Performance of Orthogonal Beamforming for SDMA With Limited Feedback

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.     

A study of opportunism for multiple-antenna systems

Recently proposed opportunistic beamforming exploits the multiuser diversity to reduce the feedback by not requiring the precoding information used for closed-loop schemes to be known at the transmitter. Opportunism could also be beneficially employed for other multiple-antenna transmission techniques like cophasing and antenna selection. For opportunistic beamforming and antenna selection, we give closed-form expressions for throughput that closely approximate the performance of these schemes with a Proportionally Fair scheduler (PFS) at low signal-to-noise ratios (SNRs). For large number of transmit antennas, opportunistic cophasing has similar performance as opportunistic beamforming. Asymptotic dependence of the required number of users to achieve the gains of opportunism on the number of transmit antennas is exponential for opportunistic beamforming (and cophasing for large numbers of transmit antennas), and at best linear for opportunistic antenna selection. For multiple-antenna receivers, we additionally examine an opportunistic multiple-input multiple-output (MIMO) scheme that transmits multiple data streams simultaneously to the same user.     

A Comparison of Time-Sharing, DPC, and Beamforming for MIMO Broadcast Channels With Many Users

In this letter, we derive the scaling laws of the sum rate for fading multiple-input multiple-output Gaussian broadcast channels using time sharing to the strongest user, dirty-paper coding (DPC), and beamforming, when the number of users (receivers) n is large. Throughout the letter, we assume a fix average transmit power and consider a block-fading Rayleigh channel. First, we show that for a system with M transmit antennas and users equipped with N antennas, the sum rate scales like MloglognN for DPC, and beamforming when M is fixed and for any N (either growing to infinity or not). On the other hand, when both M and N are fixed, the sum rate of time sharing to the strongest user scales like min(M,N)loglogn. Therefore, the asymptotic gain of DPC over time sharing for the sum rate is (M/min(M,N)) when M and N are fixed. It is also shown that if M grows as logn, the sum rate of DPC and beamforming will grow linearly in M, but with different constant multiplicative factors. In this region, the sum-rate capacity of time -sharing scales like Nloglogn     

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 the capacity of multiuser wireless channels with multiple antennas

The advantages of multiuser communication, where many users are allowed to simultaneously transmit or receive in a common bandwidth, are considered for multiple-antenna systems in a high signal-to-noise ratio (SNR) regime. Assuming channel state information at receiver (CSIR) to be available, the ergodic capacity is characterized for both unbiased and biased channels, and the quantitative capacity gain of a multiple-antenna multiuser system is analyzed for multiple-access channels. For highly biased (correlated) channels, a multiuser system is shown to be inherently superior to a single-user system (a time- or frequency-division multiple-access (TDMA or FDMA) based system) due to the underlying multiuser diversity, and the sum capacity is shown to scale linearly with the number of antennas. For unbiased channels, the characteristics of ergodic capacity are shown to transfer to outage capacity when a large degree of space diversity exists, and to deterministic capacity when the number of receive antennas is large. Also, a brief discussion on the multiuser multiple-antenna communication in broadcast channel is provided.     

Subcarrier Wise Scheduling Methods for Multi-antenna and Multi-carrier Systems

In this paper, multiuser scheduling algorithms are evaluated for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) networks. These scheduling schemes allocate M [number of transmit antennas at base station (BS)] number of independent data streams from BS to the M most favourable users experiencing the highest signal-to-interference-plus-noise-ratio (SINR). Here, SINR is used to convey the channel state information (CSI) to the BS. We have investigated the system throughput and feedback overhead attained by these scheduling schemes for different scenarios as: (a) the maximum CSI is sent to the BS by every user and (b) the maximum CSI sent to the BS corresponding to every BS antenna. The overall feedback overhead incurred by MIMO-OFDM system increases linearly with number of users, number of subcarriers and number of transmit antennas. Hence, to reduce the feedback overhead, a scheme is proposed where users with SINR values greater than or equal to a predefined threshold value are only allowed to feedback the channel state information to BS. The relation between system throughput and various thresholds is also studied. The achievable system throughput results are validated by comparing the probability density function of achieved SINR values by different scheduling schemes.

     

Joint queue control and user scheduling in MIMO broadcast channel under zero‐forcing multiplexing

This paper studies the problem of queue control and user scheduling in multi‐antenna broadcast (downlink) systems under zero forcing beamforming transmit strategy. In the system, we assume that the data packet arrives randomly to the buffered transmitter. By taking the broadcast channel as a controlled queueing system, we deduce the property of queue control function that maximizes the weighted system throughput while guarantees the delay fairness among users. We also present a low‐complexity user selection algorithm with the consideration of queue state and channel state together. Simulation results show that the joint queue control and user selection policy can achieve considerable fairness and stability among users. Copyright © 2009 John Wiley & Sons, Ltd.     

Beam Selection Strategies for Orthogonal Random Beamforming in Sparse Networks

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.     

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.     

Constrained Tensor Modeling Approach to Blind Multiple-Antenna CDMA Schemes

In this paper, we consider an uplink multiple-antenna code-division multiple-access (CDMA) system linking several multiple-antenna mobile users to one multiple-antenna base station. For this system, a constrained third-order tensor decomposition is introduced for modeling the multiple-antenna transmitter as well as the received signal. The constrained structure of the proposed tensor decomposition is characterized by two constraint matrices that have a meaningful physical interpretation in our context. They can be viewed as canonical allocation matrices that define the allocation of users' data streams and spreading codes to the transmit antennas. The distinguishing features of the proposed tensor modeling with respect to the already existing tensor-based CDMA models are: i) it copes with multiple transmit antennas and spreading codes per user and ii) it models several spatial spreading/multiplexing schemes with multiple spreading codes by controlling the constrained structure of the tensor signal model. A systematic design procedure for the canonical allocation matrices leading to a unique blind symbol (or joint blind symbol-code) recovery is proposed which allows us to derive a finite set of multiple-antenna schemes for a fixed number of transmit antennas. Identifiability of the proposed tensor model is discussed, and a blind multiuser detection receiver based on the alternating least squares algorithm is considered for performance evaluation of several multiple-antenna CDMA schemes derived from the constrained modeling approach.     

On Opportunistic Power Control for Alamouti and SM MIMO Systems

Transmit antenna diversity and single user spatial multiplexing have become attractive in practical systems, because they achieve performance gains without requiring sophisticated channel state information (CSI) feedback mechanisms. On the other hand, when fast and accurate CSI at the transmitter is available, opportunistic power control (OPC) is an attractive alternative to signal-to-interference-and-noise ratio (SINR) target following approaches, because it maximizes throughput by taking advantage of fast channel variations. In this paper we examine the question whether OPC is worth the pain of obtaining fast CSI by evaluating the gains of OPC for the downlink of a system employing multiple input multiple output (MIMO) systems with Alamouti and open loop spatial multiplexing (SM). We formulate the OPC problem as a throughput maximization task subject to power budget and fairness constraints. We solve this task by the Augmented Lagrangian Penalty Function and find that without fairness constraints, OPC in concert with SM provides superior throughput. With increasingly tight fairness constraints, Alamouti along with equal power allocation becomes a viable alternative to the SM OPC scheme. Both from fairness and throughput perspectives, Alamouti along with OPC is particularly efficient when adaptive MCS is employed and users with large differences in channel qualities have to share the total transmit power.     

QoS‐Guaranteed Multiuser Scheduling in MIMO Broadcast Channels

This paper proposes a new multiuser scheduling algorithm that can simultaneously support a variety of different quality‐of‐service (QoS) user groups while satisfying fairness among users in the same QoS group in MIMO broadcast channels. Toward this goal, the proposed algorithm consists of two parts: a QoS‐aware fair (QF) scheduling within a QoS group and an antenna trade‐off scheme between different QoS groups. The proposed QF scheduling algorithm finds a user set from a certain QoS group which can satisfy the fairness among users in terms of throughput or delay. The antenna trade‐off scheme can minimize the QoS violations of a higher priority user group by trading off the number of transmit antennas allocated to different QoS groups. Numerical results demonstrate that the proposed QF scheduling method satisfies different types of fairness among users and can adjust the degree of fairness among them. The antenna trade‐off scheme combined with QF scheduling can improve the probability of QoS‐guaranteed transmission when supporting different QoS groups.     

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.     

Optimal transmission strategies and impact of correlation in multiantenna systems with different types of channel state information

We study the optimal transmission strategy of a multiple-input single-output (MISO) wireless communication link. The receiver has perfect channel state information (CSI), while the transmitter has different types of CSI, i.e., either perfect CSI, or no CSI, or long-term knowledge of the channel covariance matrix. For the case in which the transmitter knows the channel covariance matrix, it was recently shown that the optimal eigenvectors of the transmit covariance matrix correspond with the eigenvectors of the channel covariance matrix. However, the optimal eigenvalues are difficult to compute. We derive a characterization of the optimum power allocation. Furthermore, we apply this result to provide an efficient algorithm which computes the optimum power allocation. In addition to this, we analyze the impact of correlation on the ergodic capacity of the MISO system with different CSI schemes. At first, we justify the belief that equal power allocation is optimal if the transmitter is uninformed and the transmit antennas are correlated. Next, we show that the ergodic capacity with perfect CSI and without CSI at the transmitter is Schur-concave, i.e., the more correlated the transmit antennas are, the less capacity is achievable. In addition, we show that the ergodic capacity with covariance knowledge at the transmitter is Schur-convex with respect to the correlation properties. These results completely characterize the impact of correlation on the ergodic capacity in MISO systems. Furthermore, the capacity loss or gain due to correlation is quantified. For no CSI and perfect CSI at the transmitter, the capacity loss due to correlation is bounded by some small constant, whereas the capacity gain due to correlation grows unbounded with the number of transmit antennas in the case in which transmitter knows the channel covariance matrix. Finally, we illustrate all theoretical results by numerical simulations.     

Zero-forcing methods for downlink spatial multiplexing in multiuser MIMO channels

The use of space-division multiple access (SDMA) in the downlink of a multiuser multiple-input, multiple-output (MIMO) wireless communications network can provide a substantial gain in system throughput. The challenge in such multiuser systems is designing transmit vectors while considering the co-channel interference of other users. Typical optimization problems of interest include the capacity problem - maximizing the sum information rate subject to a power constraint-or the power control problem-minimizing transmitted power such that a certain quality-of-service metric for each user is met. Neither of these problems possess closed-form solutions for the general multiuser MIMO channel, but the imposition of certain constraints can lead to closed-form solutions. This paper presents two such constrained solutions. The first, referred to as "block-diagonalization," is a generalization of channel inversion when there are multiple antennas at each receiver. It is easily adapted to optimize for either maximum transmission rate or minimum power and approaches the optimal solution at high SNR. The second, known as "successive optimization," is an alternative method for solving the power minimization problem one user at a time, and it yields superior results in some (e.g., low SNR) situations. Both of these algorithms are limited to cases where the transmitter has more antennas than all receive antennas combined. In order to accommodate more general scenarios, we also propose a framework for coordinated transmitter-receiver processing that generalizes the two algorithms to cases involving more receive than transmit antennas. While the proposed algorithms are suboptimal, they lead to simpler transmitter and receiver structures and allow for a reasonable tradeoff between performance and complexity.     

MIMO Broadcast Scheduling with Limited Feedback

We consider multiuser scheduling with limited feedback of partial channel state information in MIMO broadcast channels. By using spatial multiplexing at the base station (BS) and antenna selection for each user, we propose a multiuser scheduling method that allocates independent information streams from all M transmit antennas to the M most favorable users with the highest signal-to-interference-plus-noise ratio (SINR). A close approximation of the achievable sum-rate throughput for the proposed method is obtained and shown to match the simulation results very well. Moreover, two reduced feedback scheduling approaches are proposed. In the first approach, which we shall refer to as selected feedback scheduling, the users are selected based on their SINR compared to a predesigned threshold. Only those selected users are allowed to feed back limited information to the BS. The resultant feedback load and achievable throughput are derived. It will then be demonstrated that with a proper choice of the threshold, the feedback load can be greatly reduced with a negligible performance loss. The second reduced feedback scheduling approach employs quantization for each user, in which only few bits of quantized SINR are fed back to the BS. Performance analysis will show that even with only 1-bit quantization, the proposed quantized feedback scheduling approach can exploit the multiuser diversity at the expense of slight decrease of throughput.     

The optimality of beamforming in uplink multiuser wireless systems

This paper considers the optimal uplink transmission strategy that achieves the sum-capacity in a multiuser multi-antenna wireless system. Assuming an independent identically distributed block-fading model with transmitter channel side information, beamforming for each remote user is shown to be necessary for achieving sum-capacity when there is a large number of users in the system. This result stands even in the case where each user is equipped with a large number of transmit antennas, and it can be readily extended to channels with intersymbol interference if an orthogonal frequency division multiplexing modulation is assumed. This result is obtained by deriving a rank bound on the transmit covariance matrices, and it suggests that all users should cooperate by each user using only a small portion of available dimensions. Based on the result, a suboptimal transmit scheme is proposed for the situation where only partial channel side information is available at each transmitter. Simulations show that the suboptimal scheme is not only able to achieve a sum rate very close to the capacity, but also insensitive to channel estimation error.     

Antenna diversity in multiuser data networks

We consider the use of multiple antennas at the transmitter and/or the receiver to provide open-loop spatial diversity in a multiuser wireless data network. With channel quality information (CQI) available to the transmitter, and by always scheduling the transmission to the active user having the best channel conditions at the time of scheduling, another form of diversity, termed multiuser diversity, is obtained in a data system. This paper provides an analysis of the interaction between these two forms of diversity. From a network point of view, we prove that the asymptotic sum rate, in the limit of a large number of active homogeneous users and subject to the same average total transmit power, is inversely related to the number of transmit antennas for independent and identically distributed (i.i.d.) flat Rayleigh fading channels. In the case of i.i.d. flat Rician fading, the asymptotic sum rate also depends inversely on the number of transmit antennas, but directly on the number of receive antennas. Numerically, we show that the total diversity gain is also constrained by finite CQI quantization and channel fading statistics.     

多用户MIMO系统下行链路的随机多波束复用技术

该文提出了一种随机多波束多用户复用技术,充分利用多用户分集以及基站多天线的空间自由度来提高系统吞吐量。不同于传统的随机波束形成技术,该技术首先在给定预编码码本内随机选取一个码字,然后调度多个空分复用用户以及其余预编码矩阵。该文采用了一种逐次调度的方式,第一次训练调度一个主发送用户并确定一个次发送预编码矩阵,通过第二次训练选择次发送用户,这种方式能以很小的反馈开销有效控制复用用户之间的相互干扰。同时,该文所提技术能进一步推广到用户具有不同天线配置的异构情形。仿真结果表明,该文技术在具有不同相关性的信道环境下都能获得较优的系统吞吐量。     

Capacity of multiple-antenna systems with both receiver and transmitter channel state information

The capacity of multiple-antenna systems operating in Rayleigh flat fading is considered under the assumptions that channel state information (CSI) is available at both transmitter and receiver, and that the transmitter is subjected to an average power constraint. First, the capacity of such systems is derived for the special case of multiple transmit antennas and a single receive antenna. The optimal power-allocation scheme for such a system is shown to be a water-filling algorithm, and the corresponding capacity is seen to be the same as that of a system having multiple receive antennas (with a single transmitter antenna) whose outputs are combined via maximal ratio combining. A suboptimal adaptive transmission technique that transmits only over the antenna having the best channel is also proposed for this special case. It is shown that the capacity of such a system under the proposed suboptimal adaptive transmission scheme is the same as the capacity of a system having multiple receiver antennas (with a single transmitter antenna) combined via selection combining. Next, the capacity of a general system of multiple transmitter and receiver antennas is derived together with an equation that determines the cutoff value for such a system. The optimal power allocation scheme for such a multiple-antenna system is given by a matrix water-filling algorithm. In order to eliminate the need for cumbersome numerical techniques in solving the cutoff equation, approximate expressions for the cutoff transmission value are also provided. It is shown that, compared to the case in which there is only receiver CSI, large capacity gains are available with optimal power and rate adaptation schemes. The increased capacity is shown to come at the price of channel outage, and bounds are derived for this outage probability.