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     

Receive antenna selection for closely-spaced antennas with mutual coupling

We investigate the achievable rate of receive antenna selection MIMO systems in the presence of mutual coupling and spatial correlation. For that, we assume the antenna array to consist of dipole antennas placed side-by-side in a linear pattern and in a very limited physical space. In a first step, we will assume perfect channel state information at the receiver side only and a negligible training overhead compared with the payload. We will demonstrate that in contrast to what might be expected based on results for cases without mutual coupling, MIMO receive antenna selection can achieve higher data rates than the system using all antennas provided that the total number of receive antennas is larger than a critical value that we will further discuss. We then propose an optimal antenna selection processing that ensures rate maximization regardless of the number of antennas used. In a later step, we will address the impact of training overhead on the system achievable rate when the training overhead is considerable. We will show that such a rate is reduced dramatically due to the large amount of training overhead arising from the presence of mutual coupling. To overcome this problem, we will thus propose a novel channel estimation method, which reduces the training overhead greatly and improves the system achievable rate performance.     

协同信道空时优化MIMO无线传输系统

该文提出一种基于虚拟信道的空时优化多输入多输出(MIMO)无线传输系统。通过在发射端产生不同的空时虚拟信道,与实际空间无线信道级联,构成系统的整体传输信道即协同空分信道。系统可以根据接收端的反馈信息采用模拟退火算法来优化虚拟信道,改善误码率(BER)性能。利用虚拟信道方法,可以使一根MIMO发射天线在同一时间、同一频段传输多路叠加合并后的数据信号,从而可以使发射的不同数据信号的总路数超过发射天线的数量,突破了现有MIMO系统在同一时间、同一频段最多只能发射与发射天线数量相等的不同数据信号的传统方式,可以显著提高系统的频谱效率。仿真结果和基于ZC706和AD9361硬件平台的微波暗室实际测试结果充分验证了新MIMO系统的有效性。     

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.

     

Asymptotic Mutual Information Statistics of Separately Correlated Rician Fading MIMO Channels

The asymptotic probability distribution of the mutual information of a separately correlated Rician fading multiple-input multiple-output (MIMO) channel is addressed. The mean and variance of the mutual information are derived when the number of transmit and receive antennas grows asymptotically large while their ratio approaches a finite constant. This derivation is based on the replica method, widely used in theoretical physics and, more recently, in the analysis of communication systems (code-division multiple access (CDMA) and MIMO). Though the replica method allows to analyze complex systems in a comparatively simple way, some authors pointed out that its assumptions are not always rigorous. It is shown that the mutual information converges asymptotically to a Gaussian distribution under mild technical conditions, which are tantamount to assuming that the spatial correlation structure has no asymptotically dominant eigenmodes. The accuracy of the asymptotic approach is assessed by numerical results. It is shown that the approximation is very accurate in a wide range of system settings, even when the number of transmit and receive antennas is as small as a few units.     

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.     

Fundamental Limits in MIMO Broadcast Channels

This paper studies the fundamental limits of MIMO broadcast channels from a high level, determining the sum-rate capacity of the system as a function of system parameters, such as the number of transmit antennas, the number of users, the number of receive antennas, and the total transmit power. The crucial role of channel state information at the transmitter is emphasized, as well as the emergence of opportunistic transmission schemes. The effects of channel estimation errors, training, and spatial correlation are studied, as well as issues related to fairness, delay and differentiated rate scheduling.     

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.     

Small-Size 6-Port Antenna for Three-Dimensional Multipath Wireless Channels

We discuss the issues of designing small-size antennas for multiple-input multiple-output (MIMO) communication systems. Introduction of the notion "potential antenna" facilitates antenna performance estimations to a great extent. Potential antenna is an idealized perfect antenna capable of absorbing the absolute entirety of information from the electromagnetic field present in a given region of space. The potential antenna concept proves instrumental in demonstrating that the optimal number of spatial subchannels for a small-size receive region in a three-dimensional (3-D) omnidirectional channel is 6. We present a compact 6-port receive antenna for 3-D wireless channels. Evidence is given to show that the suggested antenna assures a channel capacity that approximates to the theoretical limit thus making the antenna fit for use in high data rate mobile MIMO systems     

Joint antenna selection and link adaptation for MIMO systems

Multi-input multi-output (MIMO) systems, with multiple antennas at both the transmitter and the receiver, are anticipated to be widely employed in future wireless networks due to their predicted tremendous system capacity. To protect the transmitted data against random channel impairment, it is desirable to consider link adaptation, such as rate adaptation and power control, to improve the system performance and guarantee certain quality of service. Based on the observation that link adaptation and antenna selection problems are often coupled, we propose a joint antenna subset selection and link adaptation study for MIMO systems. After the formulation of the multidimensional joint optimization problem, the main contribution of this paper lies in the design of efficient algorithms approaching the optimal solution for both uncorrelated and correlated MIMO channels. Specifically, we propose one simplified antenna selection and link adaptation rule based on the expected optimal number of active antennas for uncorrelated MIMO with Rayleigh fading and one for correlated MIMO channels only based on the slowly varying channel correlation information. Our proposed algorithms are verified through numerical results, demonstrating significant gains over traditional MIMO signaling, while feasible for practical implementation.     

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.     

Optimization of Training and Scheduling in the Non-Coherent SIMO Multiple Access Channel

Channel state information (CSI) is important for achieving large rates in MIMO channels. However, in time-varying MIMO channels, there is a tradeoff between the time/energy spent acquiring channel state information (CSI) and the time/energy remaining for data transmission. This tradeoff is accentuated in the MIMO multiple access channel (MAC), since the number of channel vectors to be estimated increases with the number of users. Furthermore, the problem of acquiring CSI is tightly coupled with the problem of exploiting CSI through multiuser scheduling. This paper considers a block-fading MAC with coherence time T, n uncoordinated users-each with one transmit antenna and the same average power constraint, and a base station with M receive antennas and no a priori CSI. For this scenario, a training-based communication scheme is proposed and the training and multiuser-scheduling aspects of the scheme are jointly optimized. In the high-SNR regime, the sum capacity of the non-coherent SIMO MAC is characterized and used to establish the SNR-scaling-law optimality of the proposed scheme. In the low-SNR regime, the sum-rate of the proposed scheme is found to decay linearly with vanishing SNR when flash signaling is incorporated. Furthermore, this linear decay is shown to be order-optimal through comparison to the low-SNR sum capacity of the non-coherent SIMO MAC. A by product of these SNR-asymptotic analyses is the observation that non-trivial scheduling (i.e., scheduling a strict subset of trained users) is advantageous at low SNR, but not at high SNR. The sum-rate and per-user throughput are also explored in the large-n and large-M regimes. Non-coherent capacity, training, multiple access channel, multiuser scheduling, opportunistic scheduling.     

Dynamics of spatial correlation and implications on MIMO systems

The use of multiple antennas has found various applications in the area of wireless communications. One such application has recently become very popular and is referred to as the multiple-input multiple-output (MIMO) antenna system. The main idea behind MIMO is to establish independent parallel channels between multiple transmit and receive antennas. Each channel uses the same frequency, and the transmissions occur simultaneously. In such a configuration, the amount of data transmitted increases linearly with the number of parallel channels, which is what makes MIMO so popular in the wireless world. The enormous capacity offered by MIMO systems is not realizable when the parallel channels are highly correlated. The goal of this article is to highlight the correlation concept and its impact on MIMO systems. Although correlation can be defined in many dimensions, here we focus on spatial correlation, and specifically consider antenna correlations in mobile units. We provide an overview of spatial correlation and present its underlying parameters in detail. Special attention is given to mutual coupling since it has signal decorrelation and antenna gain reduction effects. We then present how correlation in a MIMO system affects the amount of data that can be transmitted (MIMO capacity) and briefly review how power should be distributed with the knowledge of correlation. Analyses indicate that in real propagation environments, the high capacity gain of MIMO systems can be realized with improved antenna selection algorithms and power allocation strategies.     

Capacity of MIMO channels in the presence of co‐channel interference

This paper presents analytical results on the capacity of multiple‐input‐multiple‐output (MIMO) fading channels in the presence of co‐channel interference (CCI). We consider the scenario in which the desired and CCI users are all subject to Rayleigh fading. We assume that channel realizations of both the desired and CCI users are known at the receiver. Moreover, we consider the case where the transmitter does not have any CSI and as such equal‐power allocation among transmit antennas is used. Given this setup, we derive the moment generating function (MGF) and the mean of the mutual information (MI). We then study the complementary cumulative distribution function of the MI using a Gaussian approximation. Finally, we present and discuss numerical examples to illustrate the mathematical formalism and to show the effect of various parameters on the capacity of MIMO channels in the presence of CCI. Copyright © 2006 John Wiley & Sons, Ltd.     

Novel limited feedback scheme under the MIMO broadcast system

By deducing the distribution of the normalized channel covariance matrix, a novel limited feedback scheme is proposed under multiple users (MU) multiple-input multiple-output (MIMO) broadcast channel (BC) system. The proposed scheme has advantages in three aspects. First, it has no constraints on the number of users or antennas. Second, each user's feedback bits are independent of the number of receiving antennas. Third, the proposed scheme avoids the storage of large-size codebook on the transceivers. Simulation results show that the performance of the proposed scheme is close to the perfect channel state information (CSI) case and it just needs a small number of feedback bits.     

Spatial precoder design for space–time coded MIMO systems: based on fixed parameters of MIMO channels

In realistic channel environments the performance of space–time coded multiple-input multiple output (MIMO) systems is significantly reduced due to non-ideal antenna placement and non-isotropic scattering. In this paper, by exploiting the spatial dimension of a MIMO channel we introduce the novel idea of linear spatial precoding (or power-loading) based on fixed and known parameters of MIMO channels to ameliorate the effects of non-ideal antenna placement on the performance of coherent (channel is known at the receiver) and non-coherent (channel is un-known at the receiver) space–time codes. Antenna spacing and antenna placement (geometry) are considered as fixed parameters of MIMO channels, which are readily known at the transmitter. With this design, the precoder is fixed for fixed antenna placement and the transmitter does not require any feedback of channel state information (partial or full) from the receiver. We also derive precoding schemes to exploit non-isotropic scattering distribution parameters of the scattering channel to improve the performance of space–time codes applied on MIMO systems. However, these schemes require the receiver to estimate the non-isotropic parameters and feed them back to the transmitter. Closed form solutions for precoding schemes are presented for systems with up to three receive antennas. A generalized method is proposed for more than three receive antennas.     

On transceiver design and channel quantization for downlink multiuser MIMO systems with limited feedback

We consider a MIMO broadcast channel where both the transmitter and receivers are equipped with multiple antennas. Channel state information at the transmitter (CSIT) is obtained through limited (i.e., finite-bandwidth) feedback from the receivers that index a set of precoding vectors contained in a predefined codebook. We propose a novel transceiver architecture based on zero-forcing beamforming and linear receiver combining. The receiver combining and quantization for CSIT feedback are jointly designed in order to maximize the expected SINR for each user. We provide an analytic characterization of the achievable throughput in the case of many users and show how additional receive antennas or higher multiuser diversity can reduce the required feedback rate to achieve a target throughput.We also propose a design methodology for generating codebooks tailored for arbitrary spatial correlation statistics. The resulting codebooks have a tree structure that can be utilized in time-correlated MIMO channels to significantly reduce feedback overhead. Simulation results show the effectiveness of the overall transceiver design strategy and codebook design methodology compared to prior techniques in a variety of correlation environments.     

Characterizing the statistical properties of mutual information in MIMO channels

We consider Gaussian multiple-input multiple-output (MIMO) frequency-selective spatially correlated fading channels, assuming that the channel is unknown at the transmitter and perfectly known at the receiver. For Gaussian codebooks, using results from multivariate statistics, we derive an analytical expression for a tight lower bound on the ergodic capacity of such channels at any signal-to-noise ratio (SNR). We show that our bound is tighter than previously reported analytical lower bounds, and we proceed to analytically quantify the impact of spatial fading correlation on ergodic capacity. Based on a closed-form approximation of the variance of mutual information in correlated flat-fading MIMO channels, we provide insights into the multiplexing-diversity tradeoff for Gaussian code books. Furthermore, for a given total number of antennas, we consider the problem of finding the optimal (ergodic capacity maximizing) number of transmit and receive antennas, and we reveal the SNR-dependent nature of the maximization strategy. Finally, we present numerical results and comparisons between our capacity bounds and previously reported bounds.     

Vector Precoding for Wireless MIMO Systems and its Replica Analysis

This paper studies a nonlinear vector precoding scheme which inverts the wireless multiple-input multiple-output (MIMO) channel at the transmitter so that simple symbol-by-symbol detection can be used in lieu of sophisticated multiuser detection at the receiver. In particular, the transmit energy is minimized by relaxing the transmitted symbols to a larger alphabet for precoding, which preserves the minimum signaling distance. The so-called replica method is used to analyze the average energy savings with random MIMO channels in the large-system limit. It is found that significant gains can be achieved with complex-valued alphabets. The analysis applies to a very general class of MIMO channels, where the statistics of the channel matrix enter the result via the R-transform of the asymptotic empirical distribution of its eigenvalues. Moreover, we introduce polynomial-complexity precoding schemes for binary and quadrature phase-shift keying in complex channels by using convex rather than discrete relaxed alphabets. In case the number of transmit antennas is more than twice the number of receive antennas, we show that a convex precoding scheme, despite its polynomial complexity, outperforms NP-hard precoding using the popular Tomlinson-Harashima signaling.     

Tomlinson-Harashima Precoded MIMO in wireless networks: to THP or not to THP?

We investigate a wireless network architecture that utilizes Tomlinson Harashima Precoded Multiple Input Multiple Output (THP MIMO) technique for improved system capacity. We consider THP MIMO in a multi user scenario, together with a proposed smart scheduling technique and we explore the capacity performance through extensive capacity analysis considering varying SNR levels, varying number of users and number of transmit/receive antennas, under fading and shadowing, also considering errors in channel state information (CSI). We also evaluate the complexity of THP MIMO and present a low-complexity scheduling algorithm that employs Gram-Schmidt algorithm for incremental implementation of THP’s QR factorization. In the end, we identify the network and channel conditions under which THP MIMO can be preferred over classical conventional MIMO, and we conclude that for practical transceivers with up to four antennas, THP MIMO can provide significant capacity enhancement over conventional MIMO at lower complexity, performing slightly below the sum rate capacity bound. Another important advantage that is observed in this study is better immunity of THP MIMO to CSI errors, as compared to conventional MIMO.