Robust and Improved Channel Estimation Algorithm for MIMO-OFDM Systems

Multiple-input multiple-output (MIMO) system using orthogonal frequency division multiplexing (OFDM) technique has become a promising method for reliable high data-rate wireless transmission system in which the channel is dispersive in both time and frequency domains. Due to multiple cochannel interferences in a MIMO system, the accuracy of channel estimation is a vital factor for proper receiver design in order to realize the full potential performance of the MIMO-OFDM system. A robust and improved channel estimation algorithm is proposed in this paper for MIMO-OFDM systems based on the least squares (LS) algorithm. The proposed algorithm, called improved LS (ILS), employs the noise correlation in order to reduce the variance of the LS estimation error by estimating and suppressing the noise in signal subspace. The performance of the ILS channel estimation algorithm is robust to the number of antennas in transmit and receive sides. The new algorithm attains a significant improvement in performance in comparison with that of the regular LS estimator. Also, with respect to mean square error criterion and without using channel statistics, the ILS algorithm achieves a performance very close to that of the minimum mean square error (MMSE) estimator in terms of the parameters used in practical MIMO-OFDM systems. A modification of the ILS algorithm, called modified ILS (MILS), is proposed based on using the second order statistical parameters of channel. Analytically, it is shown that the MILS estimator achieves the exact performance of the MMSE estimator. Due to no specific data sequences being required to perform the estimation, in addition to the training mode, the proposed channel estimation algorithms can also be extended and used in the tracking mode with decision-aided method.     

Channel Estimation in OFDM Systems Using a Controlled Superimposition of Training Sequences

This work pertains to the use of superimposed training (ST) for channel estimation in orthogonal frequency division multiplexing (OFDM) based systems. A time domain coherent averaging based channel estimator is derived from the least squares criterion. By exploiting the periodicity of the training sequences in the time domain and inserting zeros instead of data at some of the training sequence subcarrier locations depending on the desired estimation accuracy, a controlled superimposition technique is proposed. This method includes the flexibility to trade off between bandwidth efficiency and performance. The mean squared estimation error (MSEE) performance of such a system is mathematically analyzed and a training sequence selection criterion optimizing the same is proposed. The simulation performance of the scheme is presented in terms of the MSEE and the bit error rate (BER) of the OFDM system. Such a scheme is attractive in high data rate scenarios in closed loop OFDM systems.     

Data Aided Iterative Channel Estimation in OFDM Systems Using a Controlled Superimposition of Training Sequences

This work pertains to the use of superimposed training for channel estimation in orthogonal frequency division multiplexing (OFDM) based systems. An iterative time domain Least Squares based channel estimator is proposed. The estimator is generalized to provide scope for exploiting the coherence time and the coherence bandwidth of the channel. By exploiting the periodicity of the training sequences in the time domain and inserting zeros instead of data at some of the training sequence subcarrier locations depending on the desired estimation accuracy, a controlled superimposition technique is proposed. This method includes the flexibility to trade off between bandwidth efficiency and performance without any change in the structure of the channel estimator. The mean squared estimation error (MSEE) performance of such a system is mathematically analyzed and a training sequence selection criterion optimizing the same is proposed. The simulation performance of the scheme is presented in terms of the MSEE and also its impact on the bit error rate is shown. Such a scheme is attractive in high data rate scenarios in closed loop OFDM systems.     

无线OFDM系统传输信道模型化参数检测

利用导频子载波时频相位相关性统计检测与QAM信号解映射判决误差统计，提出了一种适用于频域导频无线OFDM系统的传输信道模型化参数检测方案，包括信道最大多径时延、最大多普勒频率和信噪比检测；能够有效解决传统的OFDM信道估计算法通常按照最恶劣信道情况上限进行设计，以及基于MMSE准则最优信道估计器中信道先验信息统计运算复杂度高的缺陷；仿真结果表明，在低复杂度条件下可以有效获知当前传输信道模型参数的近似统计信息。     

一种基于LMS滤波的OFDM系统信道估计方法

提出了一种适用于OFDM系统的最小均方(LMS)滤波的信道估计算法,对发送序列中导频位置的信道响应进行LMS滤波,进一步得出所有子载波上的信道响应。仿真结果表明,该方法同基于离散傅里叶变换(DFT)的信道估计算法相比,改善了估计的均方误差(MSE)和误码率(BER)性能。     

Recursive maximum likelihood estimation of time‐varying carrier frequency offset for orthogonal frequency‐division multiplexing systems

A recursive maximum likelihood carrier frequency offset (CFO) estimator is proposed in this work, where redundancy information contained in the cyclic prefix of multiple consecutive orthogonal frequency‐division multiplexing (OFDM) symbols is exploited in an efficient recursive fashion. Because the estimator is based on multiple OFDM symbols, the time‐varying CFO must be considered. We investigate the effect of time‐varying CFO on the performance of the estimator and the trade‐off between fast tracking ability and low estimation variance. We show that, without channel noise, the mean squared error (MSE) of estimation due to CFO estimation variation increases approximately quadratically with n, where n is the number of OFDM symbols used for CFO estimation (estimation window size), whereas the MSE due to channel noise decreases proportionally to 1/n (approximately) if the CFO is constant. A closed‐form expression of the optimal estimation window size (approximately) is derived by minimizing the MSE caused by both time‐varying CFO and channel noise. For wireless systems with time‐varying rate of change for CFO, the proposed estimator can be implemented adaptively. In addition, typical optimal estimation window sizes for WiMAX, DVB‐SH and MediaFLO systems are evaluated as an example. Copyright © 2011 John Wiley & Sons, Ltd.     

Least Square Channel Estimation for Two‐Way Relay MIMO OFDM Systems

This letter considers the channel estimation for two‐way relay MIMO OFDM systems. A least square (LS) channel estimation algorithm under block‐based training is proposed. The mean square error (MSE) of the LS channel estimate is computed, and the optimal training sequences with respect to this MSE are derived. Some numerical examples are presented to evaluate the performance of the proposed channel estimation method.     

Channel Estimation for MIMO-OFDM Systems by Modal Analysis/Filtering

In this paper, we investigate the benefits of exploiting the a priori information about the structure of the multipath channel on the performance of channel estimation for multiple-input multiple-output (MIMO)-orthogonal frequency-division multiplexing (OFDM) systems. We first approach this problem from the point of view of estimation theory by computing a lower bound on the estimation error and studying its properties. Then, based on the insight obtained from the analysis, efficient channel estimators are designed that perform close to the derived limit. The proposed channel estimators compute the long-term features of the multipath channel model through a subspace tracking algorithm by identifying the invariant (over multiple OFDM symbols) space/time modes of the channel (modal analysis). On the other hand, the fast-varying fading amplitudes are tracked by using least-squares techniques that exploit temporal correlation of the fading process (modal filtering). The analytic treatment is complemented by thorough numerical investigation in order to validate the performance of the proposed techniques. MIMO-OFDM with bit-interleaved coded modulation and MIMO-turbo equalization is selected as a benchmark for performance evaluation in terms of bit-error rate.     

信道反馈延迟时MIMO中继系统的线性预编码算法

针对采用放大转发(Amplify and Forward, AF)中继技术的多入多出(Multiple Input Multiple Output, MIMO)系统, 考虑信道估计误差及反馈存在延迟的情况, 提出一种基于最小均方误差(Minimum Mean Squared Error, MMSE)准则的预编码设计方案.假设基站-中继端及中继端-终端的信道均存在估计误差与反馈延迟, 在基站和中继端功率都受限条件下, 以MMSE为准则, 推导得到了基站预编码矩阵、中继转发矩阵和终端解码矩阵的闭式解.数值仿真结果表明, 该方案所提出的预编码算法能有效地改善系统的误比特率与均方误差.     

Performance Analysis of Tikhonov Regularized LS Channel Estimation for MIMO OFDM Systems with Virtual Carriers

In this paper the effect of virtual carriers (VCs) on channel estimation performance is considered for multiple input multiple output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. The link between the number of VCs and the inverse problem in a conventional LS channel estimation is identified. It is observed that a linear increase in VCs contributes to an exponential increase of the system inverse problem as the condition number of the inverse matrix is exponentially increased. A solution is proposed using a low complexity modified LS channel estimation. The performance analysis of the modified LS channel estimation, regarding the effect of VCs, show gains in both the mean square error (MSE) performance of channel estimation as well as bit error rate (BER) system performance compared to conventional LS. The performance is improved irrespective of the increasing number of VCs as the estimator is shown to be insensitive to the increase of VCs in the OFDM system. The complexity reduction is also considered and an approach is proposed showing a similar complexity as LS.     

Interleaving-Based Cyclic Delay Diversity OFDM Systems over Spatially Correlated Channels

Cyclic delay diversity employing multiple transmit antenna provides increased frequency selectivity and thereby improves the frequency diversity in coded orthogonal frequency division multiplexing (OFDM). However, spatial correlation due to insufficient spacing between transmit antennas degrades the diversity performance. In this paper, the correlation of effective channel frequency response (CFR) of CDD OFDM is analysed and then propose constellation rotation and adjacent interleaving (CRAI) scheme over spatially correlated channel. In the proposed scheme, the subcarrier constellation is rotated by a known angle and then imaginary parts of rotated adjacent subcarriers are interleaved. The squared Euclidean distance of the codewords is derived to show the effect of constellation rotation. Adjacent interleaving is shown to exploit the frequency diversity by reducing the variation in average channel power (ACP) due to spatial correlation. Simulation results reveal that the proposed scheme performs well in spatial correlated channel and thereby improves the bit error rate (BER) performance.     

Analysis of low-complexity windowed DFT-based MMSE channelestimator for OFDM systems

Low-complexity windowed discrete Fourier transform (DFT)-based minimum mean square error (MMSE) channel estimators are proposed and analyzed for both the interpolation and noninterpolation cases for orthogonal frequency-division multiplexing (OFDM) mobile communications systems. In the proposed method, the frequency domain data windowing is used to reduce the aliasing errors for the interpolation case and get better noise filtering performance for the noninterpolation case. The time domain MMSE weighting is also used to suppress the channel noise for both cases. Moreover, the optimal generalized Hanning window shape is searched to minimize the channel estimation mean square error (MSE). Analysis and simulation results show that the proposed method performance is close to the optimal MMSE estimator and is much better than the direct DFT-based estimator for both cases. Compared with the optimal MMSE estimator, however, the computation load of the proposed method can be significantly reduced because the IDFT/DFT transforms can be implemented with the fast algorithms IFFT/FFT     

Research on an iterative algorithm of LS channel estimation in MIMO OFDM systems

An iterative Least Square (LS) channel estimation algorithm for MIMO OFDM systems was proposed in this paper. Compared to common LS channel estimation, this algorithm can greatly improve estimation accuracy, and the low-pass filtering in time domain reduces AWGN and ICI significantly. MIMO OFDM system with this algorithm also works well in mobile situations. Simulation results have shown good MSE performance for this algorithm.     

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。     

An Efficient Scheme to Achieve Differential Unitary Space‐Time Modulation on MIMO‐OFDM Systems

Differential unitary space‐time modulation (DUSTM) has emerged as a promising technique to obtain spatial diversity without intractable channel estimation. This paper presents a study of the application of DUSTM on multiple‐input multiple‐output orthogonal frequency division multiplexing (MIMO‐OFDM) systems with frequency‐selective fading channels. From the view of a correlation analysis between subcarriers of OFDM, we obtain the maximum achievable diversity of DUSTM on MIMO‐OFDM systems. Moreover, an efficient implementation strategy based on subcarrier reconstruction is proposed, which transmits all the signals of one signal matrix in one OFDM transmission and performs differential processing between two adjacent OFDM blocks. The proposed method is capable of obtaining both spatial and multipath diversity while reducing the effect of time variation of channels to a minimum. The performance improvement is confirmed by simulation results.     

Improved Channel Estimation Based on Parametric Channel Approximation Modeling for OFDM Systems

Orthogonal frequency division multiplexing (OFDM) together with high order modulation scheme requires accurate channel estimation to perform coherent demodulation. In this paper, improved channel estimation methods based on a parametric channel approximation model are proposed for the OFDM system using pilot subcarriers. This channel model is called fraction taps channel approximation (FTCA) model, which is defined as a finite impulse response (FIR) on some definitive delay taps that have a fraction tap delay spacing relative to the sampling interval. Then, based on the FTCA channel model, the minimum mean square error (MMSE) and least square (LS) estimators are derived. Simulations over non-sample-spaced channels prove that the use of the FTCA channel model can effectively eliminate the problem of multi-path delay estimation and reduce the signal subspace dimension of the channel correlation matrix, where the full-rank estimators using pilot subcarriers can be adopted, and consequently, improve the channel estimation performance.     

Low complexity joint estimation of synchronization impairments in sparse channel for MIMO–OFDM system

Low complexity joint estimation of synchronization impairments and channel in a single-user MIMO–OFDM system is presented in this paper. Based on a system model that takes into account the effects of synchronization impairments such as carrier frequency offset, sampling frequency offset, and symbol timing error, and channel, a Maximum Likelihood (ML) algorithm for the joint estimation is proposed. To reduce the complexity of ML grid search, the number of received signal samples used for estimation need to be reduced. The conventional channel estimation techniques using Least-Squares (LS) or Maximum a posteriori (MAP) methods fail for the reduced sample under-determined system, which results in poor performance of the joint estimator. The proposed ML algorithm uses Compressed Sensing (CS) based channel estimation method in a sparse fading scenario, where the received samples used for estimation are less than that required for an LS or MAP based estimation. The performance of the estimation method is studied through numerical simulations, and it is observed that CS based joint estimator performs better than LS and MAP based joint estimator.     

An Efficient Adaptive Channel Estimation Algorithm for MIMO OFDM Systems—Study of Doppler Spread Tolerance

In this paper we develop an adaptive MIMO channel estimation algorithm for space–time block coded OFDM systems. The presented algorithm is based on Expectation Maximization (EM) technique by decomposing the superimposed received signals into their signal components, and estimating the channel parameters of each signal component separately. We also study and compare our proposed EM-based algorithm with a previously introduced recursive-least-squares based algorithm for MIMO OFDM systems. At each iteration the EM algorithm decomposes the problem of multi-channel estimation into channel estimation for each transmit–receive link. In this paper we also study the Doppler spread tolerance of our proposed algorithm in a fast fading environment, and investigate how it affects the system BER performance.     

Lower bound on training-based channel estimation error for frequency-selective block-fading Rayleigh MIMO channels

A lower bound on the error correlation matrix of training-based channel estimators is derived for multiple-input multiple-output (MIMO) systems over block-fading frequency-selective channels with symbol-spaced receivers. The bound is obtained in a constructive way by evaluating the asymptotic performance of an estimator that fully exploits the algebraic structure of the multipath channel. In particular, the estimator is assumed to be able to estimate the long-term features of the channel consistently (e.g., second order statistics of fading, delays, angles) while tracking the fast-varying fading fluctuations by Wiener filtering. Known estimators that are able to attain the bound under simplified settings are referred to, and general guidelines for designing novel estimators are discussed. Based on the simple analytical expression of the bound, the impact of channel estimation error on the link capacity is investigated for different system parameters and channel characteristics (e.g., Doppler shift, spatial correlation of fading). Numerical results are provided to corroborate the analysis.     

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。