基于延迟输出反馈的上行多小区MIMO蜂窝干扰网络自由度分析

针对具有反馈时延的上行多小区MIMO（Multiple-Input Multiple-Output）蜂窝干扰网络,提出一种基于延迟输出反馈（OF,Output Feedback）的回溯干扰重构（RIR,Retrospective Interference Reconstruction）方案.该方案首先通过在基站构造接收波束成形矩阵,将重构的OF下传至用户.然后用户对延迟的OF预编码并传输至基站,基站利用预编码信息消除小区间干扰.分析了上行任意多小区MIMO蜂窝干扰网络的RIR方案适用条件、系统和速率和可达自由度（DoF,Degrees of Freedom）,并将RIR方案与回溯干扰对齐方案和TDMA方案进行对比仿真分析,结果表明,RIR方案能获得更多自由度.     

On the Capacity and Design of Limited Feedback Multiuser MIMO Uplinks

The theory of multiple-input–multiple-output (MIMO) technology has been well developed to increase fading channel capacity over single-input–single-output (SISO) systems. This capacity gain can often be leveraged by utilizing channel state information at the transmitter and the receiver. Users make use of this channel state information for transmit signal adaptation. In this correspondence, we derive the capacity region for the MIMO multiple access channel (MIMO MAC) when partial channel state information is available at the transmitters, where we assume a synchronous MIMO multiuser uplink. The partial channel state information feedback has a cardinality constraint and is fed back from the basestation to the users using a limited rate feedback channel. Using this feedback information, we propose a finite codebook design method to maximize the sum rate. In this correspondence, the codebook is a set of transmit signal covariance matrices. We also derive the capacity region and codebook design methods in the case that the covariance matrix is rank one (i.e., beamforming). This is motivated by the fact that beamforming is optimal in certain conditions. The simulation results show that when the number of feedback bits increases, the capacity also increases. Even with a small number of feedback bits, the performance of the proposed system is close to an optimal solution with the full feedback.      

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。     

Signature optimization for CDMA with limited feedback

We study the performance of joint signature-receiver optimization for direct-sequence code-division multiple access (DS-CDMA) with limited feedback. The receiver for a particular user selects the signature from a signature codebook, and relays the corresponding B index bits to the transmitter over a noiseless channel. We study the performance of a random vector quantization (RVQ) scheme in which the codebook entries are independent and isotropically distributed. Assuming the interfering signatures are independent, and have independent and identically distributed (i.i.d.) elements, we evaluate the received signal-to-interference plus noise ratio (SINR) in the large system limit as the number of users, processing gain, and feedback bits B all tend to infinity with fixed ratios. This SINR is evaluated for both the matched filter and linear minimum mean-squared error (MMSE) receivers. Furthermore, we show that this large system SINR is the maximum that can be achieved over any sequence of codebooks. Numerical results show that with the MMSE receiver, one feedback bit per signature coefficient achieves close to single-user performance. We also consider a less complex and suboptimal reduced-rank signature optimization scheme in which the user's signature is constrained to lie in a lower dimensional subspace. The optimal subspace coefficients are scalar-quantized and relayed to the transmitter. The large system performance of the quantized reduced-rank scheme can be approximated, and numerical results show that it performs in the vicinity of the RVQ bound. Finally, we extend our analysis to the scenario in which a subset of users optimize their signatures in the presence of random interference.     

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.     

A performance analysis framework for limited feedback beamforming in correlated fading

Limited or finite rate, feedback is an efficient way to implement beamforming in multiple antenna systems using frequency division duplexing. Unfortunately, closed-form performance analysis of limited feedback beamforming has not been investigated. This paper provides an analytical framework for the correlated limited feedback beamforming problem by treating selection of the beamforming vector from the codebook as a multibranch selection problem.     

Capacity of a Multiple-Antenna Fading Channel With a Quantized Precoding Matrix

Given a multiple-input multiple-output (MIMO) channel, feedback from the receiver can be used to specify a transmit precoding matrix, which selectively activates the strongest channel modes. Here we analyze the performance of random vector quantization (RVQ), in which the precoding matrix is selected from a random codebook containing independent, isotropically distributed entries. We assume that channel elements are independent and identically distributed (i.i.d.) and known to the receiver, which relays the optimal (rate-maximizing) precoder codebook index to the transmitter using $B$ bits. We first derive the large system capacity of beamforming (rank-one precoding matrix) as a function of $B$, where large system refers to the limit as $B$ and the number of transmit and receive antennas all go to infinity with fixed ratios. RVQ for beamforming is asymptotically optimal, i.e., no other quantization scheme can achieve a larger asymptotic rate. We subsequently consider a precoding matrix with arbitrary rank, and approximate the asymptotic RVQ performance with optimal and linear receivers (matched filter and minimum mean squared error (MMSE)). Numerical examples show that these approximations accurately predict the performance of finite-size systems of interest. Given a target spectral efficiency, numerical examples show that the amount of feedback required by the linear MMSE receiver is only slightly more than that required by the optimal receiver, whereas the matched filter can require significantly more feedback.      

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.     

Channel Adaptive Quantization for Limited Feedback MIMO Beamforming Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques. In the absence of full channel knowledge at the transmitter, the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low-rate feedback channel. In the literature, quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution, commonly the uncorrelated Rayleigh distribution. When the channel is not uncorrelated Rayleigh, however, these quantization strategies result in a degradation of the receive signal-to-noise ratio (SNR). In this paper, switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution. The codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel. The convergence properties of the codebook selection algorithm are studied assuming a block-stationary model for the channel. In the case of a nonstationary channel, it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in SNR. Simulation results show that in the case of correlated channels, the SNR performance of the link can be significantly improved by adaptation, compared with nonadaptive quantization strategies designed for uncorrelated Rayleigh-fading channels     

On the performance of random vector quantization limited feedback beamforming in a MISO system

In multiple antenna wireless systems, beamforming is a simple technique for guarding against the negative effects of fading. Unfortunately, beamforming requires the transmitter to have knowledge of the forward-link channel which is often not available a priori. One way of overcoming this problem is to design the beamforming vector using a limited number of feedback bits sent from the receiver to the transmitter. In limited feedback beamforming, the beamforming vector is restricted to lie in a codebook that is known to both the transmitter and receiver. Random vector quantization (RVQ) is a simple approach to codebook design that generates the vectors independently from a uniform distribution on the complex unit sphere. This correspondence presents performance analysis results for RVQ limited feedback beamforming     

Design and analysis of transmit-beamforming based on limited-rate feedback

This paper deals with design and performance analysis of transmit beamformers for multiple-input multiple-output (MIMO) systems based on bandwidth-limited information that is fed back from the receiver to the transmitter. By casting the design of transmit beamforming based on limited-rate feedback as an equivalent sphere vector quantization (SVQ) problem, multiantenna beamformed transmissions through independent and identically distributed (i.i.d.) Rayleigh fading channels are first considered. The rate-distortion function of the vector source is upper-bounded, and the operational rate-distortion performance achieved by the generalized Lloyd's algorithm is lower-bounded. Although different in nature, the two bounds yield asymptotically equivalent performance analysis results. The average signal-to-noise ratio (SNR) performance is also quantified. Finally, beamformer codebook designs are studied for correlated Rayleigh fading channels, and a low-complexity codebook design that achieves near-optimal performance is derived.     

Transmission Scheme for 2D Antenna Array MIMO Systems with Limited Feedback

Three-dimensional (3D) multiple-input multiple-output (MIMO) systems exploit spatial richness and provide another degree of freedom to transmit signals and eliminate spatial interference. Currently, however, there is no 3D codebook for two-dimensional (2D) antenna array MIMO systems with limited feedback. In this paper, based on the existing 2D codebook, we present a limited feedback and transmission scheme for 2D antenna array MIMO systems. In this scheme, the mobile station (MS) has imperfect channel knowledge, and the base station (BS) only acquires partial information relating the channel instantiation. MS must feed back two channel state information (CSI) instances, i.e., the horizontal and vertical CSIs. After receiving the two CSI instances, the BS interpolates a new vertical precoding vector using the vertical CSI. Then, the BS re-constructs a 3D beamforming vector using horizontal and vertical precoding vectors and compensates the reported horizontal channel quality indicator. System level simulation is employed, and the simulation results show that the proposed method improves the system spectral efficiency and the cell-edge SE significantly.     

Limited feedback unitary precoding for spatial multiplexing systems

Multiple-input multiple-output (MIMO) wireless systems use antenna arrays at both the transmitter and receiver to provide communication links with substantial diversity and capacity. Spatial multiplexing is a common space-time modulation technique for MIMO communication systems where independent information streams are sent over different transmit antennas. Unfortunately, spatial multiplexing is sensitive to ill-conditioning of the channel matrix. Precoding can improve the resilience of spatial multiplexing at the expense of full channel knowledge at the transmitter-which is often not realistic. This correspondence proposes a quantized precoding system where the optimal precoder is chosen from a finite codebook known to both receiver and transmitter. The index of the optimal precoder is conveyed from the receiver to the transmitter over a low-delay feedback link. Criteria are presented for selecting the optimal precoding matrix based on the error rate and mutual information for different receiver designs. Codebook design criteria are proposed for each selection criterion by minimizing a bound on the average distortion assuming a Rayleigh-fading matrix channel. The design criteria are shown to be equivalent to packing subspaces in the Grassmann manifold using the projection two-norm and Fubini-Study distances. Simulation results show that the proposed system outperforms antenna subset selection and performs close to optimal unitary precoding with a minimal amount of feedback.     

基于机会通信的多天线蜂窝系统小区间干扰协调

通过研究有限反馈波束赋形蜂窝系统中小区间同信道干扰变化的特性,提出了一种基于机会通信的有限权值机会波束方法。该方法通过在预先设计的有限数量的赋形权值码本中随机选择赋形权值,使目标小区的干扰变化与邻小区用户调度无关,从而使干扰测量和速率预测更为准确,降低了反馈时延和干扰变化造成的中断率。理论分析和仿真均表明:采用正比公平调度的有限权值机会波束与有限反馈波束赋形具有相近的发射速率,从而系统吞吐量得到提高。     

Recursive and Trellis-Based Feedback Reduction for MIMO-OFDM with Rate-Limited Feedback

We investigate an adaptive MIMO-OFDM system with a feedback link that can only convey a finite number of bits. We consider three different transmitter configurations: i) beamforming applied per OFDM subcarrier, ii) precoded spatial multiplexing applied per subcarrier, and iii) precoded orthogonal space time block coding applied per subcarrier. Depending on the channel realization, the receiver selects the optimal beamforming vector or precoding matrix from a finite-size codebook on each subcarrier, and informs the transmitter through finite-rate feedback. Exploiting the fact that the channel responses across OFDM subcarriers are correlated, we propose two methods to reduce the amount of feedback. One is recursive feedback encoding that selects the optimal beamforming/precoding choices sequentially across the subcarriers, and adopts a smaller-size time-varying codebook per subcarrier depending on prior decisions. The other is trellis-based feedback encoding that selects the optimal decisions for all subcarriers at once along a trellis structure via the Viterbi algorithm. Our methods are applicable to different transmitter configurations in a unified fashion. Simulation results demonstrate that the trellis-based approach outperforms the recursive method as well as an existing interpolation-based alternative at high signal-to-noise-ratio, as the latter suffers from "diversity loss"     

Unitary space vector quantization codebook design for spatial correlated limited feedback MIMO system

In the transmitting, beamforming, and receiving combing （TBRC） MIMO system, a codebook based feedback strategy is usually used to provide the transmitter with the beamforming vector. The adopted codebook affects the system performance considerably. Therefore, the codebook design is a key technology in the TBRC MIMO system. In this article, the unitary space vector quantization （USVQ） codebook design criterion is proposed to design optimal codebooks for various spatial correlated MIMO channels. And the unitary space K-mean （USK） codebook generating algorithm is provided to generate the USVQ codebooks. Simulations show that the capacities of the feedback based TBRC systems using USVQ codebooks are very close to those of the ideal cases.     

Performance analysis of MIMO beamforming with imperfect feedback

The quality of channel state information at the transmitter (CSIT) is critical to MIMO beamforming systems. However, in practical wireless systems, CSIT suffers from imperfections originating from quantization effects, feedback error and feedback delay. In this paper, we study the impact of feedback error and delay on the symbol error rate of MIMO beamforming systems with finite rate feedback. The feedback channel is modeled as a uniform symmetric channel. We derive an symbol error rate upper bound that is tight for a good beamformer. We also quantify the diversity gain and array gain loss due to the feedback error and delay. The codebook design method that is applicable to the beamforming systems with error or delay feedback is discussed. Both analytical and simulation results show that feedback error and delay will make the system behave badly at high signal‐to‐noise ratios. Copyright © 2012 John Wiley & Sons, Ltd.     

Performance Analysis of Quantized Beamforming MIMO Systems

Multiple-input multiple-output (MIMO) wireless systems can achieve significant diversity and array gain by using single-stream transmit beamforming and receive combining. A MIMO beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single-user scenario. The performance of this system in uncorrelated Rayleigh flat fading channels is studied from the point-of-view of signal-to-noise ratio (SNR) and outage probability. In this paper, lower bounds are derived on the expected SNR loss and the outage probability of systems that have a single receive antenna or two transmit antennas. For arbitrary transmit and receive antennas, approximations for the SNR loss and outage are derived. In particular, the SNR loss in a quantized MIMO beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas. The analytical expressions are proved to be tight with asymptotically large feedback rate. Simulations show that the bounds and approximations are tight even at low feedback rates, thereby providing a benchmark for feedback system design     

RF beamforming for MIMO cognitive user

Using Multiple Input Multiple Output (MIMO) architecture in cognitive radio (CR) secondary users improves the system performance in terms of interference cancellation and data rate enhancement but at the expense of adding complexity and cost. A solution to reduce this complexity is employing radio frequency (RF) beamforming networks at the transmitter/receiver front-ends. In this paper, we consider a MIMO secondary user equipped with such RF beamforming network. Moreover, we find the transmit/receive optimum RF beamforming network for a MIMO spatial multiplexing system. We evaluate the performance of the optimally designed RF beamforming technique over a Rician channel via computer simulations. The simulation results are assessed for different RF beamforming structures and the number of primary transmitters which cause interference on the secondary receiver.     

Channel quality-to-interference ratio quantization criterion for limited feedback beamforming in MIMO systems

The discrete Fourier transform (DFT)-based codebook is employed in this paper to quantize channel state information so that the amount of feedback can be reduced in the multiple input multiple output (MIMO) downlink of long term evolution (LTE) system. And a novel beamforming (BF) scheme based on the proposed channel quality-to-interference (QIR) quantizing criteria is developed, which uses only the index of the optimal codebook for the beamforming at the base station (BS), and dramatically reduces the amount of feedback. The proposed BF scheme jointly considers the influences of the quality of the quantized channels and the mutual interference among the sub-channels. The extensive simulation results verify that throughput of the proposed BF scheme is better than that of the random BF with a little feedback, and that of the eigen-beamforming even under low signal noise ratio (SNR) scenario.