but also provide significant diversity gain and improved error rate performance.     

基于列正交变换实现串行干扰消除的MIMO检测算法

针对用于多输入多输出（MIMO）通信系统检测的按序QR分解（SQRD）算法在多径瑞利慢衰落信道中检测误码率较高的不足,提出了一种基于列正交（CO）变换的串行干扰消除（SIC）算法——COSIC。该算法对信道矩阵按列正交变换,避免了求上三角矩阵的运算,并且在判决信号过程中,将先判决出的信号通过信道后的输出向量作为干扰进行消除,在略微增加系统时间复杂度的基础上,使系统检测性能得到了明显改善。在多散射物的无线通信环境下进行的仿真实验证实,与传统的SQRD算法相比,所提算法误码率显著下降．系统检测性能明显改善。     

Sparse hierarchical solvers with guaranteed convergence

Solving sparse linear systems from discretized partial differential equations is challenging. Direct solvers have, in many cases, quadratic complexity (depending on geometry), while iterative solvers require problem dependent preconditioners to be robust and efficient. Approximate factorization preconditioners such as incomplete LU factorization provide cheap approximations to the system matrix. However, even a highly accurate preconditioner may have deteriorating performance when the condition number of the system matrix increases. By increasing the accuracy on low-frequency errors, we propose a novel hierarchical solver with improved robustness with respect to the condition number of the linear system. This solver retains the linear computational cost and memory footprint of the original algorithm.     

Sum Rate Maximization-based Fair Power Allocation in Downlink NOMA Networks

Non-orthogonal multiple access (NOMA) has been seen as a promising technology for 5G communication. The performance optimization of NOMA systems depends on both power allocation (PA) and user pairing (UP). Most existing researches provide sub-optimal solutions with high computational complexity for PA problem and mainly focuses on maximizing the sum rate (capacity) without considering the fairness performance. Also, the joint optimization of PA and UP needs an exhaustive search. The main contribution of this paper is the proposing of a novel capacity maximization-based fair power allocation (CMFPA) with low-complexity in downlink NOMA. Extensive investigation and analysis of the joint impact of signal to noise ratio (SNR) per subcarrier and the channel gains of the paired users on the performance of NOMA in terms of the capacity and the user fairness is presented. Next, a closed-form equation for the power allocation coefficient of CMFPA as a function of SNR, and the channel gains of the paired users is provided. In addition, to jointly optimize UP and PA in NOMA systems an efficient low-complexity UP (ELCUP) method is proposed to be incorporated with the proposed CMFPA to compromise the proposed joint resource allocation (JRA). Simulation results demonstrate that the proposed CMFPA can improve the capacity and fairness performance of existing UP methods, such as conventional UP, and random UP methods. Furthermore, the simulation results show that the proposed JRA significantly outperforms the existing schemes and gives a near-optimal performance.     

毫米波大规模MIMO系统波束选择方案的设计

针对毫米波大规模MIMO系统采用全数字预编码时,所需射频链路数量过多而导致能量消耗高的问题,提出了一种基于透镜的波束选择方案。该方案首先通过分析用户受干扰的可能性,将所有的用户分为干扰用户组和非干扰用户组,然后对于非干扰用户,直接利用最大功率准则进行波束选取,而对于干扰用户,则通过低复杂度增量算法选择合适的波束使系统和速率最大化。仿真结果表明,在有效减少系统所需射频链路数量和降低计算复杂度的基础上,该方案的系统和速率能够达到接近全数字预编码方案的水平,并且能够获得更高的能量效率。     

一种低复杂度的下行MIMO多用户分组策略

在研究了多用户MIMO线性处理技术和多用户选择方法的基础上,提出了多用户分组的思想。为了降低分组过程的复杂度,提出了基于最小奇异值和信道向量的内积的分组评价准则,并且给出了一种低复杂度的快速分组算法。仿真结果显示所提出的算法可以明显提升系统性能：随着系统中激活用户数量的增加,逐渐接近单用户点对点MIMO通信系统的性能;在一个具有4个发射天线的基站的系统中,当发射信噪比达到15dB,分组数量达到10时,采用了快速分组策略后,块对角化和规格化反转方法的各态历经性信道容量分别提升4bits／Hz和3bits／Hz以上。     

Numerical expansion-iterative method for analysis of integral equation models arising in one- and two-dimensional electromagnetic scattering

Most integral equations of the first kind are ill-posed, and obtaining their numerical solution needs often to solve a linear system of algebraic equations of large condition number. So, solving this system may be difficult or impossible. Since many problems in one- and two-dimensional scattering from perfectly conducting bodies can be modeled by Fredholm integral equations of the first kind, this paper presents an effective numerical expansion-iterative method for solving them. This method is based on vector forms of block-pulse functions. By using this approach, solving the first kind integral equation reduces to solve a recurrence relation. The approximate solution is most easily produced iteratively via the recurrence relation. Therefore, computing the numerical solution does not need to directly solve any linear system of algebraic equations and to use any matrix inversion. Also, the method practically transforms solving of the first kind Fredholm integral equation which is inherently ill-posed into solving second kind Fredholm integral equation. Another advantage is low cost of setting up the equations without applying any projection method such as collocation, Galerkin, etc. To show convergence and stability of the method, some computable error bounds are obtained. Test problems are provided to illustrate its accuracy and computational efficiency, and some practical one- and two-dimensional scatterers are analyzed by it.     

基于隔离非线性的实体单元模型与计算效率分析

实体有限元模型计算中往往需要较多的计算单元与结点数量,且这些单元状态判定以及大规模的刚度矩阵分解将消耗大量的计算资源,计算效率低。该文基于隔离非线性法理论建立了线性四面体与六面体等参单元分析模型,采用直接积分格式的6积分点替代六面体等参单元的8高斯点作为非线性应变插值点,能够在保证计算精度的同时提高单元状态判定效率。控制方程采用Woodbury公式与组合近似法联合求解,使得整个求解过程只有矩阵回代以及矩阵与向量的乘积,进一步提高了求解效率。基于时间复杂度的计算效率分析表明:随着结点自由度数目的增加,该文方法的计算效率相对传统变刚度法显著提高,数值算例验证了实体单元模型的正确性以及算法的高效性。     

Matrix partitioning methods for interior point algorithms

We consider here a linear programming problem whose rows of the constraint matrix can be partitioned into two parts. Such natural partitions exist in several special linear programs, including the assignment problem, the transportation problem, the generalized upper-bounded variable problem, the block diagonal linear program; and can also be used to induce sparsity patterns in Cholesky factorizations. In this paper, we propose a matrix partitioning method for interior point algorithms. The proposed method independently generates Cholesky factorizations of each part, and reduces the complexity to that of solving generally, a dense linear system involving several rank one updates of the identity matrix. Here, we propose solving this linear system by an inductive use of the Sherman-Morrison-Woodbury formula. The proposed method is easily implemented on a vector, parallel machine as well as on a distributed system. Such partitioning methods have been popular in the context of the simplex method, where the special structure of the basis matrix is exploited.     

Fast computation of an optimal controller for large-scale adaptive optics

The linear quadratic Gaussian regulator provides the minimum-variance control solution for a linear time-invariant system. For adaptive optics (AO) applications, under the hypothesis of a deformable mirror with instantaneous response, such a controller boils down to a minimum-variance phase estimator (a Kalman filter) and a projection onto the mirror space. The Kalman filter gain can be computed by solving an algebraic Riccati matrix equation, whose computational complexity grows very quickly with the size of the telescope aperture. This "curse of dimensionality" makes the standard solvers for Riccati equations very slow in the case of extremely large telescopes. In this article, we propose a way of computing the Kalman gain for AO systems by means of an approximation that considers the turbulence phase screen as the cropped version of an infinite-size screen. We demonstrate the advantages of the methods for both off- and on-line computational time, and we evaluate its performance for classical AO as well as for wide-field tomographic AO with multiple natural guide stars. Simulation results are reported.     

Normalized explicit approximate inverse preconditioning for solving 3D boundary value problems on uniprocessor and distributed systems

Normalized explicit approximate inverse matrix techniques, based on normalized approximate factorization procedures, for solving sparse linear systems resulting from the finite difference discretization of partial differential equations in three space variables are introduced. Normalized explicit preconditioned conjugate gradient schemes in conjunction with normalized approximate inverse matrix techniques are presented for solving sparse linear systems. The convergence analysis with theoretical estimates on the rate of convergence and computational complexity of the normalized explicit preconditioned conjugate gradient method are also derived. A Parallel Normalized Explicit Preconditioned Conjugate Gradient method for distributed memory systems, using message passing interface (MPI) communication library, is also given along with theoretical estimates on speedups, efficiency and computational complexity. Application of the proposed method on a three‐dimensional boundary value problem is discussed and numerical results are given for uniprocessor and multicomputer systems. Copyright © 2005 John Wiley & Sons, Ltd.     

7CDMA解相关多用户检测的快速处理方法摘要]针对CDMA多用户检测的解相关方法运算过程的复杂度较高、异步情况下难以实现等问题进行了研究,提出了一种解相关多用户检测的快速处理方法,从而便于实现及快速软件处理.仿真结果表明,该方法使运算复杂度大大降低,同时又使误码率较传统

针对CDMA多用户检测的解相关方法运算过程的复杂度较高、异步情况下难以实现等问题进行了研究,提出了一种解相关多用户检测的快速处理方法,从而便于实现及快速软件处理。仿真结果表明,该方法使运算复杂度大大降低,同时又使误码率较传统接收机和解相关接收机下降。     

Performance of spatially multiplexed MC-CDM with zero-forcing unified successive interference cancellation detection

Spatially multiplexed multicarrier code-division multiplexing (SM-MC-CDM) is a multiple-input multiple-output, orthogonal frequency division multiplexing (MIMO-OFDM) communication technique with multiple antennas used for spatial multiplexing and with frequency domain spreading on each antenna. Unified successive interference canceller (U-SIC) is an efficient detector recently introduced for SM-MC-CDM. This paper presents an analytical approach to the performance of zero-forcing (ZF) U-SIC for SM-MC-CDM communications. For a system with an equal number of transmit and receive antennas, an approximation for the probability density function of post-detection signal-to-noise ratio (SNR) is used to derive a closed-form analytical upper bound and approximations for the probability of error and ergodic capacity. It is shown that SM-MC-CDM with ZF U-SIC is able to achieve higher diversity order than that achieved by ZF and minimum mean squared error (MMSE) V-BLAST detectors used on each subcarrier of a MIMO-OFDM system with the same number of subcarriers. The diversity order obtained increases with the number of subcarriers. It is also shown that the ergodic capacity of the system decreases with increasing number of subcarriers.     

Performance analysis of multiple-input multipleoutput singular value decomposition transceivers during fading and other cell interference

A generalised method is derived to compute the error probabilities of singular value decomposition (SVD)-based receivers for a multiple-input multiple-output (MIMO) system with uncoded transmission. The method can be used for a wide class of flat fading environments, including independent and identically distributed (i.i.d.) and semi-correlated Rayleigh and i.i.d. Ricean channels. Although the method is applied to equal-power binary phase shift keying, it can easily be extended to higher-order M-ary phase shift keying (M-PSK) and M-ary quadrature amplitude modulation (M-QAM) signal constellations and adaptive 'water-filling' schemes. The error probability curves derived from closed-form formulas and simulations demonstrate very close agreement. The error performances of channel inversion, minimum mean square error and zero forcing receivers are compared with the SVD receiver for a single-user system. The impact of multiple users is considered by studying the performance of an adaptive MIMO SVD transmission scheme operating in a cellular environment. In particular, the effect of inter-cell interference on the performance of the scheme is quantified, modelling the interference as increased Gaussian noise. A number of cellular layouts are examined and the impact of the resulting singal-to-interference and noise ratio on the constellation sizes that can be supported, the BER and so on is considered. The primary metric used for our performance analysis is the error-free transmission rate, which is derived for our adaptive system. For the cellular scenarios considered, it can be found that the effect of interference is considerable and the performance of the adaptive MIMO SVD scheme is only marginally better than that provided by conventional diversity methods.     

Outage Capacity Analysis for Cognitive Non-Orthogonal Multiple Access Downlink Transmissions Systems in the Presence of Channel Estimation Error

In this paper, we propose a downlink cognitive non-orthogonal multiple access (NOMA) network, where the secondary users (SUs) operate in underlay mode. In the network, secondary transmitter employs NOMA signaling for downlink transmission, and the primary user (PU) is interfered by the transmission from SU. The expressions for the outage probabilities are derived in closed-form for both primary and secondary users in the presence of channel estimation error. Numerical simulation results show that the channel estimation error and the inter-network interference cause degradation of the downlink outage performance. Also the power allocation and the location have a significant impact on the outage probability. The numerical experiments demonstrate that the analytic expressions of the outage probabilities match with the simulation results.