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.     

空间相关莱斯衰落信道下基于部分信道信息的多用户预编码与调度算法

在空间相关的莱斯衰落信道模型下,针对多用户MIMO(Multiple-Input Multiple-Output)系统潜在的多用户分集增益和空间分集增益,该文提出了一种基于部分信道信息的多用户预编码与调度算法。结合部分瞬时信道信息和统计信息,利用约束最大似然估计对各用户信道矢量进行估计,然后利用估计的各用户信道调度多个用户进行预编码。仿真结果表明,该方案以较少的反馈开销,获得了较大的性能增益。     

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.     

基于泊松点过程分布的多蜂窝协作系统中干扰对齐技术研究

在多蜂窝MIMO(Multiple-Input Multiple-Output)协作通信系统中,该文研究了基站站点服从泊松点过程(PPP)分布时,协作基站(BSs)和用户对采用干扰对齐技术的中断概率和网络吞吐量性能,推导了完全信道状态信息(CSI)和部分CSI两种情况下的上述性能的解析表达式,并分析了系统性能与协作参数的单调关系。仿真分析发现:在完全CSI情况下,网络吞吐量随着基站密度、协作基站数、天线数的增加而增加;在部分CSI情况下,由于综合考虑了信道训练和有限反馈带来的资源开销以及量化CSI引入的信道失真,存在一个使网络吞吐量最大的最优协作基站数,当天线数较少或用户移动速度较小时,应有较多的基站参与协作,当天线数较多或用户移动速度较大时,应适当减少协作基站数。     

Opportunistic Feedback for Multiuser MIMO Systems With Linear Receivers

A novel multiuser scheduling and feedback strategy for the multiple-input multiple-output (MIMO) downlink is proposed in this paper. It achieves multiuser diversity gain without substantial feedback requirements. The proposed strategy uses per-antenna scheduling at the base station, which maps each transmit antenna at the base station (equivalently, a spatial channel) to a user. Each user has a number of receive antennas that is greater than or equal to the number of transmit antennas at the base station. Zero-forcing receivers are deployed by each user to decode the transmitted data streams. In this system, the base station requires users' channel quality on each spatial channel for scheduling. An opportunistic feedback protocol is proposed to reduce the feedback requirements. The proposed protocol uses a contention channel that consists of a fixed number of feedback minislots to convey channel state information. Feedback control parameters including the channel quality threshold and the random access feedback probability are jointly adjusted to maximize the average throughput performance of this system. Multiple receive antennas at the base station are used on the feedback channel to allow decoding multiple feedback messages sent simultaneously by different users. This further reduces the bandwidth of the feedback channel. Iterative search algorithms are proposed to solve the optimization for selection of these parameters under both scenarios that the cumulative distribution functions of users are known or unknown to the base station     

Multiuser MIMO Systems with Random Transmit Beamforming

This paper considers the wireless downlink transmissions in a single cell environment, for which the base station (BS) is assumed to schedule its transmission to each mobile station (MS) on a time-slot basis. Only one MS is selected for transmission during each time-slot and the selected MS possibly changes from one time-slot to another. This transmission scheme is thus referred to as dynamic time-division multiple-access (D-TDMA). Random transmit beamforming with the feedback of effective signal-to-noise ratio (ESNR) was proposed by Viswanath and Tse [IEEE Transactions on Information Theory, Vol. 48, No. 6, pp. 1277–1294, 2002] for D-TDMA-based systems in which multiple transmit antennas are equipped at the BS but only single receive antenna is equipped at each MS, or the so-called “MISO” systems. It was also shown in [Viswanath and Tse, 2002] that when the number of MSs in the system becomes large, the system throughput achieved by random transmit beamforming converges to that by coherent transmit beamforming which, however, requires the complete channel state information (CSI) of each MS at the BS. This paper extends upon the work in [Viswanath and Tse, 2002] to a more general scenario for which multiple transmit antennas and multiple receive antennas are equipped at the BS and each MS, respectively, or the so-called “MIMO” systems. We also consider several linear and nonlinear receiver structures and propose novel power allocation schemes to further improve the achievable system throughput. The throughput performance of the proposed receivers and power allocations schemes is compared through computer simulations and their fast convergence to the system throughput by coherent transmit beamforming is demonstrated.

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。     

A Limited Feedback SDMA Scheme with Dynamic Multiplexing Order

The employment of a fixed number of active beams in limited feedback SDMA schemes usually results in severe inter-user interferences in sparse networks. Targeting a good tradeoff between the multiplexing gain and the inter-user interferences, this paper proposes a novel kind of limited feedback SDMA scheme, which employs a variable number of active beams, i.e., a dynamic multiplexing order. The proposed two transmit schemes consist of the modification of conventional feedback information and the development of two novel scheduling algorithms based on a maximum likelihood (ML) estimation of possible user interferences. More specifically, the ML estimation utilizes a combination of the feedback partial instantaneous channel state information (CSI) and the long-term channel correlation, and the two new scheduling algorithms select the active beam subset as well as the user group with the criterion of maximizing the estimated sum throughput. Simulation results demonstrate that in sparse networks the proposed SDMA schemes considerably outperform some conventional schemes in terms of the sum throughput, with a comparable feedback overhead.     

An Efficient CSI Feedback Scheme for MIMO-OFDM Wireless Systems

For antenna-array-based multiple-input multiple- output orthogonal-frequency-division-multiplexing (MIMO-OFDM) wireless systems, gain in channel throughput reduced through sufficient feedback of the channel state information (CSI) is significant, particularly when the number of transmit antennas is larger than the number of receive antennas. In this letter, we demonstrate that, in such scenarios, (1) the CSI of each OFDM sub-carrier can be parameterized into a short bit stream by a proposed low-complexity QR decomposition on the corresponding MIMO channel matrix, (2) the overall CSI can be reliably represented by a proposed parameter interpolation on the above bit streams of only a fraction of sub-carriers, and (3) a MIMO-OFDM system with a low-rate CSI feedback parameterized above can provide a channel throughput comparable to the channel capacity.     

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.     

Exploiting Multiuser Diversity With Imperfect One-Bit Channel State Feedback

It has been well recognized that significant throughput gains can be leveraged in multiuser wireless communication systems by exploiting multiuser diversity with a smart scheduler. This scheduler collects channel state information (CSI) from all users and allocates the resources to the user(s) experiencing favorable channel conditions. However, for a frequency-division-duplex system with a large number of users, how to efficiently collect the required CSI will be a challenging task, especially when the feedback links are of limited capacity. In this paper, we propose a scheduling algorithm to exploit multiuser diversity with possibly imperfect one-bit channel state feedback. The basic idea is to define a threshold lambda and let each user report one-bit information to the scheduler about the comparison between its measured channel fading level and lambda. Correspondingly, the scheduler uses these feedback bits to classify all users into two sets and assigns the channel to one user belonging to the set experiencing favorable channel conditions. Several implementation schemes are developed by attacking the optimization of lambda under different system configurations, covering both the case when the one-bit feedback is perfect and those when the one-bit feedback is imperfect. Computer simulations show that when the user number is large, say, more than ten users, the proposed scheduling supports significantly larger data rate over the round-robin scheduling, while in comparison with the optimum scheduling with complete CSI, the performance loss is limited if the one-bit feedback is of high reliability. In addition, our studies show that we can effectively enhance the robustness against feedback imperfectness by incorporating the feedback reliability into optimization of lambda     

Novel SINR‐Based User Selection for an MU‐MIMO System with Limited Feedback

This paper presents a novel user selection method based on the signal‐to‐interference‐plus‐noise ratio (SINR), which is approximated using limited feedback data at the base stations (BSs) of multiple user multiple‐input multiple‐output (MU‐MIMO) systems. In the proposed system, the codebook vector index, the quantization error obtained from the correlation between the measured channel and the codebook vector, and the measured value of the largest singular value are fed back from each user to the BS. The proposed method not only generates precoding vectors that are orthogonal to the precoding vectors of the previously selected users and are highly correlated with the codebook vector of each user but also adopts the quantization error in approximating the SINR, which eventually provides a significantly more accurate SINR than the conventional SINR‐based user selection techniques. Computer simulations show that the proposed method enhances the sum rate of the conventional SINR‐based methods by at least 2.4 (2.62) bps/Hz when the number of transmit antennas and number of receive antennas per user terminal is 4 and 1(2), respectively, with 100 candidate users and an SNR of 30 dB.     

Differentiated rate scheduling for the down-link of cellular systems

We consider the problem of differentiated rate scheduling for the downlink (i.e., multi-antenna broadcast channel), in the sense that the rates required by different users must satisfy certain constraints on their ratios. When full channel state information (CSI) is available at the transmitter and receivers, the problem can be readily solved using dirty paper coding (DPC) and the application of convex optimization techniques on the dual problem which is the multiple access channel (MAC). Since in many practical application full CSI may not be feasible and computational complexity prohibitive when the number of users is large, we focus on other simple schemes that require very little CSI: time-division opportunistic (TO) beamforming where in different time slots (of different lengths) the transmitter performs opportunistic beamforming to the users requiring the same rate, and weighted opportunistic (WO) beamforming where the random beams are assigned to those users having the largest weighted SINR. For single antenna systems we also look at the capacity-achieving superposition coding (SC) scheme. In all cases, we determine explicit schedules to guarantee the rate constraints and show that, in the limit of large number of users, the throughput loss compared to the unconstrained throughput (sum-rate capacity) tends to zero. We further provide bounds on the rate of convergence of the sum-rates of these schemes to the sum-rate capacity. Finally, we provide simulation results of the performance of different scheduling schemes considered in the paper.     

BER analysis using zero-forcing linear precoding scheme for massive MIMO under imperfect channel state information

ABSTRACT

In massive MIMO systems, inter-user interference has effect on the transmitted signals, so linear precoding techniques are employed for multiuser transmission channels to remove this inter-user interference. It is very complicated to design a suitable linear precoding technique having low computational complexity, which will give an excellent Bit Error Rate (BER) performance. In this paper, we analyse BER under imperfect Channel-State-Information (CSI) using Zero-Forcing (ZF) linear precoding scheme in the downlink, massive MIMO in Time-Division-Duplex (TDD) mode. We derive the closed-form expressions for BER that are obtained from the new expressions derived for Signal-Interference-Noise Ratio (SINR), and then analysis with different parameters using numerical and Monte Carlo simulated results is carried out in MATLAB under imperfect CSI. It was found that our theoretical analysis agrees well with the simulated results. In our analysis, BER was observed in most cases to be good when the number of Base Station (BS) antennas is large enough to accommodate the served users, but when the number of users grows up, the BER performance degrades depending on how many BS antennas are capable of handling the additional users. Also, increasing the downlink transmit power was found to improve the performance, but it is not an energy-efficient way for massive MIMO.     

多用户MIMO系统在有限反馈下结合预编码与调度算法的研究

捅要：研究了多用户多输入多输出（MIMO）系统在有限反馈下的一种结合单位预编码与用户调度算法的方案。在该系统中每一用户都具有多个接收天线,该方案具有较大的多用户分集增益和较小的计算复杂度,从而能够减少系统中的用户间干扰。每个用户独立地决定自己的天线合并矢量,并将最优波束矢量以及对应的估计信干噪比通过有限反馈信道反馈给基站,此时基站获取了相应的用户信道信息和用户间干扰信息。基于接收到的反馈信息,基站从预定义的码本中选取和速率最大的最优子集进行系统预编码,然后依照预编码矩阵调度欧氏距离最小的用户且用户个数不超过发送天线的数目。仿真结果显示该方案有效地改善了系统速率,特别是在用户数目较多或者信道环境较好的情况下。     

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.     

Exact bit-error rate analysis for the combined system of beamforming and Alamouti's space-time block code

The simplest Alamouti's space-time block code can be coupled with more than two transmit antennas via the beamforming technique to enhance the performance gain without code rate reduction. Beamforming is performed at the transmitter, dependent on the channel state information (CSI) which is obtained by using feedback through a feedback link or estimated using reciprocity in duplexing schemes. In this letter, we derived the exact bit-error rate for the combined system with two transmit and one receive antennas in slow Rayleigh flat fading channels. It is assumed that the receiver has the perfect CSI. The expression can be easily extended to more than two transmit antennas.     

Capacity of Generalized UTRA FDD Closed-Loop Transmit Diversity Modes

Transmit diversity techniques have received a lot of attention recently, and open-loop and closed-loop downlink transmit diversity modes for two transmit antennae have been included into universal terrestrial radio access (UTRA) frequency division duplex (FDD) specification. Closed-loop modes provide larger system capacity than open-loop modes, but they need additional side information of the downlink channel in the transmitter. In FDD systems this requires a separate feedback channel. Quantization of channel state information (CSI) in closed-loop transmit diversity schemes decreases the performance when compared to a closed-loop system where the transmitter has access to complete CSI. In this paper, we analyze the effect of quantization of CSI and deduce approximate capacity formulae for closed-loop transmit diversity schemes that are generalizations of the closed-loop schemes included in UTRA FDD specification. Moreover, we calculate approximation error and show by simulations that our approximation is tight for flat Rayleigh fading environments with and without fast transmit power control.     

Comparison of Partial CSI Encoding Methods in Multi-User MIMO Systems

In this paper, we discuss different algorithms that can be used to encode channel state information (CSI) in realistic multi-user multiple-input multiple-output (MIMO) systems where there are only few users experiencing similar propagation conditions and the mobile user receivers do not necessarily have the same number of receive antennas. We divide systems with CSI encoding into four classes: time-division multiplexing (TDM) with and without linear pre-coding, and multiple user scheduling with and without linear pre-coding. The practical aspects such as system’s complexity and approaches for transmitting the CSI feedback and rate information from the mobile receivers to the base station are discussed and compared for different bit rates in the feedback link. We show that significant increases of the mean throughput of the multi-user scheduling systems demand much higher feedback link bit rates than TDM solutions. We also demonstrate that, while optimum, the non-linear pre-coding systems may introduce unacceptable degree of complexity into the base station design while linear pre-coding offers a very good trade-off between performance and complexity.     

The Effect of On-Off Scheduling to the Required Transmit Power in Systems with Fast Power Control

Physical layer channel-aware scheduling may significantly improve coverage and throughput of IP based services in wireless cellular networks, and the feasibility of such schedulers is actively studied within 3G and 4G systems. A channel-aware scheduler requires access to instantaneous channel state information in order to direct transmission to users with favorable channel conditions. In frequency division duplex (FDD) systems, this requires a fast feedback channel between mobile and base stations, and the overhead of the feedback control channel should be kept as low as possible.In this paper, we study the effect of control channel overhead to on-off scheduling (OOS) when fast transmit power control is applied in data and control channels. On-off scheduling is a simple channel-aware scheduling algorithm, where transmission to a user is suspended if the transmit power exceeds a given threshold. On-off scheduling is applied on the data channel while control channel is always on so that the scheduler is able to obtain channel state information from active users. The gain of OOS strongly depends on the power ratio between control and data channels, and increased interference due to control signaling and decreased interference due to channel-aware scheduling should be jointly considered in system design. Gains in the required transmit power are translated into gains in coverage and capacity assuming WCDMA parameters, and the results can be applied, e.g., when designing scheduling algorithms and corresponding signaling formats for WCDMA uplink.