Channel estimation and channel tracking for correlated block-fading channels in massive MIMO systems

This paper presents a channel estimation and tracking method for correlated block-fading channels in massive MIMO wireless cellular systems. In order to conserve resources, the proposed algorithm requires the uplink pilot signal only once, at the start of communication. By utilizing the temporal correlation between consecutive Resource Blocks (RBs) and the error correction capability of turbo codes, the channel matrix in subsequent RBs is estimated at the Base Station (BS) itself using the uplink data of current the RB and the estimated channel matrix of previous the RB. Compared to existing blind estimation methods, the proposed method places fewer limitations on the system settings such as the number of BS antennas, the number of users, and the number of coherent channel usage compared to existing blind estimation methods. Simulation results show that the proposed algorithm provides better performance for a moderate RB size, a high-order of QAM scheme, and a smaller ratio of the number of BS antennas and mobile terminals (N/K). For a reasonably small N/K (order of 10), the proposed scheme achieves a lower symbol error probability than the conventional pilot-based estimation approach.     

On channel estimation in cell-free massive MIMO for spatially correlated channels with correlated shadowing under Rician fading

This work addresses channel estimation (CE) in the uplink phase for a cell-free massive multiple-input multiple-output system operating under the time division duplex protocol. Considering that, channels are spatially correlated under the Rician fading model, where the investigated model is composed of two components: deterministic and nondeterministic, with the deterministic component describing the line-of-sight paths and the nondeterministic component describing the non-line-of-sight paths. Additionally, we dealt with correlated shadow fading that represents the most realistic situation. On the other hand, this work introduces a dynamic cooperation cluster framework in which the user is not served with the whole network ( i.e., all access points [APs]) but only the APs that present the best channel conditions regarding that user. In other words, this work proposes partial CE for each user because only APs with the best channel conditions are allowed to compute channel estimates. Consequently, we proposed partial channel estimators that perform the CE process with low complexity, namely, a partial minimum mean square error estimator and a partial element-wise minimum mean square error estimator. In addition, a simple pilot assignment technique is proposed in order to reduce interference signals so that each user experiences low interference from other users. Furthermore, the computational complexity required by each estimator is derived, where it is represented by the number of complex multiplications that each estimator requires in each consistency block. Theoretical and simulated results are provided, where the performance of each estimator is evaluated and analyzed using the normalized mean-square error metric.     

Capacity of correlated MIMO Rayleigh channels

Abstract-This paper presents some exact results on the capacity of multiple-input-multiple-output (MIMO) channels subject to correlated Rayleigh fading when perfect channel state information (CSI) is known at the receiver. The authors focus on the semicorrelated scenario in which correlation exists either at the transmitter or at the receiver., They consider two cases: 1) the transmitter does not have any CSI and as such allocates power equally among transmitter antennas and 2) the transmitter only knows the statistical distribution of the channel. The first case derives the moment generating function (MGF) of the mutual information (MI) and then deduces from this MGF the mean MI. The authors also study the cumulative distribution function (CDF) of the MI, which can serve as an upper bound to the outage probability under the capacity versus outage formulation when the channel is nonergodic. The second case studies the capacity achieved by optimum power-loading and beamforming schemes based on covariance feedback. Numerical results illustrate that the full capacity of MIMO systems can be preserved even for relatively high values of correlation coefficients.     

Semi-blind maximum-likelihood joint channel/data estimation for correlated channels in multiuser MIMO networks

The aim of this paper is to investigate receiver techniques for maximum likelihood (ML) joint channel/data estimation in flat fading multiple-input multiple-output (MIMO) channels, that are both (i) data efficient and (ii) computationally attractive. The performance of iterative least squares (LS) for channel estimation combined with sphere decoding (SD) for data detection is examined for block fading channels, demonstrating the data efficiency provided by the semi-blind approach. The case of continuous fading channels is addressed with the aid of recursive least squares (RLS). The observed relative robustness of the ML solution to channel variations is exploited in deriving a block QR-based RLS-SD scheme, which allows significant complexity savings with little or no performance loss. The effects on the algorithms’ performance of the existence of spatially correlated fading and line-of-sight paths are also studied. For the multi-user MIMO scenario, the gains from exploiting temporal/spatial interference color are assessed. The optimal training sequence for ML channel estimation in the presence of co-channel interference (CCI) is also derived and shown to result in better channel estimation/faster convergence. The reported simulation results demonstrate the effectiveness, in terms of both data efficiency and performance gain, of the investigated schemes under realistic fading conditions.     

视距相关信道下考虑非理想CSI的MIMO收发联合设计

MIMO系统收发联合设计的性能依赖于信道状态信息(CSI)的质量。在较高通信频段(如6～8GHz)下,信道的视距分量相对于较低频段显著增加,采用传统的CSI模型无法反映实际的信道特点,从而影响联合设计算法的性能。本文在相关莱斯信道下,提出一种考虑高频段环境下非理想CSI的MIMO系统下行链路收发联合设计算法。论文推导出一种基于训练序列的信道估计误差模型代替传统误差模型,并在此基础上以最小化MSE为目标迭代求解最优预编码/解码矩阵。仿真结果表明,该算法在不同的子流数、视距分量、信道相关性以及信道估计误差环境下,具有较好的误码率性能。     

目标角度估计的多输入多输出雷达发射方向图综合

针对传统多输入多输出(Multiple-Input Multiple-Output,MIMO)雷达发射功率分散导致目标角度估计性能变差的问题,提出了一种新的MIMO雷达发射方向图综合方法.首先,结合发射功率的空域聚焦范围和发射导向矢量的旋转不变性,严格控制方向图逼近误差小于给定的门限,并且最小化发射方向图的峰值旁瓣功率;其次,约束协方差矩阵的对角元素相等,以实现发射功率效率最大化,在此基础之上推导了优化模型的二阶锥规划形式,以便采用原对偶内点算法进行有效求解;最后,利用平行因子分析算法对空间目标进行了收发角度估计.仿真结果表明:优化所得加权矩阵不仅能够使发射信号在指定空域进行有效聚焦,而且确保了每个阵元的发射功率相等,因而在发射功率和角度估计方法相同时,所提方法相对传统MIMO雷达具有更好的角度估计精度.     

DWT-based joint antenna selection for correlated MIMO channels

This paper proposes a new discrete wavelet transform (DWT)-based joint antenna selection scheme for spatially correlated multiple-input multiple output (MIMO) channels. To reduce the severe performance degradation of the traditional antenna selection schemes in correlated channels, a new scheme which employ joint antenna selection (JAS) at both link ends algorithm and embed DWT operations in the receiver-end RF chains is proposed. Through extensive simulations it is demonstrated that the proposed DWT-based joint antenna selection has significant improvement of the capacity for both i.i.d and correlated MIMO channels, while requiring only a minor hardware overhead and low computational complexity for the DWT operations. Moreover, it is shown that the capacity associated with DWT-based JAS is higher than the system employing DWT-based receive antenna selection (RAS) only. This is achieved in i.i.d. and correlated MIMO channels.     

空间相关MIMO信道下的有限反馈预编码

对于独立同分布的瑞利衰落信道,Grassmann码本可以取得良好的系统性能,但是当MIMO信道存在空间相关性时,该码本不可避免的带来性能损失,本文针对空间相关的MIMO信道,通过用发送相关矩阵的平方根对传统Grassmann码本进行旋转,然后再量化,得到适用于空间相关信道下的新码本,并通过实验仿真阐释了新得到的码本对于传统码本在误码率和信道容量方面等方面的性能优势。     

Transmit antenna selection of correlated MIMO multiuser cognitive radio networks in Nakagami‐m fading channels

In this paper, we examine the impact of antenna correlation on transmit antenna selection with receive maximal ratio combining (TAS/MRC) in multiple‐input multiple‐output multiuser underlay cognitive radio network (MIMO‐MCN) over a Nakagami‐m fading environment. The secondary network under consideration consists of a single source and M destinations equipped with multiple correlated antennas at each node. The primary network composed of L primary users, each of which is equipped with multiple correlated antennas. For the considered underlay spectrum sharing paradigm, the transmission power of the proposed secondary system is limited by the peak interference limit on the primary network and the maximum transmission power at the secondary network. In particular, we derive exact closed‐form expressions for the outage probability and average symbol error rate of the proposed secondary system. To gain further insights, simple asymptotic closed‐form expressions for the outage probability and symbol error rate are provided to obtain the achievable diversity order and coding gain of the system. In addition, the impact of antenna correlation on the secondary user ergodic capacity has been investigated by deriving closed‐form expressions for the secondary user capacity. The derived analytical formulas herein are supported by numerical and simulation results to clarify the main contributions. Copyright © 2016 John Wiley & Sons, Ltd.     

Transmit antenna selection for decision feedback detection in MIMO fading channels

In this paper, we investigate a transmit antenna selection (TAS) approach for the decision-feedback detector (DFD) over Rayleigh fading channels. In particular, for a multipleinput multiple-output (MIMO) channel with M transmit and N (N ⩾ M) receive antennas, we derive a lower bound on the outage probability for the TAS approach. The selected transmit antennas are those that maximize the post-processing signalto- noise ratio (SNR) at the receiver end. It is shown that the proposed TAS approach achieves a performance close to optimal selection based on exhaustive search, introduced in the literature, but at a lower complexity. Simulation results are presented to validate and demonstrate the performance gain of the proposed TAS approach.     

Some remarkable properties of diagonally correlated MIMO channels

This paper investigates so-called diagonally correlated multiple input-multiple output (MIMO) channels, which provide higher ergodic capacity than independent and identically distributed (i.i.d.) fading channels. The presented analysis details physical scenarios leading to such channels, some properties of the channel matrix, and an analytical expression for its ergodic capacity.     

Closed-form capacity expressions of orthogonalized correlated MIMO channels

Space-time block codes are known to orthogonalize the multiple-input multiple-output (MIMO) wireless channel, thus reducing the space-time vector detection to a simpler scalar detection problem. The capacity over orthogonalized ergodic correlated Rayleigh and Ricean flat-fading MIMO channels has so far only been given in integral form. This letter derives a closed form capacity expression over such channels, hence avoiding numerical integrations or Monte Carlo simulations.     

Lower capacity bound for MIMO correlated fading channels with keyhole

It is well known that the existence of spatial fading correlation and keyhole effects severely reduces the capacity of multiple-input and multiple-output (MIMO) channels. In this letter, for correlated Rayleigh frequency-flat fading channels with keyholes, a tight lower capacity bound is given in a closed form. For the uncorrelated case, the lower bound can be proved to be tight asymptotically. The tightness of this bound for both correlated and uncorrelated channels is demonstrated by numerical examples.     

Differential space-time modulation with eigen-beamforming for correlated MIMO fading channels

In this paper, joint differential space-time modulation (DSTM) and eigen-beamforming for correlated multiple-input multiple-output (MIMO) fading channels. While DSTM does not require knowledge of each channel realization, the channel's spatial correlation can be easily estimated without training at the receiver and exploited by the transmitter to enhance the error probability performance. A transmission scheme is developed here that combines beamforming with differential multiantenna modulation based on orthogonal space-time block coding. Error probability is analyzed for both spatially correlated and independent Rayleigh fading channels. Based on the error probability analysis, power loading coefficients are derived to improve performance. The analytical and simulation results presented here corroborate that the proposed scheme can achieve considerable performance gain in correlated channels relative to DSTM without beamforming.     

FFT-based hybrid antenna selection schemes for spatially correlated MIMO channels

In this letter, we address the antenna subset selection problem in spatially correlated multiple-input multiple-output (MIMO) channels. To reduce the severe performance degradation of the traditional antenna selection scheme in correlated channels, we propose to embed fast Fourier transform operations in the RF chains. The resulting system shows a significant advantage both for diversity schemes and for the capacity of spatial multiplexing, while requiring only a minor hardware overhead.     

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.     

Receive antenna selection for MIMO systems over correlated fading channels

In this letter, we propose a novel receive antenna selection algorithm based on cross entropy optimization to maximize the capacity over spatially correlated channels in multiple-input multiple-output (MIMO) wireless systems. The performance of the proposed algorithm is investigated and compared with the existing schemes. Simulation results show that our low complexity algorithm can achieve near-optimal results that converge to within 99% of the optimal results obtained by exhaustive search. In addition, the proposed algorithm achieves near-optimal results irrespective of the mutual relationship between the number of transmit and receive antennas, the statistical properties of the channel and the operating signal-to-noise ratio.     

Optimization of nonlinear signal constellations for real-world MIMO channels

The performance of spatial multiplexing (SM) multiple-input multiple-output (MIMO) communication systems is highly dependent on the richness of scattering, the presence of dominant components, and the interelement spacings. In this paper, a new interpretation of the impact of transmit correlation on the performance of SM is given based on a so-called "symbol-related array factor." Nonlinear signal constellations for SM over real-world fading channels are then designed by minimizing an estimate of the average symbol error rate under an average transmit power constraint. The new transmission scheme exploits the spectral efficiency advantage of SM and the robustness of eigen-beamforming. Through simulations, it is shown to be more robust against fading correlations and high Ricean K-factors than SM using the classical phase shift keying (PSK) and quadrature amplitude modulation (QAM) constellations. The symbol error rate performance of this scheme is not affected by a change in the propagation environment or the interelement distance. Furthermore, if the scheme is used on the uplink, no explicit rate-consuming feedback link from the base station to the mobile station is required.     

Cross-layer design based on RC-LDPC codes in MIMO channels with estimation errors

In this paper, we propose a cross-layer design framework combining adaptive modulation and coding (AMC) with hybrid automatic repeat request (HARQ) based on rate-compatible low-density parity-check codes (RC-LDPC) in multiple-input multiple-output (MIMO) fading channels with estimation errors. First, we propose a new puncturing pattern for RC-LDPC codes and demonstrate that the new puncturing pattern performs similar to the random puncturing but is easier to apply. Then, we apply RC-LDPC codes with the new puncturing pattern to the cross-layer design combing AMC with ARQ over MIMO fading channels and derive the expressions for the throughput of the system. The effect of channel estimation errors on the system throughput is also investigated. Numerical results show that the joint design of AMC and ARQ based on RC-LDPC codes can achieve considerable spectral efficiency gain.