Transmit beamforming in multiple-antenna systems with finite rate feedback: a VQ-based approach

This paper investigates quantization methods for feeding back the channel information through a low-rate feedback channel in the context of multiple-input single-output (MISO) systems. We propose a new quantizer design criterion for capacity maximization and develop the corresponding iterative vector quantization (VQ) design algorithm. The criterion is based on maximizing the mean-squared weighted inner product (MSwIP) between the optimum and the quantized beamforming vector. The performance of systems with quantized beamforming is analyzed for the independent fading case. This requires finding the density of the squared inner product between the optimum and the quantized beamforming vector, which is obtained by considering a simple approximation of the quantization cell. The approximate density function is used to lower-bound the capacity loss due to quantization, the outage probability, and the bit error probability. The resulting expressions provide insight into the dependence of the performance of transmit beamforming MISO systems on the number of transmit antennas and feedback rate. Computer simulations support the analytical results and indicate that the lower bounds are quite tight.     

中继辅助MIMO系统中基于有限反馈的分布式波束成形

对协作式中继辅助的多输入多输出通信系统中基于有限反馈的联合波束成形问题进行了研究.首先推导了接收信噪比的下界,并基于该下界建立联合波束成形的数学模型.其次推导了分布式波束成形的最优方案.最后针对该最优方案,设计了一个迭代算法,优化得到分布式波束成形码本,从而分布式中继站的波束成形可基于码本序号的有限反馈来进行.实验结果仿真表明,所设计的联合波束成形码本在反馈开销很小的情况下获得明显的性能增益.     

Unquantized and uncoded channel state information feedback in multiple-antenna multiuser systems

We propose a channel state information (CSI) feedback scheme based on unquantized and uncoded (UQ-UC) transmission. We consider a system where a mobile terminal obtains the downlink CSI and feeds it back to the base station using an uplink feedback channel. If the downlink channel is an independent Rayleigh fading channel, then the CSI may be viewed as an output of a complex independent identically distributed Gaussian source. Further, if the uplink feedback channel is an additive white Gaussian noise channel, and the downlink CSI is perfectly known at the mobile terminal, it can be shown that UQ-UC CSI transmission (that incurs zero delay) is optimal in that it achieves the same minimum mean-squared error distortion as a scheme that optimally (in the Shannon sense) quantizes and encodes the CSI, while theoretically incurring infinite delay. Since the UQ-UC transmission is suboptimal on correlated wireless channels, we propose a simple linear CSI feedback receiver that can be used to improve the performance of UQ-UC transmission while still retaining the attractive zero-delay feature. We provide bounds on the performance of such UQ-UC CSI feedback and study its impact on the achievable information rates. Furthermore, we explore its application and performance in multiple-antenna multiuser wireless systems, and also propose a corresponding pilot-assisted channel-state estimation scheme.     

有限比率反馈对OFDM系统性能的影响

讨论了多发射天线OFDM系统中有限比率反馈对通信系统误码率的影响。通过发射端的波束成形将多天线OFDM无线信道等价为独立的并行子信道,并结合有限比率反馈下的波束成形矢量集的最优设计,推导了多发射天线下OFDM系统中反馈比特数对误码率影响的表达式,同时给出了反馈比特数对误码率的相对误差的影响。数值仿真表明,当发射天线数为2且10dB≤Es/N0≤20dB时,为使误码率的相对误差小于20%,每一子信道需3～5的反馈比特数,当发射天线数为3时则需7～8的反馈比特数,可为带反馈信道的多天线OFDM系统设计提供参考。     

Cooperative beamforming in cognitive radio systems without feedback of receiver beamforming vectors to transmitter

Wireless Networks - In this paper, we investigate the problem of transceiver beamforming and power allocation in the downlink of a multiple input multiple output Cognitive radio system. In this...     

Transmit beamforming for space-frequency coded MIMO-OFDM systems with spatial correlation feedback

This paper addresses the problem of joint optimization of transmit beamforming and space-frequency (SF) coding for MIMO-OFDM systems with spatial correlation feedback in broadband communications. This problem is challenging in the sense that the transmitter should be designed to beamform across multiple eigenspaces associated with the multipath environment simultaneously. With arbitrary transmit spatial correlation, the performance analysis for SF-coded MIMO-OFDM systems with beamforming is provided, and a general optimization problem for the beamforming design is formulated. Three suboptimal approaches to design the beamformer based on the derived design criteria are proposed: i) eigenvalue selection scheme; ii) eigenspace selection scheme; and iii) per-subcarrier approach based on decoding at each subcarrier. The proposed schemes take into account the multiple eigenspace information associated with the multipath-delay channel. Improvement in the performance over SF coding without beamforming is shown through simulations in terms of bit error rate. The eigenvalue selection scheme provides the best performance among the proposed algorithms. This scheme locates the subspace associated with the largest eigenvalues in the eigenspace of the covariance matrices. With the eigenvalue selection scheme, the performance improvement is about 3 dB over the SF coding without beamforming for highly correlated channels as shown in our simulations.     

Adaptive transmitted distributed antenna selection strategy in distributed antenna systems with limited feedback beamforming

An adaptive transmitted distributed antenna (DA) selection strategy in distributed antenna systems (DAS) with limited feedback (LFB) beamforming is proposed. By maximising the upper bound of ergodic capacity in DAS with LFB beamforming, the proposed strategy can adaptively adjust the number of transmitted DAs. Simulation results show that the proposed strategy achieves greater ergodic capacity than the strategy with a fixed number of transmitted DAs.     

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.     

Distributed beamforming in wireless relay networks with quantized feedback

This paper is on quantized beamforming in wireless amplify-and-forward (AF) relay networks. We use the generalized Lloyd algorithm (GLA) to design the quantizer of the feedback information and specifically to optimize the bit error rate (BER) performance of the system. Achievable bounds for different performance measures are derived. First, we analytically show that a simple feedback scheme based on relay selection can achieve full diversity. Unlike the previous diversity analysis on the relay selection scheme, our analysis is not aided by any approximations or modified forwarding schemes. Then, for highrate feedback, we find an upper bound on the average signalto- noise ratio (SNR) loss. Using this result, we demonstrate that both the average SNR loss and the capacity loss decay at least exponentially with the number of feedback bits. In addition, we provide approximate upper and lower bounds on the BER, which can be calculated numerically.We observe that our designs can achieve both full diversity as well as high array gain with only a moderate number of feedback bits. Simulations also show that our approximate BER is a reliable estimation on the actual BER. We also generalize our analytical results to asynchronous networks, where perfect carrier level synchronization is not available among the relays.     

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.     

A study of opportunism for multiple-antenna systems

Recently proposed opportunistic beamforming exploits the multiuser diversity to reduce the feedback by not requiring the precoding information used for closed-loop schemes to be known at the transmitter. Opportunism could also be beneficially employed for other multiple-antenna transmission techniques like cophasing and antenna selection. For opportunistic beamforming and antenna selection, we give closed-form expressions for throughput that closely approximate the performance of these schemes with a Proportionally Fair scheduler (PFS) at low signal-to-noise ratios (SNRs). For large number of transmit antennas, opportunistic cophasing has similar performance as opportunistic beamforming. Asymptotic dependence of the required number of users to achieve the gains of opportunism on the number of transmit antennas is exponential for opportunistic beamforming (and cophasing for large numbers of transmit antennas), and at best linear for opportunistic antenna selection. For multiple-antenna receivers, we additionally examine an opportunistic multiple-input multiple-output (MIMO) scheme that transmits multiple data streams simultaneously to the same user.     

Performance analysis of scheduled transmit beamforming systems under non-identically delayed feedback channels

Wireless Networks - In this paper, we investigate the performance analysis of a scheduled transmit beamforming system under non-identically delayed feedback channels. This paper derives the exact...     

Turbo coded multiple-antenna systems for near-capacity performance

For a turbo coded BLAST (Bell LAbs Space-Time architecture) system with N_t transmit antennas and N_r receive antennas, there is a significant gap between its detection threshold and the capacity in case N_t > N_r. In this paper, we show that by introducing a convolutional interleaver with block delay between the BLAST mapper and the turbo encoder, the threshold can be improved. Near-capacity thresholds can be achieved for some cases. To take advantage of the low detector complexity in Alamouti STBC (space-time block code), we also investigate a STBC system, which is the concatenation of the Alamouti STBC with a turbo trellis coded modulation. By using a proper labelling and adding a convolutional interleaver with block delay to such a STBC system, we achieve both lower error floors and lower thresholds.     

Coordinated beamforming with limited feedback in the MIMO broadcast channel

In this paper, we propose a new joint optimization of linear transmit beamforming and receive combining vectors for the multiple-input multiple-output (MIMO) broadcast channel. We consider the transmission of a single information stream to two users with two or more receive antennas. Unlike past work in which iterative computation is required to design the beamformers, we derive specific formulations for the transmit beamformers for two active users via a power iteration and a generalized eigen analysis. To enable practical implementation, a new limited feedback algorithm is proposed that exploits the structure of the algorithm to avoid full channel quantization. The feedback overhead of the proposed algorithm is independent of the number of receive antennas. Monte Carlo simulations are used to evaluate the bit error rate and the sum rate performances of the proposed algorithm. Simulation results show that the proposed method performs close to the sum capacity of the MIMO broadcast channel even with limited feedback.     

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.     

Multiantenna adaptive modulation with beamforming based on bandwidth-constrained feedback

Adaptive modulation has the potential to increase system throughput considerably by adapting transmission parameters to the time-varying channel characteristics. Crucial to adaptive systems is the requirement of a feedback channel, that is often capable of carrying only a limited number of bits. Under such a bandwidth-constrained feedback link, we aim to optimize a multiantenna system based on transmit beamforming and adaptive modulation, where the transmit power, the signal constellation, the beamforming direction, and the feedback strategy, are designed jointly. Our proposed nested iterative approach leads to an approximate, yet practical, solution. Simulation results demonstrate considerable improvement in transmission rate, as the number of feedback bits increases.     

多天线无线数据通信系统中多用户分集的研究

研究当接收天线不少于发送天线时多输入多输出(MIMO)系统的多用户分集能力。首先从理论上分析了发送天线个数等于1和2时最大似然接收和迫零接收系统的平均吞吐量和调度增益,以及仿真分析了发送天线个数大于2时系统性能。理论分析和仿真表明：在多用户的MIMO系统中,接收的平均信噪比、用户个数、收发天线个数、接收机的结构等对于多用户分集有很大的影响。当发送天线个数为1时,接收天线较少(1,2,3)和平均信噪比为．10dB时调度增益很大,但调度增益随着天线个数和发送功率增大急剧下降。和最大似然接收相比,迫零接收具有更大的多用户分集增益,因此迫零接收机的吞吐量可以很容易超过最大似然接收机。     

Achievable rate of MIMO systems with multi-user diversity and delayed feedback

The effects are investigated of delayed feedback on the system achievable rate (AR) of a multi-user diversity multiple-input multiple-output (MIMO) system over uncorrelated Rayleigh fading channels in a general framework allowing for arbitrary numbers of transmit/ receive antennas and various spatial combining schemes. Exact AR expressions are derived for different MIMO schemes, including the selective combining, maximum ratio combining and space-time block codes. Numerical results are presented to examine the validity of the theory.     

Timing estimation in multiple-antenna systems over Rayleigh flat-fading channels

The use of multiple transmit and receive antennas can offer substantial performance improvement to a wireless communication system by providing spatial diversity and supporting high data rate services. Many of the current space-time coding schemes proposed for multiple-antenna systems assume perfect timing information to achieve the expected performance gain. The lack of timing synchronization between the transmit and receive signals could degrade the system performance. In this paper, we investigate the problem of timing estimation in multiple-antenna systems with the aid of training signals. A slow, independent and identically distributed Rayleigh flat-fading channel model is considered. We derive two maximum likehood timing estimators based on two different approaches, namely, treating the channel deterministic and random and present the corresponding Crame/spl acute/r-Rao bounds (CRBs). Then, the optimal designs of training signals based on some figures of merit associated with the CRBs are discussed.