Reducing computational complexity using transmitter correlation value‐assisted schedulers in multiuser MIMO uplink

In this paper, a threshold bounded antenna selection scheduler (TBS) and a computational complexity bounded antenna selection scheduler (CCBS) are proposed to reduce computational complexity in multiple input multiple output (MIMO) uplink. In contrast to previous works, a spatially correlated MIMO channel model is considered and a transmitter correlation value (TCV) is newly introduced to assist the antenna selection in addition to the channel gain. For the TBS or CCBS, with predetermined threshold of TCV or ratio of successful antennas (RSAs), full searching (FS) and sub searching (SS) are applied more efficiently to user equipments (UEs) compared with previous schedulers. As a result, the number of candidate antennas in the scheduling set can be reduced, which translates into a lower computational complexity in terms of number of evaluated antenna combinations. Additionally, compared with the TBS, the peak computational complexity can be further reduced by the CCBS. Simulation results show that with proposed schedulers the computational complexity can be reduced by at least 50% with an acceptable compromise of capacity. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive joint precoding and pre‐equalization with reduced complexity in massive MIMO systems

In this paper, a massive multiple input multiple output downlink scenario is considered where the number of users varies in a large dynamic range. An adaptive joint precoding and pre‐equalization with reduced complexity is proposed. Specifically, the successive over‐relaxation method is employed in the pre‐equalization process to avoid the high‐dimensional channel matrix inversion, and a reduced‐length feedback filter is proposed to reduce the computational complexity of the precoding. Moreover, an adaptive transceiver structure is proposed to switch on/off the precoding process so that multiple users can be accommodated with the least cost of the computational complexity. Simulation results show that, compared with the traditional scheme, the proposed adaptive joint precoding and pre‐equalization can save about 90% of the computational complexity. Copyright © 2016 John Wiley & Sons, Ltd.     

Blind adaptive receiver for uplink multiuser massive MIMO systems

Herein, we consider uplink multiuser massive multiple‐input multiple‐output systems when multiple users transmit information symbols to a base station (BS) by applying simple space‐time block coding (STBC). At the BS receiver, two detection filters for each user are used to detect the STBC information symbols. One of these filters is for odd‐indexed symbols and the other for even‐indexed symbols. Using constrained output variance metric minimization, we first derive a special relation between the closed‐form optimal solutions for the two detection filters. Then, using the derived special relation, we propose a new blind adaptive algorithm for implementing the minimum output variance‐based optimal filters. In the proposed adaptive algorithm, filter weight vectors are updated only in the region satisfying the special relation. Through a theoretical analysis of the convergence speed and a computer simulation, we demonstrate that the proposed scheme exhibits faster convergence speed and lower steady‐state bit error rate than the conventional scheme.     

毫米波大规模MIMO系统中低复杂度混合预编码方法

针对毫米波大规模多输入多输出(MIMO)系统混合预编码方案设计的难点,提出了一种低复杂度混合预编码方法。首先基于奇异值分解,构造初始射频(RF)预编码矩阵,然后构造数字预编码矩阵。进而将残差矩阵最大左奇异矢量构造的矢量添加到RF矩阵的最后一列,以更新初始RF矩阵。经过多次迭代,从而形成最终RF预编码矩阵。最后基于最小二乘准则设计数字预编码矩阵。理论分析和仿真结果表明,相比于基于正交匹配追踪(OMP)算法的混合预编码设计方法,该方法在计算复杂度大幅下降的同时,其性能远远优于基于OMP算法的混合预编码方法,同时在数据流数相对较小时,其性能接近最优的全数字预编码设计方法。     

On proportional fairness of uplink spectral efficiency in cell‐free massive MIMO systems

This paper is concerned with the proportional fairness (PF) of the spectral efficiency (SE) maximization of uplinks in a cell‐free (CF) massive multiple‐input multiple‐output (MIMO) system in which a large number of single‐antenna access points (APs) connected to a central processing unit (CPU) serve many single‐antenna users. To detect the user signals, the APs use matched filters based on the local channel state information while the CPU deploys receiver filters based on knowledge of channel statistics. We devise the maximization problem of the SE PF, which maximizes the sum of the logarithm of the achievable user rates, as a jointly nonconvex optimization problem of receiver filter coefficients and user power allocation subject to user power constraints. To handle the challenges associated with the nonconvexity of the formulated design problem, we develop an iterative algorithm by alternatively finding optimal filter coefficients at the CPU and transmit powers at the users. While the filter coefficient design is formulated as a generalized eigenvalue problem, the power allocation problem is addressed by a gradient projection (GP) approach. Simulation results show that the SE PF maximization not only offers approximately the achievable sum rates as compared to the sum‐rate maximization but also provides an improved trade‐off between the user rate fairness and the achievable sum rate.     

Randomized Kaczmarz algorithm for massive MIMO systems with channel estimation and spatial correlation

To exploit the benefits of massive multiple‐input multiple‐output (M‐MIMO) technology in scenarios where base stations (BSs) need to be cheap and equipped with simple hardware, the computational complexity of classical signal processing schemes for spatial multiplexing of users shall be reduced. This calls for suboptimal designs that perform well the combining/precoding steps and simultaneously achieve low computational complexities. An approach on the basis of the iterative Kaczmarz algorithm (KA) has been recently investigated, assuring well execution without the knowledge of second order moments of the wireless channels in the BS, and with easiness since no tuning parameters, besides the number of iterations, are required. In fact, the randomized version of KA (rKA) has been used in this context because of global convergence properties. Herein, modifications are proposed on this first rKA‐based attempt, aiming to improve its performance‐complexity trade‐off solution for M‐MIMO systems. We observe that long‐term channel effects degrade the rate of convergence of the rKA‐based schemes. This issue is then tackled herein by means of a hybrid rKA initialization proposal, which lands within the region of convexity of the algorithm and assures fairness to the communication system. The effectiveness of our proposal is illustrated through numerical results, which bring more realistic system conditions in terms of channel estimation and spatial correlation than those used so far. We also characterize the computational complexity of the proposed rKA scheme, deriving upper bounds for the number of iterations. A case study focused on a dense urban application scenario is used to gather new insights on the feasibility of the proposed scheme to cope with the inserted BS constraints.     

大规模MIMO系统中低复杂度的稀疏信道估计

针对大规模多输入多输出（MIMO）系统信道估计算法复杂度高的缺陷,结合无线通信信道固有的稀疏性提出了一种低复杂度的稀疏信道估计算法。该算法是在传统的离散傅里叶变换（DFT）信道估计的基础上利用分离算法将信道抽头与噪声空间分离开来,使得信道估计时只需要计算信道抽头的部分,因此算法的计算复杂度被大大降低。仿真结果表明,该算法在保持低复杂度的同时,可获得接近最小均方误差（MMSE）性能。     

大规模MIMO系统中基于TFQMR的低复杂度信号检测算法

在大规模多输入多输出(Multiple-Input Multiple-Output,MIMO)系统上行链路检测算法中,最小均方误差(Minimum Mean Square Error,MMSE)算法可取得近似最优的性能,然而MMSE算法涉及高维矩阵求逆问题,其计算复杂度高达O(K3),其中K表示用户数.为此,针对极化信...     

Low complexity codebook search method in massive MIMO system

In Massive MIMO systems for 5G networks,precoding technology is one of the key technologies.Aiming at user side codebook search method of the discrete Fourier transform (DFT) rotation codebook,a low complexity search algorithm was proposed.In this algorithm,all horizontal and vertical codebooks were grouped separately according to the characteristics that the precoding vectors with the same column of DFT rotation codebooks had the smallest chordal distance and the smaller chordal distance have the stronger correlation,and then the optimal horizontal and vertical codewords with maximum channel gain were obtained to form 3D precoding code-books.The simulation results indicate that the searching complexity of the proposed method is significantly reduced under conditions of insuring the system performance,moreover,this advantage becomes greater with the number of antennas increasing.     

Bat algorithm–based beamforming for mmWave massive MIMO systems

In this paper, an optimized analog beamforming scheme for millimeter‐wave (mmWave) massive MIMO system is presented. This scheme aims to achieve the near‐optimal performance.by searching for the optimized combination of analog precoder and combiner. In order to compensate for the occurrence of attenuation in the magnitude of mmWave signals, the codebook‐dependent analog beamforming in conjunction with precoding at transmitting end and combining signals at the receiving end is utilized. Nonetheless, the existing and traditional beamforming schemes involve a more difficult and complicated search for the optimal combination of analog precoder/combiner matrices from predefined codebooks. To solve this problem, we have referred to a modified bat algorithm to find the optimal combination value. This algorithm will explore the possible pairs of analog precoder/combiner as a way to come up with the best match in order to attain near‐optimal performance. The analysis shows that the optimized beamforming scheme presented in this paper can improve the performance that is very close to the beam steering benchmark that we have considered.     

大规模MIMO系统中块高斯-赛德尔检测算法

最小均方误差(Minimum Mean Square Error,MMSE)检测算法,虽然能在大规模多输入多输出系统中获得接近最优的线性检测性能,但是涉及高维矩阵求逆运算,难以在实际应用中快速有效地实现.提出了块高斯-赛德尔(Block Gauss-Seidel,BGS)低复杂度信号检测算法,将MMSE检测器的滤波矩阵...     

Power and energy optimization with reduced complexity in different deployment scenarios of massive MIMO network

With the increase in the number of users, the role of massive MIMO has become more significant. But there is a significant increase in the power and energy consumption in the massive MIMO network for transmission, processing, and reception. Hence, the prior role is to reduce the power consumption and increase the energy efficiency of the network. In this paper, the work is done to reduce the power consumption, while maintaining the reduced complexity in the massive MIMO and small‐cell scenario, and to increase the energy efficiency, by optimizing the number of users and number of transmission antennas in the massive MIMO scenario. This paper has also found out the optimal values of the energy efficiency, number of transmission antennas, and number of users for a massive MIMO network in different deployment scenarios like indoor hotspot, ultradense, dense urban, urban, suburban, and rural areas in both single‐cell scenario and multicell scenario at the base station and user equipment side according to the ITU‐R M.2135 standard.     

大规模MIMO系统低复杂度混合迭代信号检测

在大规模MIMO系统上行链路信号检测算法中,最小均方误差(MMSE)算法能获得接近最优的线性检测性能.但是,传统的MMSE检测算法涉及高维矩阵求逆运算,由于复杂度过高而使其在实际应用中难以快速有效地实现.基于最速下降(steepest descent,SD)算法和高斯一赛德尔(Gauss-Seidel,GS)迭代的方法提出了一种低复杂度的混合迭代算法,利用SD算法为复杂度相对较低的GS迭代算法提供有效的搜索方向,以加快算法收敛的速度.同时,给出了一种用于信道译码的比特似然比(LLR)近似计算方法.仿真结果表明,通过几次迭代,给出的算法能够快速收敛并接近MMSE检测性能,并将算法复杂度降低一个数量级,保持在O(K2).     

大规模MIMO系统中基于权重二对角迭代的低复杂度预编码

大规模MIMO系统中由于系统下行链路的迫零（zero forcing,ZF）预编码中存在大矩阵求逆运算,随着用户数与天线数的增加,其复杂度随之增加。为了降低复杂度,提出了一种基于雅克比（Jacobi）迭代算法的改进预编码算法,用下二对角矩阵作为迭代矩阵,并且将迭代结果与上一步迭代结果进行权重相加来加速迭代。根据大规模MIMO系统信道矩阵的对角占优特性,将矩阵求逆的诺依曼近似的第一项作为迭代的初始值进一步加速迭代。相比于传统迫零预编码方案,提出的方案可以降低一个量级的算法复杂度,并且保证了预编码方案的性能。     

Performance analysis of achievable sum‐rate for downlink massive MIMO systems

Massive multiple‐input and multiple‐output (MIMO) has been recognized as a promising technology in the fifth‐generation wireless networks. Under perfect channel state information, we derive three tractable closed‐form expressions that corresponding to the lower bound, approximation, and upper bound on the achievable rate in a massive MIMO downlink system with maximum‐ratio transmission precoding. Based on the proposed closed‐form expressions, the power efficiency of the system is investigated as the number of transmit antennas increases. Simulation results demonstrate the tightness of our proposed closed‐form expressions for the achievable sum‐rate.     

Iterative nonlinear detection for SFBC SC–FDMA uplink MIMO transmission systems

Single‐carrier frequency division multiple access (SC‐FDMA) systems with space frequency block coding (SFBC) transmissions achieve both spatial and frequency diversity gains in wireless communications. However, SFBC SC‐FDMA schemes using linear detectors suffer from severe performance deterioration because of noise enhancement propagation and additive noise presence in the detected output. Both issues are similar to inter‐symbol‐interference (ISI). Traditionally, SC‐FDMA system decision feedback equalizer (DFE) is often used to eliminate ISI caused by multipath propagation. This article proposes frequency domain turbo equalization based on nonlinear multiuser detection for uplink SFBC SC‐FDMA transmission systems. The presented iterative receiver performs equalization with soft decisions feedback for ISI mitigation. Its coefficients are derived using minimum mean squared error criteria. The receiver configuration study is Alamouti's SFBC with two transmit and two receive antennas. New receiver approach is compared with the recently proposed suboptimal linear detector for SFBC SC‐FDMA systems. Simulation results confirm that the performance of the proposed iterative detection outperforms conventional detection techniques. After a few iterations, bit‐error‐rate performance of the proposed receiver design is closely to the matched filter bound. Copyright © 2016 John Wiley & Sons, Ltd.     

An efficient hybrid strategy for uplink channel estimation in massive MIMO systems based on spatially correlated channels

The channel estimation (CE) process is an important phase that has a considerable influence on the performance of massive multiple-input multiple-output systems, in particular, in a more realistic scenario where the channels are spatially correlated (ScD). Thereby, in this work, the uplink (UL) CE process and channel hardening (CH) feature is addressed for ScD Rayleigh fading channels using the statistical Bayesian minimum mean square error estimator. The spatial correlation (SC) of the channels is described using different models, namely, the Gaussian local scattering (GLS) model, the uniform local scattering model, and the proposed hybrid model. Each model (i.e., GLS model and the uniform local scattering model) is studied using two arrangements, that is, for a uniform linear array (ULA) and uniform planar array (UPA). Moreover, the CH feature is investigated under SC of the channels using different models. Furthermore, this study proposes an efficient hybrid strategy based on SC of the channels for UL CE; that is, this work proposes a hybrid covariance matrix (CM) for UPA arrangement by relying on the Kronecker product of the CMs generated through two ULA arrangements, where the first CM is generated through horizontal ULA using GLS model, whereas the second CM is generated through vertical ULA using uniform local scattering model (i.e., one-ring model). Numerical results regarding CE and CH are provided to assert the theoretical expressions, where the CE is evaluated using the normalized mean square error, whereas the CH is assessed using the variance of CH.     

Joint distance‐based user grouping and pilot assignment schemes for pilot decontamination in massive MIMO systems

Pilot contamination (PC) is one of the most crucial problems in massive multiple‐input multiple‐output (MIMO) systems, due to a limited source of the coherence block. In the current study, two pilot assignment schemes proposed for massive MIMO uplink transmission. We divided each cell into two groups of edge and center users under distance‐based user grouping algorithm (DUG), which the aim is finding the best user grouping boundary. The best boundary is where both signal to interference plus noise Ratio (SINR) of edge and center users is maximum, according to the user's distance to base stations (BS). We investigated the location‐aware pilot assignment (LPA) scheme to enhance the quality of services for both groups. In LPA by assuming three pilot groups for adjacent cells and determining the user's distance to BS, the planned pilots assigned to the users according to their distance to the BS. Then, we optimized pilot schedules in each group by maximizing uplink (UL) rate of each user with auction‐based optimization pilot assignment (AOPA). Simulation results show that both DUG and LPA improve the rate of edge users about 70% and the rate of center users about 30%. Joint DUG and AOPA enhance the rate of the edge and center users about 100% and 80% in each group than conventional schemes and about 50% and 10%, compared with the LPA method. Simulation results show that the proposed method is efficient in reducing PC and improving spectral efficiency.     

Capacity maximization in eigen‐MIMO with channel estimation and CSI feedback‐link throughput constraint

Water‐filled eigenchannels offer the highest multi‐input multi‐output (MIMO) information‐theoretic capacity, but digital techniques such as quadrature amplitude modulation and finite block lengths will degrade the capacity from the Shannon limit to the capacity of a digital link. Furthermore, eigen‐MIMO requires channel overheads, such as estimating the channel state information (CSI) and feeding it back to the transmitter, which further compromise the capacity. In this paper, the joint influence of channel estimation and imperfect feedback on the information‐theoretic capacity and the practicable capacity is analyzed. The channel is modeled as static over a MIMO channel block. In each block, the forward channel is used for CSI estimation and for the payload data transmission. In the back direction, the channel is used to feed back a quantized form of the CSI to the transmitter with a throughput constraint. These three channel usages are combined into an effective simplex channel simplifying the capacity analysis. The capacities are formulated as functions of the link parameters, enabling optimization of the number of training symbols, the feedback duration, and the power allocation for training and data transfer, with the criterion of maximum capacity. The results presented are subject to the usual approximations used in communications theory. Copyright © 2012 John Wiley & Sons, Ltd.     

大规模MIMO系统中收发联合阈值天线选择算法

在大规模多输入多输出(massive MIMO)系统中使用天线选择算法可提高能效和系统吞吐量,然而适用于传统MIMO系统的天线选择算法具有高复杂度,很难用于massive MIMO系统。为优化天线选择算法,以算法复杂度和系统容量为优化目标,提出了收发联合阈值天线选择算法。该算法在发射端使用最大范数双向天线选择算法进行天线选择,在接收端使用分组maxvol算法并通过仿真实验结果的预设阈值进行天线选择。仿真实验表明,收发联合阈值天线选择算法在降低复杂度的同时可以提高系统容量,与递增天线选择算法相比,系统容量最多可提高52.2 bit/s/Hz。提出的天线选择算法可以满足不同天线相关度和信噪比的传输环境。