Performance of Transmit and Receive Antenna Selection in the Presence of Channel Estimation Errors

This letter considers the effect of channel estimation errors on the performance of space-time coded (STC) systems with transmit and receive antenna selection over quasi-static flat fading channels. By performing pairwise error probability analysis and presenting numerical examples, we show that the diversity order achieved with perfect channel state information (CSI) is still achievable with imperfect CSI used both at the antenna selection and the space-time decoding processes. We note that our results apply to general STC systems with both transmit and/or receive antenna selection based on largest received powers which can be estimated by any channel estimator.     

Reliable adaptive modulation aided by observations of another fading channel

Adaptive transmission techniques, such as adaptive modulation and coding, adaptive power control, adaptive transmitter antenna diversity, etc., generally require precise channel estimation and feedback of channel state information (CSI). For fast vehicle speeds, reliable adaptive transmission also requires long-range prediction of future CSI, since the channel conditions are rapidly time variant. In this paper, we propose using past channel observations of one carrier to predict future CSI and perform adaptive modulation without feedback for another correlated carrier. We derive the minimum mean-square error (MMSE) long-range channel prediction that uses the time- and frequency-domain correlation function of the Rayleigh fading channel. An adaptive MMSE prediction method is also proposed. A statistical model of the prediction error that depends on the frequency and time correlation is developed and is used in the design of reliable adaptive modulation methods. We use a standard stationary fading channel model (Jakes model) and a novel physical channel model to test our algorithm. Significant gains relative to nonadaptive techniques are demonstrated for sufficiently correlated channels and realistic prediction range.     

Antenna selection for unitary space-time modulation

This correspondence studies receive antenna selection (AS) for multiple-antenna systems that employ unitary space-time (ST) signals, where the channel state information (CSI) is known neither at the transmitter nor at the receiver. Without CSI at the receiver, we perform AS only at the receiver and the selection is based on a maximum-norm criterion, i.e., a subset of receive antennas that have the largest received signal power is chosen. Using a Chernoff bound approach, we present theoretical performance analysis based on the pairwise error probability (PEP) and quantify the asymptotic performance at high signal-to-noise ratio (SNR) by giving the diversity and coding gain expressions. We prove that with no CSI at the receiver, the diversity gain with AS is preserved for unitary ST codes with full spatial diversity, the same as the case with known CSI. As a concrete example, for differential unitary ST modulation with M=2 transmit antennas and N=2 receive antennas, we have devised new excellent-performing parametric codes based on the derived PEP bound. The new codes, which are specifically designed for differential AS systems, outperform known differential codes when AS is employed. Corroborating simulations validate our analysis and code design.     

Capacity of Generalized UTRA FDD Closed-Loop Transmit Diversity Modes

Transmit diversity techniques have received a lot of attention recently, and open-loop and closed-loop downlink transmit diversity modes for two transmit antennae have been included into universal terrestrial radio access (UTRA) frequency division duplex (FDD) specification. Closed-loop modes provide larger system capacity than open-loop modes, but they need additional side information of the downlink channel in the transmitter. In FDD systems this requires a separate feedback channel. Quantization of channel state information (CSI) in closed-loop transmit diversity schemes decreases the performance when compared to a closed-loop system where the transmitter has access to complete CSI. In this paper, we analyze the effect of quantization of CSI and deduce approximate capacity formulae for closed-loop transmit diversity schemes that are generalizations of the closed-loop schemes included in UTRA FDD specification. Moreover, we calculate approximation error and show by simulations that our approximation is tight for flat Rayleigh fading environments with and without fast transmit power control.     

A New Union Bound on the Error Probability of Binary Coded OFDM Systems in Wireless Environments

Orthogonal Frequency Division Multiplexing (OFDM) systems are commonly used to mitigate frequency-selective multipath fading and provide high-speed data transmission. In this paper, we derive new union bounds on the error probability of a coded OFDM system in wireless environments. In particular, we consider convolutionally coded OFDM systems employing single and multiple transmit antennas over correlated block fading (CBF) channels with perfect channel state information (CSI). Results show that the new union bound is tight to simulation results. In addition, the bound accurately captures the effect of the correlation between sub-carriers channels. It is shown that as the channel becomes more frequency-selective, the performance get better due to the increased frequency diversity. Moreover, the bound also captures the effect of multi-antenna as space diversity. The proposed bounds can be applied for coded OFDM systems employing different coding schemes over different channel models.     

OFDM Carrier Frequency Offset Estimation Methods With Improved Performance

Orthogonal frequency division multiplexing (OFDM) systems are highly sensitive to carrier frequency offset and symbol timing error. This paper deals with estimation method of integer frequency offset (IFO) without the aid of pilot symbols. The proposed IFO estimator exploits two consecutive identical OFDM data symbols with only change of phase. In order to improve the accuracy of the IFO estimator, receive diversity is adopted. To demonstrate the efficiency of the proposed IFO estimators, comparisons are made with other existing estimators in terms of error performance, estimation range, and complexity.     

A Technique for Frequency Synchronization in Multi-Band OFDM in Realistic UWB Channel

This paper presents a highly accurate frequency offset estimation algorithm for multi-band orthogonal frequency division multiplexing (MB-OFDM) systems effective for realistic ultra-wideband (UWB) environment. The proposed algorithm derives its estimates based on phase differences in the received subcarrier signals of several successive OFDM symbols in the preamble. We consider different carrier frequency offsets and different channel responses in different bands to keep the analysis and simulation compatible for practical multi-band UWB scenario. Performance of the proposed algorithm is studied by means of bit error rate (BER) performance of MB-OFDM system. In order to compare the variance of the synchronizer to that of the theoretical optimum, we derive the Cramer–Rao lower bound (CRLB) of the estimation error variance and compare it with the simulated error variance both in additive white Gaussian noise and UWB channel model (CM) environments, CM1–CM4. Next, we modify the estimation algorithm by proposing a multi-band averaging frequency offset synchronization (MBAFS) scheme. We establish superior BER performance with MBAFS compared to our first scheme. We calculate modified CRLB for MBAFS and compare it with simulation results for CM1–CM4. Both analysis and simulation show that MBAFS algorithm can estimate the carrier frequency offset effectively and precisely in UWB fading channels for MB-OFDM applications. We also analyze the computational complexity of both the proposed algorithms in order to verify their feasibility of implementation in practical UWB receiver design.     

Robust Uniform Channel Decomposition and Power Allocation for MIMO Systems with Imperfect CSI

In point to point MIMO systems, uniform channel decomposition (UCD) has been proven to be optimal in bit error rate (BER) performance and strictly capacity lossless when perfect channel state information (CSI) are assumed to be available at both the transmitter and the receiver side. However, in practice, CSI can be obtained at the transmitter if there is reciprocity between the forward and reverse channels in time division duplex (TDD) systems or can be conveyed from the receiver to the transmitter via a feedback channel. In any case, channel estimation error is inevitable. In this paper, a novel robust UCD scheme and corresponding optimal robust power allocation are proposed, which are capable of improving the BER performance in the context of imperfect CSI compared with the conventional UCD scheme and the robust precoding scheme proposed by Amir D. Dabbagh and David J. Love. Simulation results show that the MIMO channel capacity of the proposed robust UCD scheme is higher than that of the conventional UCD scheme. By deriving and analyzing the MIMO channel capacity lower bound of the robust UCD scheme, we prove that our proposed robust UCD scheme is capacity lossless in a channel estimation error existing MIMO system.     

Trained Space-Time Block Decoding for Flat Fading Channels with Frequency Offsets

Space-time block coding (STBC) is a recent appealing solution to the problem of exploiting transmit diversity in multi-antenna systems for communications over flat fading channels. In a standard STBC scheme the receiver requires Channel State Information (CSI), which can be acquired via training at the expense of a reduced information rate. Alternatively, the requirement of CSI can be avoided altogether by using differential encoding. The existing trained or differential schemes for STBC assume that the channel is time-invariant during the transmission of at least two data blocks. However, wireless channels may often be time varying owing to frequency offsets induced by either Doppler shifts or carrier frequency mismatches. In this paper we present a simple trained STBC scheme for fading channels with frequency offsets. This revised version was published online in July 2006 with corrections to the Cover Date.     

Antenna selection for multiple-antenna transmission systems: performance analysis and code construction

This correspondence studies antenna selection for wireless communications systems that employ multiple transmit and receive antennas. We assume that (1) the channel is characterized by quasi-static Rayleigh flat fading, and the subchannels fade independently, (2) the channel state information (CSI) is exactly known at the receiver, (3) the selection is available only at the receiver, and it is based on the instantaneous signal-to-noise ratio (SNR) at each receive antenna, and (4) space-time codes are used at the transmitter. We analyze the performance of such systems by deriving explicit upper bounds on the pairwise error probability (PEP). This performance analysis shows that (1) by selecting the set of antennas that observe the largest instantaneous SNR, one can achieve the same diversity gain as the one obtained by using all the receive antennas, provided that the underlying space-time code has full spatial diversity, and (2) in the case of rank-deficient space-time codes, the diversity gain may be dramatically reduced when antenna selection is used. However, we emphasize that in both cases the coding gain is reduced with antenna selection compared to the full complexity system. Based on the upper bounds derived, we describe code design principles suitable for antenna selection. Specifically, for systems with two transmit antennas, we design space-time codes that perform better than the known ones when antenna selection is employed. Finally, we present numerical examples and simulation results that validate our analysis and code design principles.     

具有不完全信道状态信息MIMO系统的优化设计

 本文研究了不完全信道状态信息(CSI)对多输入多输出(MIMO)系统容量的影响.基于平均功率和平均误码率的约束条件,我们提出了一种利用不完全CSI进行功率自适应调制的优化设计方案.根据Wishart矩阵的统计分布,我们导出了该系统容量的封闭表达式.研究结果表明:在具有不完全CSI的MIMO系统中,利用不完全CSI进行设计可以显著地提高系统的容量.     

Robust Non-linear Precoder for Multiuser MISO Systems Based on Delay and Channel Quantization

In multiuser multiple-input single-output (MISO) systems, non-linear precoder is able to achieve the theoretical sum capacity of downlink channel with perfect channel state information (CSI). However, the perfect CSI is not available at the transmitter in practical system, especially in frequency division duplex (FDD) system where the imperfect CSI is the delayed, quantized channel direction information relayed back from the receiver through a dedicated feedback channel. So the performance of conventional non-linear precoder degrades significantly. In this paper, a robust non-linear Tomlinson–Harashima precoding (THP) based on sum mean squared error (SMSE) minimization for the downlink of multiuser MISO FDD systems is proposed. The proposed precoder is robust to the channel uncertainties arising from channel delay and quantization error. Furthermore, an improved non-linear THP with channel magnitude information (CMI) consideration is introduced to compensate the instantaneous CMI shortage at the transmitter. Additionally, the computational complexity of both proposed precoders can be reduced remarkably by Cholesky factorization with symmetric permutation. Simulation results demonstrate the improvement in bit error ratio performance and illustrate the SMSE performance of the proposed algorithms compared with conventional THP with perfect CSI in the literature.     

Systematic Codebook Designs for Quantized Beamforming in Correlated MIMO Channels

The full diversity gain provided by a multi-antenna channel can be achieved by transmit beamforming and receive combining. This requires the knowledge of channel state information (CSI) at the transmitter which is difficult to obtain in practice. Quantized beamforming where fixed codebooks known at both the transmitter and the receiver are used to quantize the CSI has been proposed to solve this problem. Most recent works focus attention on limited feedback codebook design for the uncorrelated Rayleigh fading channel. Such designs are sub-optimal when used in correlated channels. In this paper, we propose systematic codebook design for correlated channels when channel statistical information is known at the transmitter. This design is motivated by studying the performance of pure statistical beamforming in correlated channels and is implemented by maps that can rotate and scale spherical caps on the Grassmannian manifold. Based on this study, we show that even statistical beamforming is near-optimal if the transmitter covariance matrix is ill-conditioned and receiver covariance matrix is well-conditioned. This leads to a partitioning of the transmit and receive covariance spaces based on their conditioning with variable feedback requirements to achieve an operational performance level in the different partitions. When channel statistics are difficult to obtain at the transmitter, we propose a universal codebook design (also implemented by the rotation-scaling maps) that is robust to channel statistics. Numerical studies show that even few bits of feedback, when applied with our designs, lead to near perfect CSI performance in a variety of correlated channel conditions.     

Precoder Design for BICM-MIMO Systems Under Channel Estimation Error

If properly designed, the use of a linear precoder can achieve the maximum coding gain and diversity order in bit-interleaved coded modulation with multiple-input multiple-output systems. However, such maximum coding gain and diversity order are compromised under the practical scenario of having imperfect channel state information (CSI) at the receiver. To alleviate the impact of imperfect CSI on the coding gain and diversity order, joint linear precoder and training pattern are designed in this paper. The design is carried out by considering both the pairwise error probability and the mean square error of the channel estimator. The effectiveness of the proposed design is illustrated by comparing its performance with the performance obtained when only the training pattern is designed for an precoder optimized under the perfect CSI. In particular, simulation results show that a $1.5$ 1.5 dB gain is achieved by the proposed design.     

基于载波相位的室内AoA/ToF联合定位

当前室内定位的主流方法是基于信道状态信息(Channel State Information,CSI)的AoA/ToF(Angle of Arrival/Time of Flight)联合定位,由于天线数量和带宽的限制,导致其特征参数存在误差.为此,结合CSI中细粒度和多样化的载波相位信息,提出了一种基于载波相位的室内...     

基于复杂系统自组织MIMO无线传输分集和编码技术研究现状及其技术路线

空间分集与编码调制技术相结合的空时编码技术,可以获得分集和编码增益,具有优异的抗衰落性能。传统空时编码和多输入多输出(MIMO)技术是通过多天线来实现空间分集的,但是由于移动台的尺寸和载频的限制,使多天线技术很难实现。基于复杂系统自组织MIMO无线传输分集和编码技术成为解决这一问题的可选方案,并且无需通过信道反馈信息,动态分配资源,提高了端到端的通信服务质量(QoS)和信道容量。     

Impact of diversity reception on fading channels with codedmodulation. III. Co-channel interference

For pt.II see ibid., vol.45, no.6, p.55-67, 1997. In previous work, we have studied the impact of diversity on coded digital communication systems operating over fading channels. In particular, we have shown that diversity may be thought of as a way of making the channel more similar to a Gaussian one. The present paper extends this analysis to fading channels affected by co-channel interference (CCI). Three receiver models are examined, namely, with coherent detection and perfect channel-state information (CSI), with differential; and with pilot-tone detection. We study the effect of diversity on the irreducible error floor caused by CCI and fading, and the asymptotic behavior of the channel as the diversity order increases. Our results show that, when perfect CSI is available, diversity is able to turn asymptotically the channel into a CCI-free additive white Gaussian noise (AWGN) channel with the same signal-to-noise ratio (SNR). On the other hand, differential and pilot-tone detection do not remove interference in the limit. Nevertheless, also with these detection schemes, diversity achieves significant gains when the SNR is large enough. Calculation of the channel cutoff rate provides guidelines for the design of coded systems with CCI in fading environments. A wide range of examples, validated by computer simulation, illustrates our conclusions     

一种基于深度学习的FDD大规模MIMO系统CSI反馈方法

针对频分双工（Frequency Division Duplexing,FDD）大规模多入多出（Multiple-Input Multiple-Output,MIMO）系统中现有信道状态信息（Channel State Information,CSI）反馈方法复杂度高、反馈精度低的问题,本文提出一种基于深度学习的CSI压缩反馈方法.该方法首先采用卷积神经网络（Convolutional Neural Network,CNN）提取信道特征矢量,然后利用最大池化（Maxpooling）网络压缩CSI,最后考虑到大规模MIMO信道存在空间相关性的特点,分别对单用户和多用户场景使用双向长短期记忆（Bidirectional Long Short-Term Memory,Bi-LSTM）网络和双向卷积长短期记忆（Bidirectional Convolutional Long Short-Term Memory,Bi-ConvLSTM）网络对CSI进行重构.本文利用大规模MIMO信道数据对所提的深度学习网络进行离线训练,该网络学习到的信道信息能充分表征信道的状态.仿真结果表明,与已有的典型CSI反馈方法相比,本文所提方法反馈精度更高,运行时间更短,系统性能提升明显.     

Optimum Receiver for a Realistic Transmit–Receive Diversity System in Correlated Fading

A transmit–receive diversity system in correlated Rayleigh fading in which the receiver estimates the channel through pilot symbols, and feeds this information back to the transmitter through a feedback path, is considered. The imperfect channel state information (CSI) is used by the transmitter to obtain the transmit weight vector for data transmission. The optimum receiver in the maximum-likelihood (ML) sense obtained from the conditional distribution of the received signal vector, conditioned on the imperfect CSI and the transmit weight vector, is derived for the system. For the case of $M$-ary phase-shift keying (MPSK), an analytical expression for the conditional symbol error probability (SEP), conditioned on the channel estimate and the transmit weight vector, is obtained, with the transmit weight vector chosen to minimize this conditional SEP. For the receive-only and transmit-only correlation scenarios with ill-conditioned eigenvalues of the receive and transmit covariance matrices (that is, some of the eigenvalues are very small), we derive expressions for the diversity gain. Numerical results are presented to compare the performance of our receiver with that of a conventional receiver in case of exponentially correlated fading. These results show that the optimum receiver typically has about a 0.5-dB gain over a conventional receiver when the correlation coefficient exceeds 0.5 and the number of receive antennas is much larger than the number of transmit antennas.      

Effects of Carrier Frequency Offset and Channel Estimation Errors on the Performance of MIMO-OFDM Systems in Spatially Correlated Channels

As an effective technique for combating multipath fading and for high-bit-rate transmission over wireless channels, orthogonal frequency division multiplexing (OFDM) is extensively used in high-rate wireless communication systems, such as, the wireless local area network (WLAN) and the digital television terrestrial broadcasting (DTTB) systems, to support high performance bandwidth-efficient multimedia services. Multiple antennas and transmit or receive diversity, multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM), can be used to improve error performance and capacity of wireless systems. In this paper, we consider the effects of carrier frequency offset and channel estimation errors on the performance of MIMO-OFDM systems in spatially correlated channels. Theoretical calculations and computer simulations are done to analyze the performance degradation of MIMO-OFDM systems in spatially correlated channels due to carrier frequency offset and channel estimation errors, and the theoretical and simulated results match well.