Analytical modelling of multiservice switching networks with multiservice sources and resource management mechanisms

In this paper, we presents an analytical link capacity and outage performance analysis of downlink multiuser diversity (MUD) in multiple-input multiple-output (MIMO) system employing maximal-ratio combining (MRC) with transmit antenna selection (TAS) in the presence of imperfect channel state information (CSI) due to feedback delay over Rayleigh fading channels. The unified achievable analysis is appropriate for MUD–MIMO with TAS/MRC systems in which effective output signal-to-noise ratio (SNR) is specified as highest order statistic of chi-square distribution. Based on this framework, the closed-form channel capacity and outage probability expressions are examined for the MUD–MIMO exploiting TAS/MRC with normalized SNR based scheduling in heterogeneous wireless networks. Further, we derive approximate upper bound capacity as well as capacity at high SNR and low SNR region under delayed feedback CSI. The upper and lower bound of outage probability under delayed feedback CSI is also evaluated. 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.     

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.     

非理想反馈链路下的发送天线选择系统性能分析

该文提出了一种近似分析的方法,得到了非理想反馈链路下的发送天线选择(Transmit Antenna Selection, TAS)系统的符号差错概率(Symbol Error Probability,SEP)。这种近似的方法适用于采用任意正交空时分组码的TAS系统,并且对于发送端选择两天线的系统还给出了SEP的显式表达式。该文研究表明TAS系统的发送分集度由所选天线子集中最大的矩幅序号决定。蒙特卡罗仿真验证了当信噪比较高时,由该文近似方法得到的系统SEP和理论上的SEP非常吻合。     

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.     

End‐to‐end performance of transmit antenna selection and generalized selection combining in dual‐hop amplify‐and‐forward relay network in the presence of feedback errors

In this paper, end‐to‐end performance of transmit antenna selection (TAS) and generalized selection combining (GSC) is studied in a dual‐hop amplify‐and‐forward relay network over flat Rayleigh fading channels. In the system, source and destination equipped with multiple antennas, communicate by the help of single relay equipped with single antenna. Source‐destination link is not available. TAS is used for transmission at the source, and GSC is used for reception at the destination. By considering the relay location and the presence of error in feedback channel from the relay to the source, we derive closed‐form outage probability, moment generating function and moments of end‐to‐end signal‐to‐noise ratio, and closed‐form symbol error probability (SEP) expressions for channel state information (CSI)‐based and fixed relay gains. The diversity order and array gain of the network are obtained for both CSI‐based and fixed relay gains by deriving asymptotical outage probability and SEP expressions. The analytical results are validated by the Monte Carlo simulations. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of diversity schemes employing antenna selection in the presence of channel estimation errors and feedback delay

The main objective of this paper is to provide an extensive and complete examination on the effect of practical impairments such as channel estimation errors (CEEs) and feedback delay (FD) on the performance of diversity schemes over Nakagami‐m fading channels. Under erroneous channel estimation and outdated feedback cases, statistical expressions and several performance metrics related to the post‐processing signal‐to‐noise ratio (SNR) are derived for four different diversity schemes: transmit antenna selection (TAS)/orthogonal space–time block coding, TAS/maximal‐ratio transmission (MRT), MRT/receive antenna selection (RAS), and joint transmit and RAS. Exact analytical expressions for outage probability and average error rates of M‐ary modulations are derived in order to provide insightful perspectives on the capacity and error performance of diversity schemes that experience both CEE and FD. The asymptotic diversity order of the investigated diversity schemes are derived via a high‐SNR approximation approach. In order to assess the real‐world performance of the investigated diversity schemes and to observe their robustness or sensitivities in practical imperfections, various configurations are considered together with several performance comparisons. Also, Monte Carlo simulations are performed in order to validate the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

混合衰落信道下存在反馈时延的多天线中继性能分析

研究了混合Rayleigh-Rician衰落信道下,存在反馈时延的多天线双跳放大转发（AF）中继系统的性能.首先,基于反馈时延波束成形（BF）模型得到混合衰落信道下中继系统的输出等效信噪比（SNR）.然后,利用无穷级数展开推导出输出信噪比中断概率（OP）和概率密度函数（PDF）的解析表达式,并进一步得到中继系统遍历容量和平均误符号率（ASER）的理论计算公式.最后,计算机仿真验证了所提出的性能分析方法的正确性,并定量分析了天线数量、反馈时延和信道参数对系统性能的影响.     

Analysis of Transmit Antenna Selection/Maximal-Ratio Combining in Rayleigh Fading Channels

In this paper, we investigate a multiple-input-multiple-output (MIMO) scheme combining transmit antenna selection and receiver maximal-ratio combining (the TAS/MRC scheme). In this scheme, a single transmit antenna, which maximizes the total received signal power at the receiver, is selected for uncoded transmission. The closed-form outage probability of the system with transmit antenna selection is presented. The bit error rate (BER) of the TAS/MRC scheme is derived for binary phase-shift keying (BPSK) in flat Rayleigh fading channels. The BER analysis demonstrates that the TAS/MRC scheme can achieve a full diversity order at high signal-to-noise ratios (SNRs), as if all the transmit antennas were used. The average SNR gain of the TAS/MRC is quantified and compared with those of uncoded receiver MRC and space-time block codes (STBCs). The analytical results are verified by simulation. It is shown that the TAS/MRC scheme outperforms some more complex space-time codes of the same spectral efficiency. The cost of the improved performance is a low-rate feedback channel. We also show that channel estimation errors based on pilot symbols have no impact on the diversity order over quasi-static fading channels.     

Performance Analysis of Multiuser Diversity in MIMO Systems with Antenna Selection

In this paper, a framework is presented to analyze the performance of multiuser diversity (MUD) in multiuser point-to-multipoint (PMP) MIMO systems with antenna selection. Based on this framework, the tight closed-form expressions of outage capacity and average symbol error rate are derived for the multiuser transmit antenna selection with maximal-ratio combining (TAS/MRC) system, by which we show how and with what characteristics antenna selection gains, MIMO antenna configurations and fading gains impact on the system performance, with an emphasis on the study of multiuser diversity influence. From both theoretical and simulation results, our study shows that in multiuser PMP TAS/MRC systems an diversity order equals to the product of the number of transmit antennas, number of receive antennas and number of users can be achieved; what's more, users plays a key role in the system performance and can be viewed as equivalent 'virtual" transmit antennas, which is the source of the multiuser diversity inherent exists in the multiuser system. This kind of diversity can be efficiently extracted in the design of multiantenna systems.     

Novel transmit antenna selection strategy for massive MIMO downlink channel

In this paper, we deal with the problem of acquiring the channel state information (CSI) at the transmitter in large-scale multiple input multiple output (MIMO) systems, so-called massive MIMO systems. Clearly, obtaining CSI plays a central role to provide high system performance. Even though, in frequency-division duplexed systems, acquiring this information requires a prohibitive amount of feedback, since it increases with the number of transmit antenna. In this work, we design an efficient transmit antenna selection strategy aware of the amount of required CSI for a point-to-multipoint transmission in massive MIMO systems. The proposed strategy provides high sum-rate with limited CSI feedback and limited computational complexity. Innovatively, the antenna selection in our strategy is performed in a decentralized fashion successively at the receiving users. Two schemes are proposed in this work to perform the antenna selection at each user. Next, taking into consideration that the large-scale MIMO transmitter suffers from imperfect knowledge of CSI, we design a new performance criterion. Computer simulations validate that, when the CSI is perfectly known, the proposed strategy is able to achieve high performance in terms of system sum-rate while a significant reduction in both CSI feedback overhead and computational complexity is observed. Moreover, assuming imperfect CSI, the new proposed criterion achieves higher performance when the estimation accuracy is low and at high SNR regime.     

Opportunistic Beamforming over Rayleigh Channels with Partial Side Information

In recent years, diversity techniques have evolved into highly attractive technology for wireless communications in different forms. For instance, the channel fluctuations of the users in a network are exploited as multiuser diversity by scheduling the user with the best signal-to-noise ratio (SNR). When fading is slow, beamforming at a multiple antenna transmitter is used to induce artificial channel fluctuations to ensure multiuser diversity in the network. Such a beamforming scheme is called opportunistic beamforming since the transmitter uses random beamforming to artificially induce opportunism in the network [1]. Opportunism requires a large number of users in the system in order to reach the performance of the true beamforming that uses perfect channel state information (CSI). In this paper we investigate the benefit of having partial CSI at an opportunistic transmitter. In the investigation, we focus on the maximum normalized SNR scheduling where user?s feedback consists of SNR relative to its channel gain. We show that opportunism can be beneficially used to increase the average throughput of the system. Simulations support the analytical average throughput results obtained as the amount of CSI and the number of users vary.     

Error performance of transmit beamforming with delayed and limited feedback

Feedback delay can severely affect the performance of transmit beamforming (TB) and the analytical quantification of the performance degradation has attracted much research interest recently. In this letter, we study the effect of delayed and limited-rate codebook index feedback on the error rate performance of TB systems over Rayleigh fading channels. We derive closed-form expressions for the moment generating function (MGF) and the probability density function (PDF) of the receiver output signal-to-noise ratio (SNR) including the effects of outdated and finite-rate feedback and further provide accurate analytical error rate expressions, which are verified by simulation results. The coding gain gap between the full-rate and limited-rate feedback and the coding gain advantage of multiple transmit antennas to the single antenna are analyzed, for limited and delayed feedback. These results are simple and concise and provide new analytical insight into the achievable diversity and combining gains and the loss caused by feedback delay for different system parameters and modulation formats.     

Simple tight approximations of the error performance for dual-hop MIMO relay systems in Rayleigh fading

In this paper we present tight approximations of the error performance for the entire signal-to-noise ratio (SNR) range of practical interest for an amplify and forward (AF) relaying system with channel state information (CSI) at the relay and destination, which employs multiple antennas at the nodes and orthogonal space–time block coding (OSTBC) transmission over a flat Rayleigh fading. Additionally, for a high value SNR range, we simplified the tight approximation expression in the simple asymptotic expression. The comparison of the error performance obtained by those two approximations with the error performance obtained by numeric integration of moment generating functions (MGF) and by Monte Carlo simulations shows close matching of the results.     

Uplink Sum-Rate Analysis of Massive MIMO System with Pilot Contamination and CSI Delay

We consider multi-cell multi-user massive MIMO system under correlated Rayleigh fading channels. Taking pilot contamination and CSI delay into consideration, we derive the equivalent channel model with MMSE channel estimation and one-tap prediction. Employing this equivalent channel model, the lower bound of the uplink sum-rate is derived, and its asymptotical performance is studied when the base station antenna number goes without bound. We find that if we schedule the \(k\) -th user of all cells who have the same prediction coefficient, the uplink sum-rate is the same as the one with no CSI delay when the number of BS antennas goes without bound at a much greater rate than the number of users. Simulation results show that the asymptotic approximation has good performance for large \(M\) , and suggest that large antenna array can compensate for the decay due to CSI delay. Simulation results also verify our guess that CSI delay does not necessarilly decrease the uplink sum-rate due to the impact of pilot contamination.     

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.     

Performance of RCPC codes with soft-decision decoding overNakagami-m fading channels

The analytical upper bounds on the pairwise error probability of rate compatible punctured convolutional (RCPC) codes, using coherent BPSK signals over slow frequency nonselective Nakagami-m fading channels with AWGN, are evaluated. With perfect channel state information (CSI) assumption, we use a direct integral with the Nakagami-m probability density function to obtain a closed form upper bound. For the case without CSI, we find an approximated upper bound for the high SNR cases and the approximation can be justified for signal to noise ratio (SNR) E _s/N₀ ≫ 1.5 dB     

Performance analysis of hybrid transmit antenna selection/maximal‐ratio transmission in Nakagami‐m fading channels

Hybrid diversity systems have been of great importance because they provide better diversity orders and robustness to the fading effects of wireless communication systems. This paper focuses on the performance analysis of multiple‐input gle‐output systems that employ combined transmit antenna selection (TAS)/maximal‐ratio transmission (MRT) techniques (i.e., hybrid TAS/MRT). The probability density function, the moment generating function and the n ^th order moments of the output signal‐to‐noise ratio of the investigated diversity scheme are derived for independent identically distributed flat Nakagami‐m fading channels. The system capacity of the hybrid TAS/MRT scheme is examined from the outage probability perspective. Exact bit/symbol error rate (BER/SER) expressions for binary frequency shift keying, M‐ary phase shift keying and square M‐ary quadrature amplitude modulation signals are derived by using the moment generating function‐based analysis method. By deriving the upper bounds for BER/SER expressions, it is also shown that the investigated systems achieve full diversity orders at high signal‐to‐noise ratios. Also, by Monte Carlo simulations, analytical performance results are validated and the effect of feedback delay, channel estimation error and feedback quantization error on BER/SER performances are examined. Copyright © 2011 John Wiley & Sons, Ltd.     

Performance Analysis of OSTBC Transmission in Amplify-and-Forward Cooperative Relay Networks

A performance analysis is presented for amplify-and-forward (AF) cooperative relay networks employing transmit antenna diversity with orthogonal space-time block codes (OSTBCs), where multiple antennas are equipped at the transmitter. We develop a symbol-error-rate (SER) and outage performance analysis for OSTBC transmissions with and without cooperative diversity over flat Rayleigh fading channels. We first derive exact probability density functions (pdf's) and cumulative distribution functions (cdf's) for the system SNR without direct transmission with an arbitrary number of transmit antennas and then present the exact closed-form SER and outage probability expressions. Next, we derive the moment-generating function (MGF) for the overall system SNR with direct transmission and present the exact SER and outage probability with joint transmit antenna diversity and cooperative diversity. The theoretical analysis is validated by simulations, which indicate an exact match between them. The results also show how the transmit antenna diversity and the cooperative diversity affect the overall system performance.      

多径衰落下多天线CDMA系统信道容量研究

该文对准静态Rayleigh衰落下MIMO-CDMA系统信道容量进行了研究,分析了扩频码为Walsh函数,基于多码检测的极大似然检测器(MLD)和解相关检测器的性能,并和MMSE多用户检测器(MUD)进行了比较;分析了对不同检测器在一定的信噪比下系统天线数目和信道容量的关系。仿真结果表明:在相同的情况下,基于Walsh码CDMA系统容量按MUD、干扰方差已知的MLD,干扰方差未知的MLD和解相关检测器递减,并且后面的3种检测器在大信噪比的时候均有渐进的平台效应;在信噪比较大且一定时,CDMA系统信道容量与天线数目呈线性关系。     

反馈时延对闭环多天线系统性能的影响

该文研究了在时间相关信道下反馈时延对基于天线选择闭环多天线系统性能的影响。在这种系统中,接收端根据瞬时最大信噪比准则选择发射端天线,并把选定天线信息通过反馈链路传送给发射端来进行天线选择。文中分析了在时变信道下反馈时延对系统平均容量、容量中断概率及在BPSK调制下系统的误比特率的影响,给出了其关系的解析表达式,数值仿真证明了理论分析的正确性。