Capacity of multiuser diversity systems with adaptive transmission and different MIMO schemes

In this paper, we present a comprehensive capacity analysis of the downlink of multiuser diversity (MD) systems with adaptive transmission over Rayleigh fading channels. First, the exact capacity of the single‐input single‐output (SISO) systems with MD and adaptive transmission technique is derived. The optimal power allocation scheme for such a system is shown to be a water‐filling algorithm. Next, we derive the exact closed‐form capacity expressions for different multiple‐input multiple‐output (MIMO) schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). In order to avoid the cumbersome numerical root finding techniques in solving the optimal cutoff SNR level below which the channel is not used, we also provide the approximate expressions for the cutoff level. For the MD MIMO systems, it is observed that the optimal power allocation strategy is to focus transmit power on a single transmit antenna (e.g. Tx‐MRC/Rx‐MRC scheme) or selecting the best transmit antennas (e.g. Tx‐SC/Rx‐MRC scheme). Copyright © 2007 John Wiley & Sons, Ltd.     

Performance analysis of MIMO systems with multiuser diversity

In this paper, we present a comprehensive performance analysis for multiple‐input multiple‐output (MIMO) systems with multiuser diversity over Rayleigh fading channels. We derive exact closed‐form expressions of the outage probability and the average bit error rate (BER) for different MIMO schemes, including the selective combining (SC), maximum ratio combining (MRC) and space‐time block codes (STBC). We also provide the explicit upper bounds on the BER performance. Finally, the mathematical formalism is verified by numeric results that study the interaction between the antenna diversity and the multiuser diversity. It is observed that the system performance is deteriorated as the number of transmit antennas increases in multiuser scenario, which is unlike the case in single‐user systems. Copyright © 2007 John Wiley & Sons, Ltd.     

Nakagami衰落上DE-QPSK在联合收发分集下的性能分析

利用高斯Q函数的高阶次幂在最大比合并（MRC）分集接收瑞利衰落信道上统计平均的结果,推导了Nakagami 衰落信道上采用组合发射选择合并（SC）/接收 MRC 天线分集的相干检测差分编码四相相移键控（DE-QPSK）的平均误符号率（ASER）精确表达式。利用高斯Q函数的近似表达式和矩生成函数（MGF）方法,推导了Nakagami衰落信道上采用组合SC/MRC天线分集的相干检测DE-QPSK 的ASER近似表达式。通过数值计算和仿真,验证了DE-QPSK的ASER精确表达式的正确性以及近似表达式的准确性。利用精确表达式和近似表达式可研究收发天线数目和衰落参数对DE-QPSK的ASER性能的影响,为实际SC/MRC天线分集方案的设计提供了理论指导。     

Performance analysis of multiuser diversity scheduling schemes in FSO communication sys-tem

Taking into consideration the aperture averaging, the system performance of a point-to-multipoint free space optical (FSO) system for various multiuser diversity scheduling schemes is studied over exponentiated Weibull (EW) fading channels. The selection principles of greedy scheduling (GS), selective multiuser diversity scheduling (SMDS), proportional fair scheduling (PFS) and selective multiuser diversity scheduling with exponential rule (SMDS-ER) schemes are introduced and compared on the basis of time-varying behavior of turbulence channel fading in the present system. The analytical average capacity expressions for the GS and SMDS schemes are derived, respectively. Then, the relative capacity simulations for PFS and SMDS-ER schemes are also provided over EW fading channels with the binary phase shift keying (BPSK) modulation. The results show that the GS scheme obtains the maximum average capacity at the cost of the fairness of users. The SMDS-ER receives the minimum capacity, but it guarantees the fairness of users. The SMDS and PFS schemes can get balance between capacity and fairness. This study can be used for FSO system design.     

Average probability of packet error with diversity reception over arbitrarily correlated fading channels

Closed form expressions for the average probability of packet error (PPE) are presented for no diversity, maximum ratio combining (MRC), selection combining (SC) and switch and stay combining (SSC) diversity schemes. The average PPE for the no diversity case is obtained in two alternative expressions assuming arbitrarily correlated Nakagami and Rician fading channels. For the MRC case, L diversity branches are considered and the channel samples are assumed to follow Nakagami distribution and to be arbitrarily correlated in both time and space. For the SC diversity scheme with L diversity branches, two bounds on the average PPE are derived for both slow and fast fading channels. The average PPE in this case is obtained in an infinite integral form for Nakagami channels while it is reduced to a closed form expression for the Rayleigh case. The average PPE is also derived in the case of SSC diversity with dual branches for both slow and fast Rayleigh fading channels. The new formulas are applicable for all modulation schemes where the conditional probability of error has an exponential dependence on the signal‐to‐noise ratio. The average PPE is then used to obtain a modified expression for the throughput for network protocols. In general, the diversity gain exhibits a little diminishing effect as the number of diversity branches increases. In addition, the system is found to be more sensitive to the space correlation than to the time correlation. The effects of different system parameters and diversity schemes are studied and discussed. Specific figures about the system performance are also provided. Copyright © 2004 John Wiley & Sons, Ltd.     

A new closed-form of ASEP and channel capacity with MRC and selection combining over Inverse Gaussian shadowing

This paper analyse and investigate the performance of communication system with maximal ratio combining (MRC) and selection combining (SC) over Inverse Gaussian (IG) fading distribution. All formats of coherent and non-coherent modulation schemes are considered and novel analytical expressions of average symbol error probability (ASEP) with diversity are derived. Gamma and IG fading distributions are popularly used as a mathematically less complex solution to lognormal in the open literature. Hence, we provide a comparative analysis between IG and gamma fading with the aim to provide a quantitative measure of the difference between the two distributions in the context of ASEP. Moreover, the novel closed-form expressions of channel capacity under transmission schemes such as optimal rate adaptation (ORA) and channel inversion fixed rate (CIFR) are derived and analysed with MRC and SC diversity over IG fading. The analytical results have been validated with the Monte Carlo simulations and the exact numerical results.     

最大比发射/选择接收技术的性能研究

为了提高系统性能并降低接收端(移动台)的硬件复杂度,提出一种新的MIMO传输技术。即在发射端(基站)按最大比发射(MRT,maximal-ratio transmit)技术,接收端则基于信噪比最大的原则仅选择一根接收天线来处理信号,记作MRT/RAS(maximal-ratio transmit/receiver antenna selection)。根据随机矩阵和排序统计的最新理论,推导出瑞利衰落信道下MRT/RAS系统的中断概率、误码率(BER)等性能指标的确切表达式。仿真结果表明MRT/RAS系统可以取得很好的阵列增益及满分集增益。相同频谱条件下,性能超过某些复杂的空时编码系统。而且在准静态衰落信道下,信道估计错误对取得的分集阶数并没有影响。仿真试验也证明了分析结果的正确性。     

Analytical level crossing rates and average fade durations for diversity techniques in Nakagami fading channels

The level crossing rates (LCRs) and average fade durations (AFDs) of a fading channel find diverse applications in the evaluation and design of wireless communication systems. Analytical expressions for these quantities are available in the literature for certain diversity reception techniques, but are generally limited to the Rayleigh fading channel, with few exceptions. Moreover, the methods employed are usually specific to a certain channel/diversity pair, and thus cannot be applied to all cases of interest. Using a unified methodology, we derive analytical expressions for the LCRs and AFDs for three diversity reception techniques and a general Nakagami (1960) fading channel. We provide novel analytical expressions for selection combining (SC) and equal-gain combining (EGC), and rederive in a more general manner the case of maximal-ratio combining (MRC). It is shown that our general results reduce to some specific cases previously published. These results are used to examine the effects of the diversity technique, the number of receiving branches and severity of the fading on the concerned quantities. It is observed that as the Nakagami m-parameter and the diversity order increase, the behavior of the combined received envelope for EGC follows closely the one for MRC, and distances itself from SC.     

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.     

Ordered Statistic Analysis for Diversity Combining Schemes over Nakagami-m Fading Channel

Order diversity combining technique is one of efficient methods to lower the complexity but not to significantly degrade performance. Recently, Eng and Milstein [1] proposed a novel order-combining technique, called the second order diversity combining (SC2) and third order diversity combining (SC3) and applied to Rayleigh fading channel. SC2 and SC3 schemes mean that the two (three) signals with the first two (three) largest amplitudes among the branches are chosen and coherently combined. However, when compared to Rayleigh distribution, the Nakagami-m distribution [10] provides a more general and versatile way to model wireless channel. For the reason, the bit error rate (BER) performance of proposed schemes were then analyzed with order statistic method and compared to the traditional diversity technique over Nakagami fading environment in this paper. The results are compared to maximal ratio combining (MRC), and conventional selection combining (SC) in coherent reception and to equal gain combining (EGC) in noncoherent reception. The results show that SC is in performance the worst for either in coherent or in noncoherent schemes, as expected. The performance differences between SC2 (SC3) and MRC (EGC) are not significant when the diversity order L 3, but the difference will increase when L 5. It is worth noting that the result of [1] is a special case with fading figure, m = 1. It is also observed the performance is much affected by the number of diversity branches L, the fading figure m, and the signal-to-noise ratio (SNR).     

DS-CDMA performance with maximum ratio combining and antenna arrays

The mobile communication channel is very hostile to a DS-CDMA signal and therefore effective techniques are needed to enhance system performance and capacity. Further, since DS-CDMA capacity and performance is limited by the uplink, ways to improve the uplink performance is needed. By implementing antenna arrays, diversity schemes or a combination of antenna arrays and diversity techniques, the uplink performance can be improved substantially. In this study we consider a single cell with a base station at the center with mobiles uniformly distributed around it. As channel model a Nakagami distributed path gain is assumed. This model was chosen for flexibility (e.g., Rayleigh and Rice channel models can be approximated) and also since empirical data suggests that path fading statistics are adequately described by this distribution. At the receiver an array of M antennas is used to discriminate between the users based on their spatial diversity. The fading process at each of the antenna elements is statistically dependent and further improvements can be realized by making use of the independent fading characteristics of the received signal. To make use of this statistical independent information, the performance of a P branch Maximum Ratio Combining (MRC) receiver is also considered. We further investigate the performance of a combination of P clusters of M antennas separated by the coherence bandwidth of the channel, thereby making use of both forms of spatial diversity. A comparison of the three schemes (antenna arrays, MRC diversity and a combination of antenna arrays and MRC diversity) under equal complexity conditions are made under multipath fading conditions. It is shown that the performance and capacity of a MRC diversity receiver outperforms the other two methods when perfect power control is assumed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Performance analysis of orthogonal space-time block codes in spatially correlated MIMO Nakagami fading channels

Orthogonal space-time block coding (STBC) is an open-loop transmit diversity scheme that decouples the multiple-input multiple-output (MIMO) channel, thereby reducing the space-time decoding into a scalar detection process. This characteristic of STBC makes it a powerful tool, achieving full diversity over MIMO fading channels, and requiring little computational cost for both the encoding and decoding processes. In this paper, we exploit the single-input single-output equivalency of STBC in order to analyze its performance over nonselective Nakagami fading channels in the presence of spatial fading correlation. More specifically, we derive exact closed-form expressions for the outage probability and ergodic capacity of STBC, when the latter is employed over spatially correlated MIMO Nakagami fading channels. Moreover, we derive the exact symbol error probability of coherent M-PSK and M-QAM, when these modulation schemes are used along with STBC over such fading channels. The derived formulae are then used to assess the robustness of STBC to spatial correlation by considering general MIMO correlation models and analyzing their effects on the outage probability, ergodic capacity, and symbol error probability achieved by STBC.     

Performance of coherent receivers with hybrid SC/MRC overNakagami-m fading channels

A performance analysis of two hybrid selective combining/maximal ratio combining (SC/MRC) diversity receivers over Nakagami-m (1960) fading channels with a flat multipath intensity profile is presented and numerically compared with that of the conventional SC and MRC schemes. Numerical results for particular cases of interest show that the bit error rate (BER) degradation arising from the use of hybrid SC/MRC instead of MRC is independent of the average signal-to-noise ratio (SNR) regardless of the severity of the fading and that MRC provides a higher rate of improvement than the hybrid SC/MRC as the severity of fading decreases     

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.     

分布式天线系统混合SC/MRC分集中断概率性能

在频率选择性复合Nakagami/lognormal衰落信道条件下,研究了层叠分布式天线系统(Cascade Distributed Antenna System--CDAS)采用混合SC/MRC分集的中断概率性能.针对中断概率性能,分析了多径密度函数(Multipath Intensity Profile MIP)衰减因子、空时分集维数、活动用户数、每比特平均接收信噪比以及衰落因子对系统性能的影响.仿真表明CDAS系统可以有效对抗衰落,提高系统容量,削弱对数正态阴影衰落影响.     

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.     

Robust Transmit Antenna Selection with Phase Feedback Over Correlated Fading Channels

A new transmit antenna selection (TAS) scheme with phase feedback for multiple-input multiple-output systems is proposed in this paper. This scheme allows two or more transmit antennas to simultaneously use one radio frequency chain. By grouping the transmit antennas according to their similarities in instantaneous channel coefficients into two subsets and treating each subset as a single antenna, both hardware complexity reduction and antenna array gain can be achieved. Compared with the transmit antenna selection combined with space-time block code (TAS/STBC) scheme, the proposed TAS scheme provides excellent robustness, in terms of symbol error rate performance, against spatially correlated fading channels. Moreover, the proposed TAS scheme need not use STBC encoder and decoder which used in the TAS/STBC schemes. Therefore, the proposed TAS scheme is simpler than the TAS/STBC schemes in practical hardware implementation.     

采用两条支路分集接收的相关瑞利衰落信道容量

本文研究采用两条支路最大比合并(MRC)或选择合并(SC)分集接收的相关瑞利衰落信道理论容量推导恒定发射功率自适应M进制正交幅度调制(M-QAM)的频谱效率,并将它们与独立同分布瑞利信道理论容量进行比较,其结果对收发信机之间无视距分量路径、接收机上分集天线之间的距离小于半个波长的无线通信系统设计具有指导作用.     

Performance Analysis of Ranging Process in Diversity Incorporated Wireless Systems Suffering from Narrowband Jamming

Ranging is a process where the base station (BS) identifies a mobile station (MS) among many other MSs with the help of Ranging code set, which is unique to each MS. Also, an estimation process is made to find the transition time delay which is the difference between the time at which the MS sends some data and the time at which the BS receives data. In this paper, the effect caused by jamming on the Ranging process will be analyzed. Jamming destroys orthogonality/pseudo orthogonality of the Ranging code set which affects the estimation of the codes. This in turn affects parameters like detection miss rate. This paper also discusses the improvement in the Ranging process where diversity techniques like maximal ratio combining (MRC), selection combining (SC), and equal gain combining are used. These diversity techniques are used in various fading channel models like Rayleigh, Rician, and Nakagami. The analyses indicate that for a Rayleigh fading channel, the code word error rate (CER) decreases by two orders of magnitude for a SC case as compared to the no diversity case, and that CER reduces by three orders of magnitude for an Equal Gain/MRC case as compared to the no diversity case. Similar results are observed for Rician and Nakagami fading channels also.     

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.