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     

一种基于方向标记的有限反馈量化方法

随着天线数目和反馈比特数的增加,大规模多输入多输出（Multiple-Input Multiple-Output,MIMO）信道向量量化的复杂度大幅增加。为此,提出了一种基于方向标记的有限反馈量化方法。该方法将码本中码字进行分组,每组选取一个向量作为方向标记向量,在进行量化时,信道向量首先与各组方向标记向量进行比较,将与信道向量最接近的方向标记向量所在组选为待选码本组;在待选码本组内进行下一步量化,最终选出与其最接近的量化向量为最优码字。复杂度分析与仿真结果表明,所提方法缩小了待选码字的数量从而降低了计算复杂度,是系统性能与计算复杂度的一种折中。     

一种基于码本轮转的有限反馈量化方法

大规模多输入多输出（Multiple-Input Multiple-Output,MIMO）系统中随着天线数目的增加,其反馈比特数将随之大幅度增加。为此,提出了一种基于码本轮转的有限反馈量化方法。该方法中,用户在前一时刻得到最佳码字之后,在码本中选取轮转区域构成虚拟码本,判断当前时刻的信道向量,满足轮转条件的用户将虚拟码本轮转到码本起始位置,在虚拟码本中进行量化;不满足轮转条件的用户在原始码本中进行量化,选出当前时刻的最优码字。反馈比特数分析与仿真结果表明,所提方法可轮转的虚拟码本减少了量化码字的数量,从而减少了反馈比特数,是系统性能与反馈比特数的一种折中。     

混合发射天线选择的等增益传输系统优化设计

文中研究了混合发射天线选择的等增益传输(TAS-EGT)系统优化设计问题.根据信道衰落系数的排序统计特性,给出了TAS-EGT系统的平均接收信噪比,提出了最小发射天线数的计算方法.由于TAS-EGT系统的性能并非完全正比于射频链路数,因此文中提出了最优射频链路数的计算方法.仿真结果显示增加少量的发射天线可以节省大量的射频链路.因此,文中提出的算法可以降低系统的成本和复杂度,优化系统的性能以减少不必要的开销.     

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.     

Finite State Channels With Time-Invariant Deterministic Feedback

We consider capacity of discrete-time channels with feedback for the general case where the feedback is a time-invariant deterministic function of the output samples. Under the assumption that the channel states take values in a finite alphabet, we find a sequence of achievable rates and a sequence of upper bounds on the capacity. The achievable rates and the upper bounds are computable for any $N$, and the limits of the sequences exist. We show that when the probability of the initial state is positive for all the channel states, then the capacity is the limit of the achievable-rate sequence. We further show that when the channel is stationary, indecomposable, and has no intersymbol interference (ISI), its capacity is given by the limit of the maximum of the (normalized) directed information between the input $X^{N}$ and the output $Y^{N}$ , i.e., $$C = lim _{N rightarrow infty } {{ 1}over { N}} max I(X^{N} rightarrow Y^{N} )$$ where the maximization is taken over the causal conditioning probability $Q(x^{N}Vert z^{N-1})$ defined in this paper. The main idea for obtaining the results is to add causality into Gallager's results on finite state channels. The capacity results are used to show that the source–channel separation theorem holds for time-invariant determinist feedback, and if the state of the channel is known both at the encoder and the decoder, then feedback does not increase capacity.      

Analysis of Multiple-Antenna Systems With Finite-Rate Feedback Using High-Resolution Quantization Theory

This paper considers the development of a general framework for the analysis of transmit beamforming methods in multiple-antenna systems with finite-rate feedback. Inspired by the results of classical high-resolution quantization theory, the problem of finite-rate quantized communication system is formulated as a general fixed-rate vector quantization problem with side information available at the encoder (or the quantizer) but unavailable at the decoder. The framework of the quantization problem is sufficiently general to include quantization schemes with general non-mean-squared distortion functions and constrained source vectors. Asymptotic distortion analysis of the proposed general quantization problem is provided by extending the vector version of the Bennett's integral. Specifically, tight lower and upper bounds of the average asymptotic distortion are proposed. Sufficient conditions for the achievability of the distortion bounds are also provided and related to corresponding classical fixed-rate quantization problems. The proposed general methodology provides a powerful analytical tool to study a wide range of finite-rate feedback systems. To illustrate the utility of the framework, we consider the analysis of a finite-rate feedback multiple-input single-output (MISO) beamforming system over independent and identically distributed (i.i.d.) Rayleigh flat-fading channels. Numerical and simulation results are presented that further confirm the accuracy of the analytical results     

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     

On the Information Rate of MIMO Systems With Finite Rate Channel State Feedback Using Beamforming and Power On/Off Strategy

It is well known that multiple-input multiple-output (MIMO) systems have high spectral efficiency, especially when channel state information at the transmitter (CSIT) is available. In many practical systems, it is reasonable to assume that the CSIT is obtained by a limited (i.e., finite rate) feedback and is therefore imperfect. We consider the design problem of how to use the limited feedback resource to maximize the achievable information rate. In particular, we develop a low complexity power on/off strategy with beamforming (or Grassmann precoding), and analytically characterize its performance. Given the eigenvalue decomposition of the covariance matrix of the transmitted signal, refer to the eigenvectors as beams, and to the corresponding eigenvalues as the beam's power. A power on/off strategy means that a beam is either turned on with a constant power, or turned off. We will first assume that the beams match the channel perfectly and show that the ratio between the optimal number of beams turned on and the number of antennas converges to a constant when the numbers of transmit and receive antennas approach infinity proportionally. This motivates our power on/off strategy where the number of beams turned on is independent of channel realizations but is a function of the signal-to-noise ratio (SNR). When the feedback rate is finite, beamforming cannot be perfect, and we characterize the effect of imperfect beamforming by quantization bounds on the Grassmann manifold. By combining the results for power on/off and beamforming, a good approximation to the achievable information rate is derived. Simulations show that the proposed strategy is near optimal and the performance approximation is accurate for all experimented SNRs.     

二重空间分集等增益合并算法研究

分集接收合并技术是抗信号快衰落的一种有效措施。由于等增益合并具有良好的合并效果,并且实现较简单,因此在实际中获得了广泛的应用。针对二重空间分集,分析了一种新的基于锁相环的合并方法。该合并方法利用一个鉴相器就可以实现2路接收信号的频率同步和相位同步,进而可以进行等增益合并。该合并方式可以在不影响性能的前提下简化系统的复杂度、降低同步时间,便于工程实现。     

基于相关信道统计的有限速率反馈波束形成

针对实际MIMO系统无线信道存在的空域相关性,提出了一种基于相关信道统计的改进算法.基于此算法,并采用随机码本量化信道信息形成一种新波束形成方案,它只需要有限速率反馈部分信道信息,可以同时获得系统多用户分集增益和阵列增益,解决了常规波束形成需要大量信道反馈信息和相干波束形成系统性能对信道瞬时变化信息敏感的问题.仿真结果表明,提出方案在相关信道下相当有效,其性能超过常规波束形成,即使在有限反馈限制条件下,其性能亦接近相干机会波束的性能,仅有0.2 bit/s·Hz-1的性能损失.     

Throughput-Optimal Precoding and Rate Allocation for MISO Systems With Noisy Feedback Channels

A throughput metric is considered for a multiple-input single-output (MISO) system with noisy feedback of channel state information (CSI). The goal is to optimize a precoding matrix with a medium-access control layer metric. The problem is a nonlinear multidimensional optimization. Results show that the optimal precoding turns into beamforming when the signal-to-noise ratio (SNR) of CSI feedback is sufficiently large. A necessary condition for the optimality of beamforming under the throughput metric is determined, and the necessary and sufficient condition is numerically found based on the Gauss-Chebyshev Quadrature method. Next, the rate allocation for beamforming and spatial diversity is analyzed. Then, a two-mode transmission scheme is proposed such that the transmitter is engaged in either the beamforming mode or the spatial diversity mode depending on the SNR of the CSI feedback. It is shown that at a fairly high SNR of CSI feedback, the rate allocation needs to be reduced, while at a low SNR of CSI feedback, the allocated rate should be increased. It is shown that when the SNR of CSI feedback is lower than a threshold, there always exists an SNR of the transmitted signal such that the CSI feedback can be viewed as the real CSI solely for the purpose of rate allocation. The result also shows that the throughput of two-mode transmission is almost the same as the throughput of the optimal precoding scheme, even with a low SNR and large feedback delay.     

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     

A CMOS Resistive Feedback Differential Low-Noise Amplifier With Enhanced Loop Gain for Digital TV Tuner Applications

A resistive feedback differential low-noise amplifier (LNA) with enhanced loop gain is implemented as a part of a digital TV (DTV) tuner using a 0.18-$mu{hbox{m}}$ CMOS process. A voltage buffer having higher gain, higher linearity, and lower noise figure (NF) than those of the conventional differential source follower (DSF), which is called the differential hybrid voltage buffer (DHVB) in this paper, is designed by combining the common source amplifier and source follower. By adopting the DHVB with optimized performance as a voltage buffer of the conventional resistive feedback differential LNA, the loop gain of the LNA can be increased. This leads to a highly linear resistive feedback LNA with higher gain and lower NF compared to the conventional resistive feedback LNA. For the wide gain range, the proposed LNA includes the variable gain function based on the resistive attenuator employing the T-switch. The measurement results of the proposed LNA exhibit a maximum gain of 16 dB and a gain range of 50 dB. At maximum gain, the LNA shows an average NF of 2.8 dB, a third-order input-referred intercept point of $-{hbox{1 dBm}}$, a second-order input-referred intercept point of 40 dBm, and S11 of under $-{hbox{9 dB}}$ in a frequency range from 48 to 860 MHz. The power consumption is 30.6 mW at a 1.8-V power supply and the chip area is ${hbox{0.25 mm}}^{2}$.      

Feedback Constraints for Adaptive Transmission

In this article, the feedback constraints that limit the potential of AMC and MIMO systems for FDD systems are presented. It has been shown that while adaptive transmission efficiently utilizes the available bandwidth and transmit power, feedback constraints could be a significant impediment. Channel prediction can be employed to compensate the impact of feedback delay but its effectiveness would depend on the accuracy of the channel model. It is also showed that feedback errors could cause outage regions where AMC is not feasible and could also impact the benefits of multiuser scheduling. Limited feedback is a major issue for MIMO-AMC systems because channel state information grows with the rank of the MIMO system, the number of transmission modes, and the number of users for broadcast systems. Since feedback transmission consumes resources that could otherwise be used for data transmission on the reverse channel, feedback design is extremely important especially for power-limited devices such as mobile stations. Finally, some open problems are outlined that are of interest to adaptive transmission systems     

Scheduling Over Nonstationary Wireless Channels With Finite Rate Sets

We consider a wireless basestation transmitting high-speed data to multiple mobile users in a cell. The channel conditions between the basestation and the users are time-varying and user-dependent. Our objective is to design a scheduler that determines which user to schedule at each time step. Previous work on this problem has typically assumed that the channel conditions are governed by a stationary stochastic process. In this setting, a popular algorithm known as Max-Weight has been shown to have good performance. However, the stationarity assumption is not always reasonable. In this paper, we study a more general worst-case model in which the channel conditions are governed by an adversary and are not necessarily stationary. In this model, we show that the nonstationarities can cause Max-Weight to have extremely poor performance. In particular, even if the set of possible transmission rates is finite, as in the CDMA 1xEV-DO system, Max-Weight can produce queue sizes that are exponential in the number of users. On the positive side, we describe a set of tracking algorithms that aim to track the performance of a schedule maintained by the adversary. For one of these tracking algorithms, the queue sizes are only quadratic. We discuss a number of practical issues associated with the tracking algorithms. We also illustrate the performance of Max-Weight and the tracking algorithms using simulation.     

一种计算无限增益多路反馈滤波器增益的简便方法

基于拆环法和叠加原理,提出了一种计算无限增益多路反馈滤波器增益的新方法--部分拆环法.该方法的思想是拆开距运放输入端较远的环路,保留较近的环路,再用叠加原理计算增益.与传统方法相比,该方法是化整为零计算电路,因而无需列方程、联立方程组求解增益;与开环法相比,该方法保留了距运放较近的环路,而该环路与运放组成比例电路,因而可利用已有比例电路的结论,使增益的计算更为简单、实用.因此,部分拆环法可快速计算滤波器增益,适宜推广.     

Asymptotic Capacity of Multicarrier Transmission With Frequency-Selective Fading and Limited Feedback

We study the capacity of multicarrier transmission through a slow frequency-selective fading channel with limited feedback, which specifies channel state information. Our results are asymptotic in the number of subchannels . We first assume independent and identically distributed (i.i.d.) subchannel gains, and show that, for a large class of fading distributions, a uniform power distribution over an optimized subset of subchannels, or on-off power allocation, gives the same asymptotic growth in capacity as optimal water filling, e.g., with Rayleigh fading. Furthermore, the growth in data rate can be achieved with a feedback rate as . If the number of active subchannels is bounded, the capacity grows only as with the feedback rate of . We then consider correlated subchannels modeled as a Markov process, and study the savings in feedback. Assuming a fixed ratio of coherence bandwidth to the total bandwidth, the ratio between minimum feedback rates with correlated and i.i.d. subchannels converges to zero with , e.g., as for Rayleigh-fading subchannels satisfying a first-order autoregressive process. We also show that adaptive modulation, or rate control schemes, in which the rate on each subchannel is selected from a quantized set, achieves the same asymptotic growth rates in capacity and required feedback. Finally, our results are extended to cellular uplink and downlink channel models.     

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.     

Transmit Precoding Based Low Complexity Codebooks and Finite Feedback Rate for Space Shift Keying MIMO Systems

Transmit Precoding (TPC) considerably improves the performance of Space Shift Keying (SSK) systems. Codebook-based TPC is able to tackle several difficulties encountered by non-codebook TPC techniques. Channel State Information (CSI) is required at the receiver only, and the index of the best codeword is easily identified and fed-back from receiver to transmitter with low rate message. Motivated by these advantages, this paper contributes to the codebook-based TPC in the following aspects. First, the paper presents a Factorized form of the Full-Combination (FC) codebook with phase rotation only, and shows that only four phases are needed, which significantly simplifies practical implementation. As a second contribution, the paper introduces two statistically filtered codebooks: Index-Filtration FC and Average-Filtration FC. These codebooks considerably reduce system complexity due to their small codebook size, while maintaining almost the same BER of the FC codebook. As a third contribution, this paper proposes a new codeword selection criteria based on Long term statistics of the CSI (LCSI), instead of the conventional criteria using instantaneous CSI. This reduces the feedback rate of the index of the selected codeword while providing performance improvement over non-precoded SSK. Simulation results show the effectiveness of the proposed codebooks and the performance improvement with LCSI selection criteria.