MIMO Broadcast Channels With Finite-Rate Feedback

Multiple transmit antennas in a downlink channel can provide tremendous capacity (i.e., multiplexing) gains, even when receivers have only single antennas. However, receiver and transmitter channel state information is generally required. In this correspondence, a system where each receiver has perfect channel knowledge, but the transmitter only receives quantized information regarding the channel instantiation is analyzed. The well-known zero-forcing transmission technique is considered, and simple expressions for the throughput degradation due to finite-rate feedback are derived. A key finding is that the feedback rate per mobile must be increased linearly with the signal-to-noise ratio (SNR) (in decibels) in order to achieve the full multiplexing gain. This is in sharp contrast to point-to-point multiple-input multiple-output (MIMO) systems, in which it is not necessary to increase the feedback rate as a function of the SNR     

Analysis of Multiple Antenna Systems With Finite-Rate Channel Information Feedback Over Spatially Correlated Fading Channels

This paper employs a high resolution quantization framework to study the effects of finite-rate quantization of the channel state information (CSI) on the performance of MISO systems over correlated fading channels. The contributions of this paper are twofold. First, as an application of the general distortion analysis, tight lower bounds on the capacity loss of correlated MISO systems due to the finite-rate channel quantization are provided. Closed-form expressions for the capacity loss in high-signal-to-noise ratio (SNR) and low-SNR regimes are also provided, and their analysis reveals that the capacity loss of correlated MISO channels is related to that of i.i.d. fading channels by a simple multiplicative factor which is given by the ratio of the geometric mean to the arithmetic mean of the eigenvalues of the channel covariance matrix. Second, this paper extends the general asymptotic distortion analysis to the important practical problem of suboptimal quantizers resulting from mismatches in the distortion functions, source statistics, and quantization criteria. As a specific application, two types of mismatched MISO CSI quantizers are investigated: quantizers whose codebooks are designed with minimum mean square error (MMSE) criterion but the distortion measure is the ergodic capacity loss (i.e., mismatched design criterion), and quantizers with codebook designed with a mismatched channel covariance matrix (i.e., mismatched statistics). Bounds on the channel capacity loss of the mismatched codebooks are provided and compared to that of the optimal quantizers. Finally, numerical and simulation results are presented and they confirm the tightness of theoretical distortion bounds.     

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

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

Feedback Quantization Strategies for Multiuser Diversity Systems

In a system utilizing multiuser diversity, regular feedback of channel-quality predictions to the base station is required for each user. Typically, the measure of channel quality must be quantized at each mobile station before it can be sent back. In this paper, we present two distributed scalar quantization schemes that optimize two different performance criteria: a) the minimization of the probability P _e of incorrectly identifying the user with the best channel quality and b) maximization of the resulting throughput R. For a typical Rayleigh-fading system with 30 users per sector, numerical optimization results show that the P_e and R realized by the uniform quantization strategy with 16 quantization levels for each user can be achieved by only three quantization levels using the two proposed strategies. A practical approximation of the proposed schemes is studied and is shown to provide near-optimal performance for both performance criteria as the number of quantization levels becomes large     

Channel Feedback Quantization for High Data Rate MIMO Systems

In this work, we study a multiple-input multiple-output (MIMO) wireless system where the channel state information is partially available at the transmitter through a feedback link. Based on singular value decomposition, the MIMO channel is split into independent sub-channels. Effective feedback of the required spatial channel information entails efficient quantization/encoding of a unitary matrix. We propose two schemes for quantizing unitary matrices via Givens rotations and examine the performance for a scenario where the rates allocated to the sub-channels are selected according to their corresponding gains. Numerical results show that the proposed schemes offer a significant performance improvement as compared to that of MIMO systems without feedback, with a negligible increase in the complexity     

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     

基于信道质量干扰比量化准则的有限反馈波束形成

波束形成技术是MIMO无线通信系统的关键技术之一,它能够使系统有效性与可靠性都得到显著地提高,但它需要系统所有在线用户反馈其全部瞬时变化的信道状态信息,这将使拥挤的无线频谱资源更加紧张.为了降低系统所需的反馈量,本文结合LTE系统MIMO下行链路环境,将采用DFT基码本对信道状态信息进行量化,仅需要用户给基站反馈其最优码本索引;同时本文也首次提出基于信道质量干扰比为量化准则的一种新波束形成方案,并给出了质量干扰比的详细计算公式.此量化准则能够兼顾到量化信道的质量信息和子信道之间的互干扰信息,比传统的量化准则更具优良的性能.仿真结果表明,本文提出方案不仅可以明显降低系统反馈量,而且其性能超过随机波束形成,尤其在低信噪比场景下甚至优于特征波束形成的系统性能.理论分析和仿真验证表明本文方案是一种比较好的波束形成方案.     

Quantization Methods for Equal Gain Transmission With Finite Rate Feedback

We consider the design and analysis of quantizers for equal gain transmission (EGT) systems with finite rate feedback-based communication in flat-fading multiple input single output (MISO) systems. EGT is a beamforming technique that maximizes the MISO channel capacity when there is an equal power-per-antenna constraint at the transmitter, and requires the feedback of t-1 phase angles, when there are t antennas at the transmitter. In this paper, we contrast two popular approaches for quantizing the phase angles: vector quantization (VQ) and scalar quantization (SQ). On the VQ side, using the capacity loss with respect to EGT with perfect channel information at transmitter as performance metric, we develop a criterion for designing the beamforming codebook for quantized EGT (Q-EGT). We also propose an iterative algorithm based on the well-known generalized Lloyd algorithm, for computing the beamforming vector codebook. On the analytical side, we study the performance of Q-EGT and derive closed-form expressions for the performance in terms of capacity loss and outage probability in the case of i.i.d. Rayleigh flat-fading channels. On the SQ side, assuming uniform scalar quantization and i.i.d. Rayleigh flat-fading channels, we derive the high-resolution performance of quantized EGT and contrast the performance with that of VQ. We find that although both VQ and SQ achieve the same rate of convergence (to the capacity with perfect feedback) as the number of feedback bits B increases, there exists a fixed gap between the two     

Design and Analysis of MIMO Spatial Multiplexing Systems With Quantized Feedback

This paper investigates the problem of transmit beamforming in multiple-antenna spatial multiplexing (SM) systems employing a finite-rate feedback channel. Assuming a fixed number of spatial channels and equal power allocation, we propose a new criterion for designing the codebook of beamforming matrices that is based on minimizing an approximation to the capacity loss resulting from the limited rate in the feedback channel. Using the criterion, we develop an iterative design algorithm that converges to a locally optimum codebook. Under the independent identically distributed channel and high signal-to-noise ratio (SNR) assumption, the effect on channel capacity of the finite-bit representation of the beamforming matrix is analyzed. Central to this analysis is the complex multivariate beta distribution and tractable approximations to the Voronoi regions associated with the code points. Furthermore, to compensate for the degradation due to the equal power allocation assumption, we propose a multimode SM transmission strategy wherein the number of data streams is determined based on the average SNR. This approach is shown to allow for effective utilization of the feedback bits resulting in a practical and efficient multiple-input multiple-output system design.     

Design Guidelines for Training-Based MIMO Systems With Feedback

In this paper, we study the optimal training and data transmission strategies for block fading multiple-input multiple-output (MIMO) systems with feedback. We consider both the channel gain feedback (CGF) system and the channel covariance feedback (CCF) system. Using an accurate capacity lower bound as a figure of merit that takes channel estimation errors into account, we investigate the optimization problems on the temporal power allocation to training and data transmission as well as the training length. For CGF systems without feedback delay, we prove that the optimal solutions coincide with those for nonfeedback systems. Moreover, we show that these solutions stay nearly optimal even in the presence of feedback delay. This finding is important for practical MIMO training design. For CCF systems, the optimal training length can be less than the number of transmit antennas, which is verified through numerical analysis. Taking this fact into account, we propose a simple yet near optimal transmission strategy for CCF systems, and derive the optimal temporal power allocation over pilot and data transmission.     

Digital-to-Analog Conversion of Pulse Amplitude Modulated Systems Using Adaptive Quantization

In this paper, a full analysis is presented on digital-to-analog conversion for pulse amplitude modulated (PAM) systems. By analyzing the cyclostationary nature of pulse-amplitude modulation (PAM) systems, two methods of quantization are proposed –fixed and adaptive. Examples of this quantization analysis are provided for the reverse link transmitter chain in a cdma2000 system, and for the baseband transmitter chain of an IS-136 system. In addition, the impact of D/A converter nonlinearity on resultant signal-to-noise ratio is analyzed. Simulations are provided which show that adaptive quantization provides performance benefits over fixed methods in terms of adjacent channel power rejection (ACPR) and transmitter signal-to-noise ratio.     

A General Switch-Mode Amplifier Design for Actuators Using MIMO Optimal Feedback Quantization

This paper proposes a novel switch-mode power stage architecture for actuators. For a large number of actuators, the associated power amplifier becomes costly and bulky when each actuator is controlled by an independent amplifier. The proposed architecture allows actuators to share power amplifiers, thereby reducing the number of switching devices. This architecture is mapped into the graph theorem, and acceptable actuation states are analyzed. The switching method is controlled by multiple-input multiple-output optimal feedback quantization, which is designed to minimize a weighted measure of quantization distortion. Simulation and experimental results illustrate the effectiveness of the proposed scheme.      

Design of Multivariable Feedback Systems Using Progressive Decoupling

A general procedure for the design of multivariable feedback systems is presented. The system is first rendered weakly coupled by a suitable choice of some controller ratios and then designed by conventional single-loop techniques. One major characteristic of the method is that various degree of coupling of the system can be obtained, dependent on the complexity of the controller ratios chosen. Furthermore, a criterion is given to decide when the system can be regarded as weakly coupled, such that single-loop design techniques can be applied. The method gives the designer more freedom in the design and provides him with many more choices for a suitable controller. The effectiveness of the method is demonstrated by an application to a 4 x 4 boiler furnace example.     

Thin-Pavement Thickness Estimation Using GPR With High-Resolution and Superresolution Methods

In the field of civil engineering, sounding the top layer of carriageways, i.e., the pavement layer, is classically performed using standard ground-penetrating radar (GPR), whose resolution is bandwidth dependent. The layer thickness is deduced from both the time delays of backscattered echoes and the known dielectric constant of the medium. This paper focuses on superresolution and high-resolution techniques, which serve to improve the time resolution of GPR signals, and presents a parametric technique and five subspace methods, namely, estimation of signal parameters via rotational invariance techniques (ESPRIT), multiple-signal classification (MUSIC) algorithm, Min-Norm, and their polynomial versions root-MUSIC and root-Min-Norm. The performance of these algorithms will be compared in terms of resolution power as well as root-mean-square error on the estimated thickness. The paper also presents the results of computer tests and radar measurements in the far field.     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Performance Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiency and low error rates by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the error rate performance. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. Training symbols are used to estimate the channel by means of an arbitrary linear filter at the receiver. No channel state information (CSI) is assumed at the transmitter. We present a new framework to analyze training-based multiple-antenna systems by introducing an equivalent system model that specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. We derive the maximum-likelihood (ML) detector and highlight its behavior in the limiting cases of perfect CSI and no CSI, and its relation to several mismatched detectors. We deduce new exact expressions and Chernoff bounds of the pairwise error probability (PEP) used to assess word-error and bit-error rate bounds for ML and mismatched detection. Finally, we review the code design guidelines in terms of the deleterious effect of channel uncertainty for coherent and noncoherent signaling schemes, and present numerical results.     

Multiple-Antenna Signaling Over Fading Channels With Estimated Channel State Information: Capacity Analysis

Multiple-antenna concepts for wireless communication systems promise high spectral efficiencies and improved error rate performance by proper exploitation of the randomness in multipath propagation. In this paper, we investigate the impact of channel uncertainty caused by channel estimation errors on the capacity of Rayleigh and Ricean block-fading channels. We consider a training-based multiple-antenna system that reserves a portion of time to sound the channel. The training symbols are used to estimate the channel state information (CSI) at the receiver by means of an arbitrary linear estimation filter. No CSI is assumed at the transmitter. Our analysis is based on an equivalent system model for training-based multiple-antenna systems which specifies the channel by the estimated (and hence, known) channel coefficients and an uncorrelated, data-dependent, multiplicative noise. This model includes the special cases of perfect CSI and no CSI. We present new upper and lower bounds on the maximum instantaneous mutual information to compute ergodic and outage capacities, and extend previous results to arbitrary (and possibly mismatched) linear channel estimators and to correlated Ricean fading. Several numerical results for single- and multiple-antenna systems with estimated CSI are included as illustration.     

Transmission Subspace Tracking for MIMO Systems With Low-Rate Feedback

This paper describes a feedback algorithm for tracking the dominant subspaces of continuously time-varying channels in multiantenna communication systems. The nature of the problem is quantization of subspaces. It is well known that subspaces can be mathematically modeled as points in a Grassmann manifold. We model the variations between the dominant subspaces of channels at adjacent time instants to be along geodesics in the Grassmann manifold. Instead of quantizing the subspaces themselves, we propose to quantize the geodesic trajectory connecting two subspaces. More specifically, we quantize a key entity that characterizes a geodesic arc: the velocity matrix, which resembles angular speed in a one-dimensional complex space. Two techniques are proposed for quantizing the velocity matrix of the geodesic. In the first, a 1-bit feedback is utilized to indicate the preferred sign of a random velocity matrix of the geodesic. In the other, the velocity matrix is quantized using a Gaussian vector quantization codebook. Numerical results show that the performance of the proposed 1-bit feedback algorithm is better than a previously proposed Grassmannian subspace packing scheme at low-to-medium Doppler frequencies and better than a gradient sign feedback scheme at all Doppler frequencies. In our simulations, the Gaussian vector quantization algorithm is always better than the 1-bit feedback algorithm.     

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     

Optimizing Pilot Locations Using Feedback in OFDM Systems

Pilot-aided orthogonal frequency-division multiplexing (OFDM) channel estimation has, so far, been optimized only for open-loop systems for which the uniform spacing of pilots is optimal. In this paper, we examine closed-loop OFDM systems and show how uniform pilots may no longer be optimal. In doing so, we propose a feedback technique in which the pilot allocation mechanism is adapted to the mobile channel. After deriving a general expression for the symbol error rate as a function of pilot allocation, we optimize the pilot locations and propose two practical solutions using bounds on the objective function. We proceed to formulate pilot allocation based on the maximal average OFDM channel capacity. We examine the feedback overhead that is associated with our method and make comparisons with the conventional uniform framework. Finally, we suggest the use of vector quantization in the context of the generalized Lloyd algorithm to reduce feedback and extend our method to a multiple-input–multiple-output (MIMO)-OFDM system based on the Alamouti space–time block code. Monte-Carlo simulations illustrate the error-rate/capacity performance gains via nonuniform pilots and illustrate the effects of Doppler frequency and carrier frequency offset.      

Decomposition-Based Recursive Least Squares Algorithm for Wiener Nonlinear Feedback FIR-MA Systems Using the Filtering Theory

A decomposition-based recursive least squares algorithm is developed for Wiener nonlinear systems described by finite impulse response moving average models. After transferring a finite impulse response moving average (FIR-MA) model to a controlled autoregressive model, we compute the parameters by combining the decomposition principle and the least squares method and using the filtering idea. The simulation results validate the proposed algorithm.