MIMO-OFDM系统中基于簇的有限反馈方法

本文针对有限反馈MIMO-OFDM波束形成系统,研究了基于簇的有限反馈方法。利用簇内相邻子载波信道的频率相干性,提出了一种低复杂度的信道均值分簇法,该方法以平均信道响应在给定码本中选择最佳簇波束形成向量。此外,利用簇波束形成向量之间的剩余相关性,还提出了递归反馈和基于格的反馈两种反馈速率降低方法,即将前一簇码字的邻域内码字作为当前簇的新码本,从而大幅度降低反馈比特数。仿真结果表明信道均值分簇法能以较低的计算复杂度获得较佳的BER性能,反馈降低方法相对传统分簇方法能进一步降低反馈速率,递归反馈方法有一定性能损失,而基于格的反馈方法性能损失可忽略不计。      

Design of reduced complexity feedback precoding for MIMO‐OFDM

Beamforming technique is applied to significantly increase the performance of a MIMO system, if the channel information (CI) of the communication system is available at the transmitter. For the transmitter to obtain the entire CI, however, a considerable reverse‐link bandwidth is required. To save the bandwidth, a limited‐rate closed‐loop system, therefore, uses a predetermined codebook which is derived from the CI. The codebook consists of a finite number of precoders out of which the index of the best one is transmitted from the receiver to the transmitter using only a few bits saving substantial bandwidth. However, the amount of bits that need to be fed back can still be significantly large for MIMO‐OFDM systems when the precoding matrix index (PMI) for each subcarrier should be transmitted. Such per‐subcarrier precoding scheme has high feedback overhead and also incurs huge computational cost to determine the best PMI for each subcarrier. We, therefore, propose a per‐band precoding scheme that precodes a band (group) of subcarriers by only one precoder. More importantly, we develop, for the proposed per‐band scheme, reduced‐complexity precoding selection methods that lead to the design of efficient receivers. The effectiveness of the proposed scheme is investigated through computer simulations. Copyright © 2014 John Wiley & Sons, Ltd.     

有限反馈MISO-OFDM系统中基于误码率的波束成形

该文提出了一种在有限反馈条件下多入单出正交频分复用(MISO-OFDM)系统中基于误码率的波束成形方案。将OFDM符号的所有子载波分成若干簇,从码本中选择能够最小化该簇每个子载波的平均误码率的码字,作为该簇的波束成形向量。此方案既能降低反馈量,又能取得较低误码率。同时,为避免所提方案中探求最优解时的穷尽搜索,还基于簇内不同子载波信道频响之间的相关性提出了一种简化的次优算法。仿真结果表明,在典型参数设置下,所提方案能够以较低计算复杂度取得比其他已有方案更好的误码率性能。     

Limited feedback unitary precoding for orthogonal space-time block codes

Orthogonal space-time block codes (OSTBCs) are a class of easily decoded space-time codes that achieve full diversity order in Rayleigh fading channels. OSTBCs exist only for certain numbers of transmit antennas and do not provide array gain like diversity techniques that exploit transmit channel information. When channel state information is available at the transmitter, though, precoding the space-time codeword can be used to support different numbers of transmit antennas and to improve array gain. Unfortunately, transmitters in many wireless systems have no knowledge about current channel conditions. This motivates limited feedback precoding methods such as channel quantization or antenna subset selection. This paper investigates a limited feedback approach that uses a codebook of precoding matrices known a priori to both the transmitter and receiver. The receiver chooses a matrix from the codebook based on current channel conditions and conveys the optimal codebook matrix to the transmitter over an error-free, zero-delay feedback channel. A criterion for choosing the optimal precoding matrix in the codebook is proposed that relates directly to minimizing the probability of symbol error of the precoded system. Low average distortion codebooks are derived based on the optimal codeword selection criterion. The resulting design is found to relate to the famous applied mathematics problem of subspace packing in the Grassmann manifold. Codebooks designed by this method are proven to provide full diversity order in Rayleigh fading channels. Monte Carlo simulations show that limited feedback precoding performs better than antenna subset selection.     

有限反馈MISO-OFDM系统中最大化容量的波束成形

该文提出了一种在有限反馈条件下多输入单输出正交频分复用(MISO-OFDM)系统中基于最大化容量的波束成形方案。将OFDM符号的所有子载波分成若干簇,从码本中选择能够最大化该簇每个子载波平均容量的码字,作为该簇的波束成形向量。在低信噪比区域,求出了最优波束成形向量的闭合解;鉴于在高信噪比区域无法求出闭合解,基于簇内不同子载波信道频响之间的相关性提出了一种简化的次优算法以降低搜索最优解时的计算复杂度。仿真结果表明,在典型参数设置下,所提方案能够取得比其他已有方案更高的容量和更低的误码率。     

Interpolation Based Unitary Precoding for Spatial Multiplexing MIMO-OFDM With Limited Feedback

Spatial multiplexing with linear precoding is a simple technique for achieving high spectral efficiency in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Linear precoding requires channel state information for each OFDM subcarrier, which can be achieved using feedback. To reduce the amount of feedback, this paper proposes a limited feedback architecture that combines precoder quantization with a special matrix interpolator. In the proposed system, the receiver sends information about a fraction of the precoding matrices to the transmitter and the transmitter reconstructs the precoding matrices for all the subcarriers. A new interpolator is proposed inspired by spherical interpolation that respects the orthogonal columns of the precoding matrices and the performance invariance to right multiplication by a unitary matrix. The interpolator is parameterized by a set of unitary matrices; a construction of a suitable set is briefly described. Simulations illustrate the performance of limited feedback precoding with coding, estimation or prediction error, and time variation for bit error rate (BER), mutual information, and mean squared error (MSE)     

Adaptive OFDM Techniques With One-Bit-Per-Subcarrier Channel-State Feedback

In the orthogonal frequency-division multiplexing (OFDM) scheme, some subcarriers may be subject to a deep fading. Adaptive techniques can be applied to mitigate this effect if the channel-state information (CSI) is available at the transmitter. In this paper, we study the performance of an OFDM-based communication system whose transmitter has only one bit of CSI per subcarrier, obtained through a low-rate feedback. Three adaptive approaches are considered to exploit such a CSI feedback: adaptive subcarrier selection; adaptive power allocation (APA); and adaptive modulation selection (AMS). Under the conditions of a constant raw data rate and perfect feedback channel, the performance of these approaches are analyzed and compared in terms of raw bit-error rate. It is shown that one-bit CSI feedback can greatly enhance the system performance. Moreover, imperfections of the feedback channel are considered, and their impact on the performance of these techniques is studied. It is shown that by exploiting the knowledge that the feedback channel is imperfect, the performance of the APA and AMS techniques can be substantially improved     

Interpolation based transmit beamforming for MIMO-OFDM with limited feedback

Transmit beamforming and receive combining are simple methods for exploiting spatial diversity in multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) system. Optimal beamforming requires channel state information in the form of the beamforming vectors for each OFDM subcarrier. This paper proposes a limited feedback architecture that combines beamforming vector quantization and smart vector interpolation. In the proposed system, the receiver sends a fraction of information about the optimal beamforming vectors to the transmitter and the transmitter computes the beamforming vectors for all subcarriers through interpolation. A new spherical interpolator is developed that exploits parameters for phase rotation to satisfy the phase invariance and unit norm properties of the transmitted beamforming vectors. The beamforming vectors and phase parameters are quantized at the receiver and the quantized information is provided to the transmitter. The proposed quantization system provides only a moderate increase in complexity versus over comparable approaches. Numerical simulations show that the proposed scheme performs better than existing diversity techniques with the same feedback data rate.     

一种OFDM中继系统的有限反馈预编码方法

基于正交频分复用的放大转发协作中继系统,为了减少系统误比特率、增加信道容量和增强实用性,该文提出一种实用的源节点预编码和中继节点预编码的联合优化有限比特反馈的预编码方法。利用3节点构成的两个下行链路,实现两跳协作通信方式;采用SVD分解和QR(orthogonal triangular)分解相结合设计预编码,其中源节点预编码每帧只要一个;优选量化码本,把预编码矩阵量化后反馈到发射端。仿真结果表明,该方案能提高平均和速率、降低误码率和改善中断概率特性,且反馈比特数较少具有更好的实用价值。     

The Effect of Finite Rate Feedback on CDMA Signature Optimization and MIMO Beamforming Vector Selection

We analyze the effect of finite rate feedback on code-division multiple-access (CDMA) signature optimization and multiple-input multiple-output (MIMO) beamforming vector selection. In CDMA signature optimization, for a particular user, the receiver selects a signature vector from a codebook to best avoid interference from other users, and then feeds the corresponding index back to the specified user. For MIMO beamforming vector selection, the receiver chooses a beamforming vector from a given codebook to maximize the instantaneous information rate, and feeds back the corresponding index to the transmitter. These two problems are dual: both can be modeled as selecting a unit norm vector from a finite size codebook to ldquomatchrdquo a randomly generated Gaussian matrix. Assuming that the feedback link is rate limited, our main result is an exact asymptotic performance formula where the length of the signature/beamforming vector, the dimensions of interference/channel matrix, and the feedback rate approach infinity with constant ratios. The proof rests on the large deviations of the underlying random matrix ensemble. Further, we show that random codebooks generated from the isotropic distribution are asymptotically optimal not only on average, but also in probability.     

Performance of Orthogonal Beamforming for SDMA With Limited Feedback

On the multiantenna broadcast channel, the spatial degrees of freedom support simultaneous transmission to multiple users. The optimal multiuser transmission, which is known as dirty paper coding, is not directly realizable. Moreover, close-to-optimal solutions such as Tomlinson-Harashima precoding are sensitive to channel state information (CSI) inaccuracy. This paper considers a more practical design called per user unitary and rate control (PU2RC), which has been proposed for emerging cellular standards. PU2RC supports multiuser simultaneous transmission, enables limited feedback, and is capable of exploiting multiuser diversity. Its key feature is an orthogonal beamforming (or precoding) constraint, where each user selects a beamformer (or precoder) from a codebook of multiple orthonormal bases. In this paper, the asymptotic throughput scaling laws for PU2RC with a large user pool are derived for different regimes of the signal-to-noise ratio (SNR). In the multiuser interference-limited regime, the throughput of PU2RC is shown to logarithmically scale with the number of users. In the normal SNR and noise-limited regimes, the throughput is found to scale double logarithmically with the number of users and linearly with the number of antennas at the base station. In addition, numerical results show that PU2RC achieves higher throughput and is more robust against CSI quantization errors than the popular alternative of zero-forcing beamforming if the number of users is sufficiently large.     

Adaptive precoding and power allocation in distributed antenna systems with limited feedback

This paper introduces the limited feedback precoding into the distributed antenna system and proposes to adapt the predetermined orthogonal space time block codes to the available channel state information at the transmitter. The optimal representation of precoding information, namely the precoder, with least bits therefore becomes the key problem. Inspired by the characteristics of the distributed antenna system, we focus our work on the precoder construction, adaptable in response to the large and small scale fading, such that the symbol error probability is significantly reduced over that of a fixed, non‐adaptive, independent and identically distributed precoder codebook design. Furthermore, a suboptimal power‐loading strategy is presented by minimizing the derived tight upper bound on the average pairwise error probability of the precoded orthogonal space time block codes, which approaches the optimal performance asymptotically without additional channel knowledge other than the available feedback information. We prove that the proposed precoded orthogonal space time transmission scheme can achieve full diversity order. In particular, the robustness of our proposed transmission scheme to channel estimation error and feedback delay is respectively investigated in some detail, and numerical results show that it obviously improves the link reliability and obtains substantial gains even with few bits of feedback in comparison with conventional antenna selection scheme. Copyright © 2013 John Wiley & Sons, Ltd.     

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.      

一种前向放大中继通信系统中的有限反馈中继预编码方案

 本文首先给出了前向放大中继通信系统中,在给定QoS要求下的最优中继预编码矩阵的设计. 进而,针对实际通信系统中反馈信道带宽的限制,给出了一种有限反馈中继预编码码本的设计方案. 计算机仿真表明,本文所提新码本有限反馈中继预编码方案的系统性能随着反馈比特数的增加接近完全反馈下的系统性能,且在相同反馈比特数下的系统容量和误码率均明显优于将传统MIMO通信系统中的Grassmannian码本或随机码本直接应用于中继预编码的有限反馈方案.     

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.      

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     

Precoding for Orthogonal Space–Time Block-Coded OFDM Downlink: Mean or Covariance Feedback?

This paper presents linear and nonlinear precoding design for error-rate improvement in orthogonal space–time block-coded (OSTBC) multiple-input–multiple-output (MIMO) orthogonal frequency-division-multiplexed (OFDM) downlink, where both the conditional mean of the channel gain matrix and the channel gain covariance matrix may be available at the transmitter. The conditional means of the channel matrix are derived for a general transmit-antenna-correlated frequency-selective fading MIMO channel with estimation errors and feedback delay. Mean-feedback linear precoding and nonlinear Tomlinson–Harashima precoding (THP) are developed to maximize the signal-to-noise power ratio (SNR). The intuition that when the mean feedback becomes accurate the mean-feedback precoding outperforms covariance precoding is confirmed. Dual-mode precoding is also proposed, in which the novel mean-feedback precoding or covariance precoding is adaptively chosen at the receiver. The precoding-mode switching metric is the maximized SNR, which is an indicator of the error rate. The receiver calculates its metric, selects the mode that achieves a higher SNR, and decides whether mean feedback is necessary. Our proposed precoders (both mean feedback and adaptive) significantly reduce the system error rate. Nonlinear precoding is shown to outperform linear precoding. Adaptive precoding outperforms both mean-feedback precoding and covariance precoding if individually applied in OSTBC OFDM.      

Adaptive Bit-Interleaved Coded OFDM With Reduced Feedback Information

If the channel is static and is perfectly known to both the transmitter and the receiver, the water-filling technique with adaptive modulation is known to be optimal (Gallager, 1968). However, for orthogonal frequency-division multiplexing (OFDM) systems, this requires intensive traffic overheads for reporting channel state information on all subcarriers to the transmitter. In this paper, we consider an adaptive modulation and coding scheme for bit-interleaved coded OFDM with reduced feedback information satisfying a specified quality of service level. We propose a rate adaptation scheme, which utilizes the estimated bit error rate for supportable transmission rates. In this scheme, a user equipment chooses a modulation and coding scheme (MCS) level, which can provide the maximum spectral efficiency based on one OFDM symbol rather than on all subchannels. Then the user needs to send back only the selected MCS level index. The proposed scheme does not require the water-filling procedure, and the amount of the feedback information reduces to a single integer value irrespective of the number of subcarriers. Simulation results show that the proposed scheme can significantly reduce the system complexity while minimizing the performance loss compared to the optimum water-filling scheme.     

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.     

QoS-Driven Jointly Optimal Subcarrier Pairing and Power Allocation for Decode-and-Forward OFDM Relay Systems

In this paper, we investigate the quality-of-service (QoS) driven subcarrier pairing and power allocation for two-hop decode-and-forward (DF) OFDM relay systems. By integrating the concept of effective capacity, our goal is to maximize the system throughput subject to a given delay-QoS constraint. Based on whether the destination can receive the signal transmitted by the source, we consider two scenarios, i.e. OFDM DF relay systems without diversity and OFDM DF relay systems with diversity, respectively. For OFDM DF relay systems without diversity, we demonstrate that the jointly optimal subcarrier pairing and power allocation can be implemented with two separate steps. For OFDM DF relay systems with diversity, we propose an iterative algorithm to achieve jointly optimal subcarrier pairing and power allocation. Furthermore, we find that the analytical results show different conclusions for the two types of OFDM relay systems. For OFDM relay systems without diversity, the optimal power allocation depend on not only the channel quality of subcarriers but also the delay QoS constraints, while the optimal subcarrier pairing just depends on the channel quality of subcarriers. For OFDM relay systems with diversity, both the optimal subcarrier pairing and power allocation depend on the channel quality of subcarriers and the delay QoS constraints. Simulation results show that our proposed scheme offers a superior performance over the existing schemes.