Analytical assessment of multi-user vs. spatial diversity trade-offs with delayed channel state information

In this letter, we explore the combined use of spatial and multi-user diversity in a cellular system where channel state information is subject to delays in the feedback channel. First, we analytically derive the probability and cumulative density functions of the post-scheduling signal-to-noise ratio (SNR) for both a single-input single-output (SISO) and an orthogonal space-time block coding (OSTBC) transmission schemes. Then, we obtain the closed-form expressions of the corresponding average system capacities. By evaluating those expressions, we analytically show that the OSTBC scheme is far less sensitive to delays in the feedback channel.     

基于独立分量分析的正交空时分组编码盲检测方案

通过在不同天线发射的信号之间引入时域和空域信息,正交空时分组编码(OSTBC)可以获得发射分集增益,而且可以在不牺牲带宽的情况下获得更高的编码增益。但是其译码却需要精确的信道状态信息(CSI),因此,信道信息估计的准确性严重影响系统的性能。基于独立分量分析(ICA)的盲源分离(BSS)技术可以在不进行信道估计的情况下对发射信号实现有效检测。通过利用OSTBC的正交特性,提出了2种基于ICA的盲检测方案,同时,一些基于信道估计的检测算法也被用来进行性能比较。瑞利衰落信道下的仿真结果表明,2种新方案均具有较好的系统适应性和误码率性能。     

Performance Analysis of Multiuser Diversity on OSTBC MIMO Systems with Antenna Selection in the Presence of Feedback Delay CSI

In this paper, we studied a comprehensive analytical symbol error probability (SEP) performance analysis of downlink multiuser diversity (MUD) on orthogonal space–time block code (OSTBC) system with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The novel analytical approach is suitable for MUD with TAS/OSTBC systems in which effective receiver signal-to-noise ratio (SNR) is described as highest order statistic of Chi square distribution. Based on this framework, the closed-form SEP expressions are evaluated for the MUD exploiting TAS/OSTBC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate SEP; upper bound and lower bound SEP at high SNR under delayed feedback CSI. Thereafter the impact of feedback delay and antenna structures with significance on the consideration of MUD on the performance of the system has been analyzed.

     

MIMO系统中空时分组编码仿真实现

空时分组码是一种结合信道编码和分集技术的新型的编码和信号处理方法。它可以不需增加带宽,大幅度的提高无线通信系统的信息容量和传输速率,从而提供远高于传统单天线系统的频带利用率。采用广义平稳非相关散射下的多径时变瑞利信道模型,对多输入多输出（MIMO）系统中空时分组编码进行了仿真研究。仿真结果表明：MIMO系统中正交空时分组编码在误码率性能上优于Alamouti编码。     

Analysis of transmit antenna selection/orthogonal space‐time block coding with receive selection and combining in the presence of feedback errors

Examining the effect of imperfect transmit antenna selection (TAS) caused by the feedback link errors on the performance of hybrid TAS/orthogonal space‐time block coding (OSTBC) with single receive antenna selection (i.e., joint transmit and receive antenna selection (JTRAS)/OSTBC) and TAS/OSTBC (with receive maximal‐ratio combining‐like combining structure) over slow and frequency‐flat Nakagami‐m fading channels is the main objective of this paper. Under ideal channel estimation and delay‐free feedback assumptions, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio are derived by defining a unified system model concerning both JTRAS/OSTBC and TAS/OSTBC schemes. Exact analytical expressions for outage probability (OP) and bit/symbol error rates of M‐ary modulations are presented in order to provide a detailed examination on the OP and error performances of the unified system that experiences feedback errors. Also, the asymptotic diversity order analysis, which shows that the diversity order of the investigated schemes is equal to the diversity order provided by OSTBC transmission itself, is included in the paper. Moreover, we have validated the theoretical results via Monte Carlo simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

高速铁路无线通信中基于正交空时码的格型正交重构算法

分析了基于正交空时码的开环和闭环MIMO系统,并着重研究了高铁场景下速度对正交空时码的影响：高速移动导致的快时变信道将会破环正交空时码的正交结构,降低由此获得的分集增益,从而引起了误码率性能的降低。提出了格型正交重构算法,通过givens变换对正交空时码进行码内正交重构;算法在恢复码内正交性的同时,也改变了发射端波束成形方向。因此,在高速移动场景下,所提算法使发射端获得了波束成形的阵列增益以及与用户静止时相同的分集增益。从系统性能仿真中看出,所提算法提升了高铁场景下基于正交空时码MIMO系统的误码性能。     

Achievable Performance of Orthogonal STBC Over Spatially Correlated Rician Channels

The effect of spatial correlation on the performance of orthogonal space-time block codes (OSTBCs) over multiple-input-multiple-output (MIMO) Rician fading channels is studied. Asymptotic error-rate formulas for OSTBC with high average signal-to-noise ratios (ASNRs) over arbitrarily correlated Rician MIMO channels are derived in terms of the diversity and coding gains. Our results show that, in correlated fading, the phase vector phi of the channel line-of-sight (LOS) components affects the effective Rice K-factor at the OSTBC receiver output and, hence, may result in a coding gain that is significantly higher than that for independent Rician MIMO channels. Furthermore, when the channel covariance matrix is rank deficient and under some additional mild conditions, the error and outage probabilities of OSTBC achieve those in a nonfading additive-white-Gaussian-noise channel. For both cases of full-rank and rank-deficient channel covariance matrices, analytical expressions of optimal and worst case phase vectors phi, and exact upper and lower bounds of OSTBC performance are derived. These results provide new insights into the achievable performance of OSTBC over correlated Rician MIMO channels and, if incorporated into future multiple antenna systems design, will bring about significant performance enhancement     

Full-Diversity and Fast ML Decoding Properties of General Orthogonal Space-Time Block Codes for MIMO-OFDM Systems

In this letter we apply the general orthogonal space-time block codes (OSTBC) to MIMO-OFDM systems over frequency-selective fading channels and aim to exploit the potential multipath diversity. By replacing the scalar entry of an OSTBC matrix with the vector of repeated symbols, we obtain a new OSTBC which can achieve both spatial diversity and multipath diversity. Moreover, a fast maximum likelihood (ML) decoding is admitted. Simulation results show that the proposed OSTBC, for two transmit antennas, can obtain a higher diversity gain than the Alamouti code at the same ML decoding complexity     

Timing error detector design and analysis for orthogonal space-time block code receivers

A general framework for the design of low complexity timing error detectors (TEDs) for orthogonal space-time block code (OSTBC) receivers is proposed. Specifically, we derive sufficient conditions for a difference-of-threshold-crossings timing error estimate to be robust to channel fading. General expressions for the S-curve, estimation error variance and the signal-to-noise ratio are also obtained. As the designed detectors inherently depend on the properties of the OSTBC under consideration, we derive and evaluate the properties of TEDs for a number of known codes. Simulations are used to assess the system performance with the proposed timing detectors incorporated into the receiver timing loop operating in tracking mode. While the theoretical derivations assume a receiver with perfect channel state information and symbol decisions, simulation results include performance for pilot-symbol-based channel estimation and data symbol detection errors. For the case of frequency-flat Rayleigh fading and QPSK modulation, symbol-error-rate results show timing synchronization loss of less than 0.3 dB for practical timing offsets. In addition it is shown that the receiver is able to track timing drift with a normalized bandwidth of up to 0.001.     

Performance analysis for transmit antenna diversity with/withoutchannel information

Transmit antenna diversity (TAD) for the downlink channel has been investigated to improve the performance of wireless communications using multiple transmit antennas. We present a performance analysis for TAD with/without channel information. For performance analysis, we use the pairwise error probability and cutoff rate. For the closed-loop TAD in frequency-division duplex (FDD) mode, the downlink channel information should be transmitted to the base station from the mobile station. The feedback channel information may be imperfect because of the feedback delay, quantization error, and feedback error. The impact of imperfect channel information has been considered to analyze the performance of the TAD. We also present a performance analysis for a TAD technique that does not use the channel information, called space-time transmit diversity (STTD). Looking at the cutoff rates for the TAD techniques, the trellis-coded modulation (TCM) has been considered for better performance. Simulation results are shown to see the impact of the TCM on TAD systems     

基于独立分量分析的实正交空时分组码盲识别

提出一种基于独立分量分析的正交空时分组码(OSTBC)盲识别方法。首先给出了接收信号模型,利用独立分量分析得到含有编码矩阵的虚拟信道矩阵,然后利用编码矩阵特性,证明得到正交空时分组码的虚拟信道矩阵的相关矩阵为对角矩阵;最后提出用于正交空时分组码识别的2个特征参数:稀疏度和方差。仿真结果表明,所提出方法能够较好地识别正交空时分组码。     

Conventional and modified TAS/OSTBC schemes in dual‐hop fixed‐gain amplify‐and‐forward relaying systems with imperfect feedback

Modified transmit antenna selection (TAS)/orthogonal space‐time block coding (OSTBC) (M‐TAS/OSTBC) schemes have been shown to achieve superior error performance together with a reduced‐rate feedback channel in the presence of feedback errors (FEs) when compared with the conventional TAS/OSTBC (C‐TAS/OSTBC) schemes. This paper focuses on the bringing of fixed‐gain amplify‐and‐forward (FGAF) relaying schemes that employ M‐TAS/OSTBC schemes at both hops that provides reduced feedback‐rate and robust error performance in the presence of erroneous‐feedback channels. The exact expressions of the outage and error probabilities for both dual‐hop FGAF relaying schemes in Nakagami‐m fading channels have been derived and validated via Monte Carlo simulations. Additionally, with the help of high signal‐to‐noise ratio (SNR) (i.e., asymptotic) approaches and some analytical approximations, the asymptotic diversity order analysis has been carried out. Besides, by providing a simulation‐based examination on the inclusion of power allocation within the modified scheme, the additional advantages on the performance have been exhibited. The extensive investigation and comparisons to the conventional schemes have shown that M‐TAS/OSTBC schemes employed at each transmission link provide full diversity order and considerable error performance as the C‐TAS/OSTBC scheme in ideal feedback cases and also achieve more robust error performance in the presence of FEs. Thus, by using M‐TAS/OSTBC schemes, the overall performances of the dual‐hop FGAF relaying schemes have been enhanced, which would result in reductions on the average SNR requirements to achieve a specified error rate constraint. Copyright © 2015 John Wiley & Sons, Ltd.     

Transmit Diversity Versus Opportunistic Beamforming in Data Packet Mobile Downlink Transmission

We compare space-time coding (transmit diversity) and random "opportunistic" beamforming in a space-division multiple access/time-division multiple access single-cell downlink system with random packet arrivals, correlated block-fading channels, and non-perfect channel state information at the transmitter due to a feedback delay. Our comparison is based on system stability. The ability of accurately predicting the channel signal-to-noise ratio dominates the performance of opportunistic beamforming, even under the optimistic assumption that the sequence of beamforming matrices is perfectly known a priori by the receivers. Our results show that the relative merit of opportunistic beamforming versus space-time coding strongly depends on the channel Doppler bandwidth. Therefore, previous naive conclusions on the fact that transmit diversity always hurts the system performance under multiuser-diversity scheduling should be taken with great care     

正交空时分组编码系统的信号检测技术

正交空时分担编码（OSTBC）技术可以提高信道容量和误码性能,准静态平坦衰落信道和时变平坦衰落信道下正交空时分组编码率的信号检测技术得到广泛研究。利用正交频分复用技术（OFDM）,研究了时变多径衰落信道下OSTBC-OFDM的信号检测方法,提出了一种能够有效利用无线信道的多径传播效应的发射天线数目等于4的OSTBC信号检测算法,仿真结果表明,发射天线书等于4,接收天线数等于2时,与已有信号检测算法相比,提出的算法有4.5dB性能增益。     

基于单载波频域均衡的异步空时协作传输机制

 异步环境下,空时协作传输系统的各中继站点无法精确同步,导致不能直接使用正交空时分组码;异步还可能导致采样时刻的不理想,由于脉冲成型滤波器的缘故,使得平衰落信道变成频率选择性衰落信道,严重影响系统性能.针对这些问题,本文提出一种基于单载波频域均衡的异步空时协作传输机制.各中继站点基于正交空时分组码的思想对数据执行逆序共轭等简单操作后发送;目的站点对接收数据进行快速傅立叶变换(FFT)后,通过线性组合分离重叠在一起的数据帧,然后对组合输出的数据执行频域均衡,最后执行快速傅立叶逆变换(IFFT)还原发送数据.由于FFT和IFFT有快速算法,因此新机制有较低的复杂度.理论分析和仿真结果表明:即使在异步环境下,提出的新机制也能获得空时分组码所提供的分集增益.     

Outage probability analysis of a MIMO relay channel with orthogonal space-time block codes

We investigate the performance of a cooperative multiple-input multiple-output (MIMO) relay channel in which the source and relay use the same orthogonal space-time block code (OSTBC) for transmission whereas the relay and destination use maximum-ratio-combining (MRC) for reception. Considering that perfect channel state information is available at the relay and destination, we derive a closed-form expression for the outage probability of the destination signal-to-noise ratio (SNR) in terms of the confluent hypergeometric function of two variables in a Rayleigh flat-fading environment. The validity of the closed-form expression is confirmed with the numerical results.     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

Orthogonal Space-Time Block Codes with Feedback

In this paper we consider how Orthogonal Space-Time Block Codes (OSTBC) can be used in the presence of feedback from the receiver to the transmitter. First, we survey how some of the feedback techniques for AWGN channels with fading can be applied to OSTBC. Then we consider a simple scheme with diagonal weighting. The optimal diagonal weighting matrix, which minimizes the probability of error, is derived. The optimal weights depend on the channel and, hence, a feedback becomes necessary. However, the required feedback can be accomplished using log₂ (n _t) bits, where n _t is the number of transmit antennas. Simulations show that relatively significant gains can be achieved with the diagonal weighting scheme. In a practical system it is quite possible that the bits that are fed back to the transmitter are in error. In that case we show that there will be a loss of diversity. To overcome this loss, we develop weighting schemes that are error tolerant and always perform better than the unweighted OSTBC (even in the presence of feedback errors).     

Transmit antenna shuffling for quasi-orthogonal space-time block codes with linear receivers

In this letter, we propose a transmit antenna shuffling scheme for quasi-orthogonal space-time block codes (QO-STBCs). We show that by adaptively mapping the space-time sequences of the QO-STBC to the appropriate transmit antennas depending on the channel condition, the proposed scheme can improve its transmit diversity with limited feedback information. The performance of the scheme with various numbers of shuffling patterns is analyzed. The bit error probability of the schemes is evaluated by simulations. It is demonstrated that with the linear zero-forcing (ZF) and the minimum mean squared error (MMSE) receivers, the closed-loop QO-STBC using two feedback bits can achieve almost the same performance as the ideal 4-path diversity and it is about 4-5 dB better than the open loop schemes.     

Improving BER performance of virtual QOSTBC

In this paper, we propose a new solution for improving BER performance of virtual quasi orthogonal space-time block coding (QOSTBC). The proposed solution is compared with virtual QOSTBC and virtual orthogonal space-time block coding (OSTBC). One of the main disadvantages of virtual OSTBC is its code rate, while on the other side code rate of QOSTBC equals 1, but with BER performance degradation as a consequence. The scheme proposed here provides improved BER performance in comparison with QOSTBC, and has preserved code rate of 1. The considered schemes are used for creating virtual 4 × 1 multiple input-single output channel. These schemes include one base station, one relay station, both equipped with two antennas, and one mobile station with a single antenna.