The Performance of Multiuser Diversity Scheduling for MIMO Channels With Spatially Correlated Fading

We study a cellular network with one multiantenna base station and a number of multiantenna users. Correlated fading may exist at the base station or at the users, or at both sides. With time-varying fading, multiuser diversity is exploited by always allowing the base station to transmit to the user with the best channel. For this network, we find that if the number of transmitter antennas and the number of receiver antennas grow with a fixed ratio, the multiuser diversity gain will approximately remain constant.     

Scheduling Algorithms and Throughput Maximization for the Downlink of Packet-Data Cellular Systems with Multiple Antennas at the Base Station

The capacity-achieving coding scheme for the multiple-input multiple-output (MIMO) broadcast channel is dirty-paper coding. With this type of transmission scheme the optimal number of active users that receive data and the optimal power allocation strategy are highly dependent on the structure of the channel matrix and on the total transmit power available. In the context of packet-data access with adaptive transmission where mobile users are equipped with a single receive antenna and the base station has multiple transmit antennas, we study the optimal number of active users and the optimal power allocation. In the particular case of two transmit antennas, we prove that the optimal number of active users can be a non-monotonic function of the total transmit power. Thus not only the number of users that should optimally be served simultaneously depends on the user channel vectors but also on the power available at the base station transmitter. The expected complexity of optimal scheduling algorithms is thus very high. Yet we then prove that at most as many users as the number of transmit antennas are allocated a large amount of power asymptotically in the high-power region in order to achieve the sum-capacity. Simulations confirm that constraining the number of active users to be no more than the number of transmit antennas incurs only a marginal loss in spectral efficiency. Based on these observations, we propose low-complexity scheduling algorithms with sub-optimal transmission schemes that can approach the sum-capacity of the MIMO broadcast channel by taking advantage of multiuser diversity. The suitability of known antenna selection algorithms is also demonstrated. We consider the cases of complete and partial channel knowledge at the transmitter. We provide simulation results to illustrate our conclusions.     

On Scheduling for Multiple-Antenna Wireless Networks Using Contention-Based Feedback

Multiuser diversity gain is an effective technique for improving the performance of wireless networks. This gain can be exploited by scheduling the users with the best current channel conditions. However, this kind of scheduling requires that the base station (or access point) knows some kind of channel quality indicator (CQI) information for every user in the system. When the wireless link lacks channel reciprocity, each user must feed back this CQI information to the base station. The required feedback load makes exploiting multiuser diversity extremely difficult when the number of users becomes large. To alleviate this problem, this paper considers a contention-based CQI feedback where only users whose channel gains are larger than a threshold are allowed to transmit their CQI information through a spread-spectrum based contention channel. Considering the capture effect in this contention channel, it is shown that i) the multiuser diversity gain can be exploited regardless of the number of transmit antennas at the base station and ii) the total system throughput exponentially approaches that of the full feedback scheme as the spreading code length of the contention channel linearly increases. In addition, it is also shown that multiuser diversity can be maintained with the feedback delay of time-variant channels. We also consider the issue of differentiated rate scheduling, in which the base station gives different rates to different subsets of mobiles. In this scenario, mobiles feed back their CQI with some access probability, and we show this technique causes only a negligible throughput loss compared to the case without supporting differentiated rate.     

A lower bound on achievable rate of MRT precoding in multicell multiuser massive MIMO networks with Rician flat fading

A multicell multiuser massive multiple‐input‐multiple‐output (MIMO) network with Rician flat fading is considered. Given channel reciprocity, non‐orthogonal uplink channel training in conjunction with minimum mean square error channel estimation at the base stations are used to acquire channel state information. In the forward link, using maximal ratio transmission precoding, base stations send data to corresponding users. In this paper, first, a closed‐form expression for signal to interference and noise ratio and a lower bound on achievable rate are obtained for arbitrary number of base station antennas. Then, using random matrix theory, a simplified approximate expression for large number of base station antennas (i.e., massive MIMO scenario) are calculated. This simplified expression shows that in a multicell multiuser massive MIMO network with Rician flat fading, like Rayleigh fading, as the number of base station antennas goes to infinity, the effects of uncorrelated noise and intercell and intracell interferences tend to zero. The only factor limiting the performance of system is the correlated intercell interference, that is, pilot contamination, due to non‐orthogonality of channel training sequences in adjacent cells. Numerical results show that our obtained closed‐form expression is a good lower bound on sum‐rate for various system parameters. Copyright © 2016 John Wiley & Sons, Ltd.     

On CDMA with space-time codes over multipath fading channels

We explore code-division multiple-access systems with multiple transmitter and receiver antennas combined with algebraic constellations over a quasi-static multipath fading channel. We first propose a technique to obtain transmit diversity for a single user over quasi-static fading channels by combining algebraic constellations with full spatial diversity and spreading sequences with good cross-correlation properties. The proposed scheme is then generalized to a multiuser system using the same algebraic constellation and different spreading sequences. We also propose a linear multiuser detector based on the combination of linear decorrelation with respect to all users, and the application of the sphere decoder to decode each user separately. Finally, we consider the generalization to multipath fading channels where the additional diversity advantage due to multipath is exploited by the sphere decoder, and a method of blind channel estimation based on subspace decomposition is examined.     

BLIND CHANNEL ESTIMATION IN DELAY DIVERSITY FOR FREQUENCY SELECTIVE CHANNELS1

Delay diversity is an effective transmit diversity technique to combat adverse effects of fading. Thus far, previous work in delay diversity assumed that perfect estimates of current channel fading conditions are available at the receiver and training symbols are required to estimate the channel from the transmitter to the receiver. However, increasing the number of the antennas increases the required training interval and reduces the available time with in whichdata may be transmitted. Learning the channel coefficients becomes increasingly difficult for the frequency selective channels. In this paper, with the subspace method and the delay character of delay diversity, a channel estimation method is proposed, which does not use training symbols. It addresses the transmit diversity for a frequency selective channel from a single carrier perspective in the form of a simple equivalent flat fading model. Monte Carlo simulations give the performance of channel estimation and the performance comparison of our channel-estimation-based detector with decision feedback equalization, which uses the perfect channel information.     

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.     

多天线无线数据通信系统中多用户分集的研究

研究当接收天线不少于发送天线时多输入多输出(MIMO)系统的多用户分集能力。首先从理论上分析了发送天线个数等于1和2时最大似然接收和迫零接收系统的平均吞吐量和调度增益,以及仿真分析了发送天线个数大于2时系统性能。理论分析和仿真表明：在多用户的MIMO系统中,接收的平均信噪比、用户个数、收发天线个数、接收机的结构等对于多用户分集有很大的影响。当发送天线个数为1时,接收天线较少(1,2,3)和平均信噪比为．10dB时调度增益很大,但调度增益随着天线个数和发送功率增大急剧下降。和最大似然接收相比,迫零接收具有更大的多用户分集增益,因此迫零接收机的吞吐量可以很容易超过最大似然接收机。     

空间相关MIMO信道中一种自适应的天线选择算法

该文研究了空间相关性对于多输入多输出空间复用(MIMO-SM)系统性能影响问题,并提出了一种适用于迭代迫零软干扰抵消接收机的天线选择算法。平坦衰落信道中,发送天线相关性将降低接收天线选择算法的性能,该文所研究的算法采用可变的接收天线数以获得不同的接收分集,增加一定的硬件实现复杂度但可以显著减小发送天线相关性引起的误码性能下降。在2个发送天线,4个接收天线的天线配置场合,计算机仿真证实该算法在帧误码率上优于简单的行相关算法(CBM)。     

On the capacity of MIMO broadcast channels with partial side information

In multiple-antenna broadcast channels, unlike point-to-point multiple-antenna channels, the multiuser capacity depends heavily on whether the transmitter knows the channel coefficients to each user. For instance, in a Gaussian broadcast channel with M transmit antennas and n single-antenna users, the sum rate capacity scales like Mloglogn for large n if perfect channel state information (CSI) is available at the transmitter, yet only logarithmically with M if it is not. In systems with large n, obtaining full CSI from all users may not be feasible. Since lack of CSI does not lead to multiuser gains, it is therefore of interest to investigate transmission schemes that employ only partial CSI. We propose a scheme that constructs M random beams and that transmits information to the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. For fixed M and n increasing, the throughput of our scheme scales as MloglognN, where N is the number of receive antennas of each user. This is precisely the same scaling obtained with perfect CSI using dirty paper coding. We furthermore show that a linear increase in throughput with M can be obtained provided that M does not not grow faster than logn. We also study the fairness of our scheduling in a heterogeneous network and show that, when M is large enough, the system becomes interference dominated and the probability of transmitting to any user converges to 1/n, irrespective of its path loss. In fact, using M=/spl alpha/logn transmit antennas emerges as a desirable operating point, both in terms of providing linear scaling of the throughput with M as well as in guaranteeing fairness.     

Efficient signal processing techniques for exploiting transmitantenna diversity on fading channels

A class of powerful and computationally efficient strategies for exploiting transmit antenna diversity on fading channels is developed. These strategies, which require simple linear processing at the transmitter and receiver, have attractive asymptotic characteristics. In particular, given a sufficient number of transmit antennas, these techniques effectively transform a nonselective Rayleigh fading channel into a nonfading, simple white marginally Gaussian noise channel with no intersymbol interference. These strategies, which we refer to as linear antenna precoding, can be efficiently combined with trellis coding and other popular error-correcting codes for bandwidth-constrained Gaussian channels. Linear antenna precoding requires no additional power or bandwidth and is attractive in terms of robustness and delay considerations. The resulting schemes have powerful and convenient interpretations in terms of transforming nonselective fading channels into frequency- and time-selective ones     

Distributed approaches for exploiting multiuser diversity in wireless networks

In wireless fading channels, multiuser diversity can be exploited by scheduling users to transmit when their channel conditions are favorable. This leads to a sum throughput that increases with the number of users and, in certain cases, achieves capacity. However, such scheduling requires global knowledge of every user's channel gain, which may be difficult to obtain in some situations. This paper addresses contention-based protocols for exploiting multiuser diversity with only local channel knowledge. A variation of the ALOHA protocol is given in which users attempt to exploit multiuser diversity gains, but suffer contention losses due to the distributed channel knowledge. The growth rate of the sum throughput for this protocol is characterized in a backlogged system under both short-term and long-term average power constraints. A simple "fixed-rate" system is shown to be asymptotically optimal and to achieve the same growth rate as in a system with an optimal centralized scheduler. Moreover, asymptotically, the fraction of throughput lost due to contention is shown to be 1/e. Also, in a system with random arrivals and an infinite user population, a variation of this ALOHA protocol is shown to be stable for any total arrival rate, given that users can estimate the backlog.     

基于Schmidt正交化的多天线选择复用

该文从提高信道传输有效性的角度,提出了一种新的多天线选择发送策略--贪婪搜索(GS)法,使用这种方法挑选出使容量最大化的发送天线组合作为传输信号的天线。此法在结合注水(waterfilling)法进行天线功率分配的情况下,与理想的全天线注水法相比,可以减小发射机的复杂度,在独立信道下传输容量略有损失,在相关信道下可以提高传输容量,并且所付出的代价是仅需要对信道矩阵进行Schmidt正交化变换。这种方法一般用于信道矩阵列不满秩,即发送端天线数大于接收端天线数,发送端已知信道矩阵的情况(与注水法结合)或者接收端已知信道矩阵的情况(等功率分配)。     

Opportunistic beamforming using dumb antennas

Multiuser diversity is a form of diversity inherent in a wireless network, provided by independent time-varying channels across the different users. The diversity benefit is exploited by tracking the channel fluctuations of the users and scheduling transmissions to users when their instantaneous channel quality is near the peak. The diversity gain increases with the dynamic range of the fluctuations and is thus limited in environments with little scattering and/or slow fading. In such environments, we propose the use of multiple transmit antennas to induce large and fast channel fluctuations so that multiuser diversity can still be exploited. The scheme can be interpreted as opportunistic beamforming and we show that true beamforming gains can be achieved when there are sufficient users, even though very limited channel feedback is needed. Furthermore, in a cellular system, the scheme plays an additional role of opportunistic nulling of the interference created on users of adjacent cells. We discuss the design implications of implementing. this scheme in a complete wireless system     

Multiple-antenna capacity in correlated Rayleigh fading with channel covariance information

We analyze a mobile multiple input multiple output wireless link with M transmit and N receive antennas operating in a spatially correlated Rayleigh flat fading environment. Only the correlations between the channel coefficients are assumed to be known at the transmitter and the receiver. The channel coefficients are correlated in space and uncorrelated in time from one coherence interval to another. These coefficients remain constant for a coherence interval of T symbol periods after which they change to another independent realization according to the spatial correlation model. For this system we characterize the structure of the input signal that achieves capacity. The capacity achieving transmit signal is expressed as the product of an isotropically distributed unitary matrix, an independent nonnegative diagonal matrix and a unitary matrix whose columns are the eigenvectors of the transmit fade covariance matrix. For the case where the number of transmit antennas M is larger than the channel coherence interval T, we show that the channel capacity is independent of the smallest M-T eigenvalues of the transmit fade covariance matrix. In contrast to the previously reported results for the spatially white fading model where adding more transmit antennas beyond the coherence interval length (M>T) does not increase capacity, we find that additional transmit antennas always increase capacity as long as their channel fading coefficients are spatially correlated with the other antennas. We show that for fast hopping or fast fading systems (T=1) with only channel covariance information available to the transmitter and receiver, transmit fade correlations are beneficial. Mathematically, we prove this by showing that capacity is a Schur-convex function of the vector of eigenvalues of the transmit fade correlation matrix. We also show that the maximum possible capacity gain due to transmitter fade correlations is 10logM dB.     

Limiting performance of block-fading channels with multipleantennas

We derive the performance limits of a radio system consisting of a transmitter with t antennas and a receiver with r antennas, a block-fading channel with additive white Gaussian noise (AWGN), delay and transmit-power constraints, and perfect channel-state information available at both the transmitter and the receiver. Because of a delay constraint, the transmission of a codeword is assumed to span a finite (and typically small) number M of independent channel realizations; therefore, the relevant performance limits are the information outage probability and the “delay-limited” (or “nonergodic”) capacity. We derive the coding scheme that minimizes the information outage probability. This scheme can be interpreted as the concatenation of an optimal code for the AWGN channel without fading to an optimal beamformer. For this optimal scheme, we evaluate minimum-outage probability and delay-limited capacity. Among other results, we prove that, for the fairly general class of regular fading channels, the asymptotic delay-limited capacity slope, expressed in bits per second per hertz (b/s/Hz) per decibel of transmit signal-to-noise ratio (SNR), is proportional to min (t,r) and independent of the number of fading blocks M. Since M is a measure of the time diversity (induced by interleaving) or of the frequency diversity of the system, this result shows that, if channel-state information is available also to the transmitter, very high rates with asymptotically small error probabilities are achievable without the need of deep interleaving or high-frequency diversity. Moreover, for a large number of antennas, delay-limited capacity approaches ergodic capacity     

Tradeoff between diversity gain and interference suppression in a MIMO MC-CDMA system

In this paper, the uplink of an asynchronous multi-carrier direct-sequence code-division multiple-access (MC-DS-CDMA) system with multiple antennas at both the transmitter and the receiver is considered. We analyze the system performance over a spatially correlated Rayleigh fading channel with multiple-access interference (MAI), and evaluate the antenna array performance with joint fading reduction and MAI suppression. Assuming perfect channel knowledge available at the transmitter, maximal ratio transmission is employed to weight the transmitted signal optimally in terms of combating signal fading. At the receiver, adaptive beamforming reception is adopted to both suppress MAI and combat the fading. Note that while correlations among the fades of the antennas in the receive array reduce the diversity gain against fading, the array still has the capability for interference suppression. We examine the effect of varying the number of transmit and receive antennas on both the diversity gain and the interference suppression.     

MIMO系统信道容量研究

针对单用户MIMO系统信道的容量特性展开研究。首先详细推导了无衰落信道下信道容量表达式,然后重点分析了瑞利衰落信道下,接收端已知信道状态信息,发射端已知信道状态分布时的容量特性。最后分别针对瑞利衰落信道下,采用发射分集、接收分集以及BLAST传输结构的系统容量进行仿真。仿真结果表明:给定发射功率,独立的瑞利衰落信道条件下,MIMO系统容量随最小天线数目的增加而线性增加,极大地提高了系统容量。     

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.     

相关衰落信道上WCDMA系统的安全性能分析

对多输入多输出（MIMO）相关衰落信道上宽带码分多址接入（WCDMA）的安全性能进行评估,一种省时高效的解决方案是理论分析法。推导了相关 Nakagami 衰落信道上采用空时分组码和二维瑞克接收机（2D-Rake）的 WCDMA 系统的非零安全容量概率和安全中断概率的精确解析表达式。利用上述表达式,可以快速地评估收发天线数、天线相关系数、Nakagami衰落系数、平均路径衰减系数等参数对WCDMA系统安全性能造成的影响。数值计算和仿真结果相吻合,证明了以上理论分析的正确性。推导了WCDMA系统渐近安全中断概率的解析表达式。结果表明,WCDMA 系统的安全分集增益为主信道各个可分离路径上的分集增益之和,与窃听信道无关;对于恒定多径强度轮廓的同分布Nakagami衰落信道,WCDMA系统的安全分集增益为主信道的收/发天线数、多径个数以及Nakagami衰落系数四者之积。