Nonselective Fading Channel Estimation with Nonuniformly Spaced Pilot Symbols

Recently, there has been great demand for multimedia and data communications in mobile communication systems. In order to enhance voice quality and increase packet data throughput rate for the existing mobile systems and the next generation mobile systems, a number of new standards are being developed. 8-PSK/QPSK modulation has been adopted by most of these standards as one of the modulation schemes, and nonuniformly spaced pilot symbols are employed in slot structures to have successful demodulation. In this paper, an accurate and computationally efficient method is presented for estimating nondispersive channel fading with non-uniformly spaced pilot symbols. By employing a least-squares method with time-variant complex-valued coefficient polynomials, it is proven that nonselective channel fading of each slot can be estimated by the product of a constant matrix and the fading at pilot symbol locations of the slot. The constant matrix is further optimized by least-squares off-line training method provided by this paper. Using the estimated fading process, the fading on the data symbols can be removed by using the estimated amplitude and phase of the fading as the reference, greatly improving the BER. Closed form results for the BER of coherent 8-PSK are included in this paper as well. Simulation results indicate that our method provides BER performance very close to the analytic BER result.     

MIMO-OFDM快衰落信道的稀疏自适应感知估计

在多输入多输出（MIMO）-正交频分复用（OFDM） 系统中,怎样在较高频谱利用率的情况下对快时变信道进行较为准确的估计是一个具有挑战性的课题。该文在利用压缩感知理论可提高系统频谱利用率的基础上,提出了一种适合于快时变环境下MIMO-OFDM 系统的稀疏自适应信道估计方法。该方法不再受到奈奎斯特采样频率条件约束,避免了传统导频辅助信道估计方法频谱利用率低的缺点。该文方法通过构建多天线群时频结构特征稀疏基,利用多天线间和群时变OFDM符号内信道冲激响应具有更强稀疏性的特点,对MIMO-OFDM快衰落信道进行稀疏变换。由于实际MIMO-OFDM快衰落信道往往处于频率选择性、时变性和多种干扰并存的复杂环境,受到干扰的信道参数对系统而言是未知,采用该方法克服了现有基于压缩感知理论的信道估计方法需要预先知道信道冲激响应稀疏度才能重构信道参数的不足,在信道稀疏度未知道的情况下,运用稀疏自适应的方法来对不同时频结构特征的信道参数进行估计。仿真结果表明所提估计方法具有对快时变信道参数估计的鲁棒性和较高频谱利用率,且均方误差小。      

基于多中继导频频分复用的协同通信系统信道估计算法

本文针对频率选择性衰落环境下结合正交频分复用技术的放大转发多中继协同通信系统,提出了基于导频频分复用的频域信道估计算法,包括最小二乘（LS）估计算法和线性最小均方误差（LMMSE）估计算法。理论分析和仿真结果表明,该算法不仅成功分辨了多中继协同通信系统的所有频域信道衰落系数,避免了各中继节点转发的导频符号在目的节点上的混叠干扰,而且减少了频域信道估计所需的导频符号数量和时隙周期长度,提高了协同通信系统的传输效率和频谱利用率,同时显著提高了信道估计的精度,降低了算法的复杂度,具有较高的实用价值。      

基于滤波方法的OFDM信道估计研究

维纳滤波和卡尔曼滤波都是基于最小均方误差准则的滤波方法,本文主要研究这两种滤波方法在OFDM信道估计中的应用。为了跟踪频率选择性信道的变化,采用在OFDM系统中易于实现的梳状导频进行研究。传统的MMSE在统计意义上是最好的线性估计器,但是需要对矩阵求逆,是一种计算量较大,算法较复杂的方法。LMMSE是频域维纳滤波方法,其减小了MMSE的复杂度,但只适用于慢衰落信道,针对时变信道,本文提出卡尔曼滤波的信道估计方法,仿真结果表明,卡尔曼滤波的信道估计方法在时变信道中具有良好的性能。     

A robust channel estimator for DS-CDMA systems under multipath fading channels

This paper addresses the problem of channel estimation for direct-sequence code-division multiple-access (DS-CDMA) systems with time-varying multipath fading channels. The multipath fading channels are modeled as autoregressive (AR) models. A method is first proposed to convert the time-varying regression model due to the time-varying nature of users' information symbols into a time-invariant one. Then, a polynomial approach is proposed to obtain the minimum mean square error (MMSE) estimator. The uncertainty of the channel model and decision errors of the DS-CDMA detector are taken into consideration in the design of the MMSE estimator. Compared with the Kalman estimator, the computational complexity of the proposed algorithm is much lower. The simulation results show that the proposed estimator provides a comparable estimation performance with the Kalman estimator and is robust for fast-fading channels.     

WCDMA系统中结合导频与信息码的信道估计方法

研究了快衰落环境中第三代移动通信空中接口WCDMA(FDD),基于时分复用的导频信号辅助衰落信道下的信道估计。提出了同时根据导频信号及数据信号估计信道参数的信道估计方法,该方法将信道估计分为根据导频信号和数据信号两部分进行并由其加权合并完成。计算了最小均方误差下的合并系数。仿真结果表明该方法能快速跟踪信道的衰落,有效地估计出各时隙中数据段的信道参数。利用该算法,尤其在高速运动情况下,接收机的性能可得到显著的改善。     

Turbo Equalization with Prediction and Iterative Estimation of Time-Varying Frequency-Selective Channels

Turbo equalization that cooperates with channel prediction and iterative channel estimation is investigated for mobile wireless communications. Frames of information bits are encoded, interleaved, and mapped to symbols for transmission over time-varying frequency-selective fading channels. At the receiver, the Turbo equalizer consists of a maximum a posteriori probability equalizer/demapper and a soft-input soft-output maximum a posteriori probability decoder. With initial channel estimates and sparse pilot insertion across a number of frames, the receiver predicts the channel of the current frame. The effect of error propagation of channel prediction is mitigated by the de-interleaver that is embedded in the Turbo equalizer. The predicted and interpolated channel is refined through a channel estimator that uses the soft estimates of data symbols at each Turbo iteration. Due to the bandlimiting feature of channel variation, the channel estimation error can be smoothed by low-pass filters that follow the channel estimator. Simulation results show that incorporating Turbo equalization with channel prediction and iterative channel estimation can combat time- and frequency-selective fading and improve reception performance.     

Maximum a posteriori fast fading channel estimation based exclusively on pilot symbols

An innovations-based block-by-block maximum a posteriori fast fading channel estimation algorithm, based exclusively on the received samples of pilot symbols, is proposed. This algorithm enables the theoretical determination of the optimum positions of pilot symbols using the raw bit error rate criterion. Moreover, it can be reformulated simply using appropriate weighting of the projections of received pilot symbols samples on an extended orthonormal base. This base can be determined simply as a function of the statistical properties of the channel.     

Pilot symbol assisted modulation in frequency selective fadingwireless channels

Frequency-selective fading channels are typically modeled either as a combination of Doppler components or as lowpass stochastic processes. In both cases, accurate parameter and/or Doppler frequency estimation is impeded by the fact that the Doppler frequencies are typically very low (compared with the data rate) and closely spaced. This problem is mitigated in pilot symbol assisted modulation (PSAM) systems that employ distributed training. Those systems can provide information about a time-undersampled version of the channel that may be easier to identify. We address the problem of estimating the fading channel's correlation matrices from the received data by exploiting the distributed training symbols. Multichannel autoregressive (AR) models are estimated to fit the channel's variations, and the Doppler frequencies are identified through the peaks of the AR spectrum. The performance of the proposed methods is studied through analytical and experimental results. Finally, Kalman filtering ideas are employed to track the time-varying channel taps based on the estimated AR model     

Effects of imperfect channel sensing and estimation on the performance of cognitive radio systems

In realistic scenarios of cognitive radio (CR) systems, imperfect channel sensing may occur due to false alarms and miss detections. Channel estimation between the secondary user transmitter and another secondary user receiver is another challenge in CR systems, especially for frequency‐selective fading channels. In this context, this paper presents a study of the effects of imperfect channel sensing and channel estimation on the performance of CR systems. In particular, different methods of channel estimation are analyzed under channel sensing imperfections. Initially, a CR system model with channel sensing errors is described. Then, the expectation maximization (EM) algorithm is implemented in order to learn the channel fading coefficients. By exploiting the pilot symbols and the detected symbols at the secondary user receiver, we can estimate the channel coefficients. We further compare the proposed EM estimation algorithm with different estimation algorithms such as the least squares (LS) and linear minimum mean square error (LMMSE). The expressions of channel estimates and mean squared errors (MSE) are determined, and their dependencies on channel sensing uncertainty are investigated. Finally, to reduce the complexity of EM algorithm, a sub‐optimal algorithm is also proposed. The obtained results show that the proposed sub‐optimal algorithm provides a comparable bit error rate (BER) performance with that of the optimal one yet with less computational complexity.     

Pilot symbol-assisted detection of CPM schemes operating in fastfading channels

We present a coherent detection technique for continuous phase modulation (CPM) operating in the Rayleigh flat fading channel. The technique is based on the idea of inserting periodically data dependent pilot symbols that force the CPM signal to pass through known phase states. This transmission format enables the receiver to extract from the received signal the channel fading gains at regularly spaced instants. When coupled with proper channel estimation filters, very accurate channel state information (CSI) can be estimated at the receiver for fading compensation. Moreover, the accuracy of the CSI can be further refined by adopting a multiple-pass decoding approach. The paper discusses (a) the pilot symbol encoding technique required to force a M-level CPM scheme with a modulation index of p/M, p is an integer, to return periodically to a set of known phase states, (b) the optimal channel estimation filters, (c) a trellis-based precoding technique that can reduce the bit error rate in M-level CPM systems by close to 50%, and (d) a multiple-pass channel estimator/demodulator. Analytical and simulation results are presented for minimum shift keying (MSK), Gaussian MSK, and four-level continuous phase frequency shift keying with a modulation index of 1/4. It is observed that our pilot symbol-assisted CPM schemes exhibit no irreducible error floor even at a channel fade rate of three percent the symbol rate. The implicit phase coding in CPM and the accurate CSI provided by the pilot symbols lead to a diversity effect in the bit error rate curves of these modulation schemes     

Artificial Neural Network Channel Estimation Based on Levenberg-Marquardt for OFDM Systems

The many advantages responsible for the widespread application of orthogonal frequency division multiplexing (OFDM) systems are limited by the multipath fading. In OFDM systems, channel estimation is carried out by transmitting pilot symbols generally. In this paper, we propose an artificial neural network (ANN) channel estimation technique based on levenberg-marquardt training algorithm as an alternative to pilot based channel estimation technique for OFDM systems over Rayleigh fading channels. In proposed technique, there are no pilot symbols which added to OFDM. Therefore, this technique is more bandwidth efficient compared to pilot-based channel estimation techniques. Also, this technique is making full use of the learning property of neural network. By using this feature, there is no need of any matrix computation and the proposed technique is less complex than the pilot based techniques. Simulation results show that ANN based channel estimator gives better results compared to the pilot based channel estimator for OFDM systems over Rayleigh fading channel.     

基于总体最小二乘准则的OFDM系统时变信道估计

信道估计的准确程度直接影响正交频分复用系统的性能。为了提高时变信道估计算法的精度,基于总体最小二乘准则( TLS)提出了一种时变信道的估计方法。该方法用线性模型对时变信道进行建模,不仅考虑了信道噪声,同时也兼顾了模型误差。该方法能较好地跟踪信道的变化,显著消除模型误差。仿真结果表明所提算法的均方误差介于最小二乘算法与最小均方误差算法之间,在不同归一化多普勒频移下,该算法具有较好的稳健性。     

Optimal training design for MIMO OFDM systems in mobile wireless channels

This paper describes a least squares (LS) channel estimation scheme for multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems based on pilot tones. We first compute the mean square error (MSE) of the LS channel estimate. We then derive optimal pilot sequences and optimal placement of the pilot tones with respect to this MSE. It is shown that the optimal pilot sequences are equipowered, equispaced, and phase shift orthogonal. To reduce the training overhead, an LS channel estimation scheme over multiple OFDM symbols is also discussed. Moreover, to enhance channel estimation, a recursive LS (RLS) algorithm is proposed, for which we derive the optimal forgetting or tracking factor. This factor is found to be a function of both the noise variance and the channel Doppler spread. Through simulations, it is shown that the optimal pilot sequences derived in this paper outperform both the orthogonal and random pilot sequences. It is also shown that a considerable gain in signal-to-noise ratio (SNR) can be obtained by using the RLS algorithm, especially in slowly time-varying channels.     

Detection for a statistically known, time-varying dispersivechannel

Detection for the statistically known channel (SKC) is aimed at obtaining good performance in situations where our statistical knowledge of a time-varying channel is good, and where other equalization/detection schemes are either too complex to implement, or their performance is limited due to the rapidity of channel fading, or where we are simply unable to perform channel estimation. By using a statistical characterization of the channel, we develop a new detector that performs maximum-likelihood sequence estimation (MLSE) (given the channel model) on blocks of N symbols. Both symbol-spaced and fractionally spaced samples are used, to obtain two different detectors, that are generalizations of those devised for optimal block schemes on nondispersive channels. The detector that uses fractionally spaced samples is shown to outperform the detector that uses symbol-spaced samples. The performance of both appears to approach that of the corresponding known channel (KC) detector as the block length increases. We also numerically evaluate the SKC detector performance under conditions where the channel parameters (statistics) are incorrectly estimated, and show that the fractionally spaced detector is fairly robust to modeling errors. Finally, we devise a sliding block algorithm, for use when transmitting more than N symbols     

Channel estimation with ISFLA based pilot pattern optimization for MIMO OFDM system

In multiple input multiple output orthogonal frequency division multiplexing (MIMO-OFDM) systems, the channel state information should be known by the receiver for obtaining transmitted data. Channel estimation algorithms are used to examine the multipath effects of frequency selective Rayleigh fading channels. In this paper, Compressed Sensing (CS) based channel estimation technique is considered for reconstructing the signal with improved spectral efficiency. It requires transmitting the known pilot data to the receiver for estimating channel information. The optimum pilot patterns are selected through reducing the mutual coherence of measurement matrix. In order to maximize the accuracy of sparse channel estimation and to reduce the computational complexity, an optimization algorithm Improved Shuffled Frog Leaping (ISFL) is proposed. When compared with the traditional estimation methods like least squares (LS), and minimal mean square error (MMSE), 4.7% of spectral efficiency is increased with ISFLA based channel estimation. Implementation results show that, by using the proposed algorithm, the bit error rate (BER) and Mean Square Error (MER) performance of the system is increased with 1.5 dB and 2 dB respectively.     

高速场景下基于叠加导频的迭代EKF信道估计方法

针对正交频分复用（Orthogonal Frequency Division Multiplexing,OFDM）系统在高速移动场景下时/频域选择性衰落（双选衰落）和非平稳特性给信道估计带来的技术挑战,本文采用导频与数据叠加的帧结构,提出一种基于基扩展模型（Basis Expansion Model,BEM）的迭代扩展卡尔曼滤波（iterative Extend-Kalman Filter,iEKF）信道估计方法.基于BEM信道模型且采用EKF信道估计方法可以联合估计出信道冲激响应（Channel Impulse Response,CIR）与时变的时域自相关系数,有效消除子载波间干扰（Inter Carrier Interference,ICI）.同时,为了进一步消除叠加导频位置处的数据符号干扰,我们提出将叠加位置处的数据和导频先解耦、后重构再进行迭代EKF的信道估计方法.仿真分析表明,相较传统叠加导频的信道估计方法和导频符号辅助调制（Pilot Symbol Assisted Modulation,PSAM）估计方法,本文提出的信道估计方法在高速场景特别是低信噪比的条件下,具有更高的估计精度,更强的鲁棒性及更大的吞吐量.     

Channel estimation for OFDM transmission in multipath fadingchannels based on parametric channel modeling

We present an improved channel estimation algorithm for orthogonal frequency-division multiplexing mobile communication systems using pilot subcarriers. This algorithm is based on a parametric channel model where the channel frequency response is estimated using an L-path channel model. In the algorithm, we employ the ESPRIT (estimation of signal parameters by rotational invariance techniques) method to do the initial multipath time delays acquisition and propose an interpath interference cancellation delay locked loop to track the channel multipath time delays. With the multipath time delays information, a minimum mean square error estimator is derived to estimate the channel frequency response. It is demonstrated that the use of the parametric channel model can effectively reduce the signal subspace dimension of the channel correlation matrix for the sparse multipath fading channels and, consequently, improve the channel estimation performance     

Maximuma posteriori fast fading channel estimation for alamouti’s space-time transmit diversity

This paper considers the Alamouti’s two-branch transmit diversity scheme. This scheme supports a maximum likelihood detection based on linear processing at the receiver. When no knowledge of the channel is available — at the transmitter and the receiver- the above scheme requires in general the estimation of the two discrete propagation channels seen from the two transmit antennas. Our objective is to evaluate the Alamouti’s technique of diversity with a realistic estimation algorithm considering a very fast time-varying channel. For a robust channel estimation, we propose an EM-based maximuma posteriori semi-blind algorithm. This algorithm requires a convenient representation of the time-varying fading channel using a discrete version of the Karhunen-Loève expansion theorem. The iterative receiver optimally uses pilot as well as unknown data symbols for improving channel estimation quality. The validity of the proposed algorithm is highlighted by simulation results. Moreover, a complexity evaluation of this algorithm and a comparison is provided for different scenarii.     

Soft-output demodulator in space-time-coded continuous phase modulation

Space-time coding has shown great promise for digital transmission in wireless communication links, especially when the channel response is known at the receiver. Space time coding combined with continuous phase modulation (CPM) can offer better tradeoffs in bandwidth and power efficiency. Because of the memory inherent in CPM, channel estimation is often harder than for linear modulations. We present an adaptive soft algorithm that performs joint channel estimation and data detection for space-time CPM systems. Properly designed pilot symbols are inserted at the very beginning to give good initial estimates of the channels. This soft receiver is further applied to the interleaved space-time CPM system to yield better performance with moderate complexity through iterative processing. Simulation results show that the receiver can often achieve near-coherent performance in quasistatic fading as well as in time-varying fading.