An Accurate and Very Low Complexity LMMSE Channel Estimation Technique for OFDM Systems

In this paper, we propose a very low linear minimum mean square error (LMMSE) channel estimation technique for orthogonal frequency division multiplexing (OFDM) systems. The conventional LMMSE, based on the autocorrelation channel matrix, requires \(O(N_P^3)\) operations (\(N_P\) represents the total number pilot in one OFDM symbol). By exploiting the structure of the channel autocorrelation matrix, we propose a very low complexity LMMSE channel estimator which requires only \(O(N_PlogN_P)\) operations. Simulation results show that the proposed technique yields the same performances as well as the classical LMMSE in terms of bit error rate and mean square error.     

Deep Learning for OFDM Channel Estimation in Impulsive Noise Environments

Impulsive noise suppression is essential in orthogonal frequency division multiplexing (OFDM) systems, since impulsive noise may cause a serious decline in channel estimation performance. To solve this problem, a channel estimator based on denoising autoencoder-deep neural network (DAE-DNN) is proposed in this paper. The proposed method is based on a data-driven deep learning framework. Firstly, DAE preprocesses signals to learn damaged data and recover the complete signal are used in the presence of impulsive noise. Then, the transmitted data processed by DAE are used to train the DNN in the offline training process. Finally, the estimated channel state information (CSI) is offered by the proposed DNN model in the online working process. The simulation results demonstrate that the proposed method improves OFDM channel estimation performance significantly. As expected, the proposed method has a better performance than existing ones, such as least squares, minimum mean square error and orthogonal matching pursuit algorithms. Moreover, the proposed method is robust under impulsive noise environments.

     

Channel Estimation for Cyclic Postfixed OFDM

A novel channel estimation algorithm is presented in this paper for the recently proposed cyclic postfix based on orthogonal frequency division multiplexing （OFDM） systems. Phase equalization with the erasure decision is used to reduce both the channel estimation error and the computational complexity. Simulation results show that the proposed channel estimation algorithm can effectively estimate the channel impulse response （CIR） and the performance of the proposed phase equalization with erasure decision is comparable with the minimal mean square error （MMSE） equalization, but it offers less computational complexity.     

A comparative investigation on channel estimation algorithms for OFDM in mobile communications

A comparative investigation on various channel estimation algorithms for OFDM system in the mobile communication environment is presented and analyzed in terms of computational complexity, mean square error, and bit error rate in this paper. As a result, Wiener filter estimation shows the best error performance. Concerning the computational complexity as well as the performance, however, the piecewise linear estimator is considered as a proper choice when the reference signal spacing is relatively narrow. And the cubic-spline estimator is a good alternative to the Wiener filter estimation if the reference signal spacing is wider than the coherent bandwidth of transmission channel.     

Joint carrier frequency synchronization and channel estimation for OFDM systems via the EM algorithm

A joint carrier frequency synchronization and channel estimation scheme is proposed for orthogonal frequency-division multiplexing (OFDM) system. In the proposed scheme, carrier frequency synchronization and channel estimation are performed iteratively via the expectation-maximization (EM) algorithm using an OFDM preamble symbol. Moreover, we analytically investigate the effect of frequency offset error on the mean square error (MSE) performance of channel estimator. Simulation results present that the proposed scheme achieves almost ideal performance for both channel and frequency offset estimation.     

An Efficient Maximum Likelihood Carrier Frequency Offset Estimator for OFDM Using Null Subcarriers and Cyclic Prefix

Accurate estimation of carrier frequency offset (CFO) is an important requirement in orthogonal frequency-division multiplexing (OFDM) based wireless communication systems. In this paper, we propose a hybrid procedure to accomplish this task efficiently. One of the key importance of the approach is the judicious combination of two independent estimators so as to reduce the bandwidth overhead and computational complexity over many conventional methods. It employs the cyclic prefix and a few null subcarriers, respectively, for the fractional and integer frequency offset estimations. We also propose a novel null subcarrier allocation scheme based on Fibonacci series. The range of frequency offset that can be estimated by the proposed technique is equal to the full OFDM bandwidth. Furthermore, performance of the proposed CFO estimator is mathematically analyzed by deriving an expression for the bit error probability of the receiver under Rayleigh fading channel and the Cramer-Rao lower bound for the mean square estimation error. For moderate SNRs, our approach is shown to greatly outperform some recently published methods in terms of BER performance, bandwidth overhead and receiver complexity.     

Computer-Assisted Collaborative Learning for Enhancing Students Intellectual Ability Using Machine Learning Techniques

This paper proposes low complexity detection for internet of underwater things communication. The signal is transmitted from the source to the destination using several sensors. To simplify the computational operations at the transmitter and the sensory nodes, a single carrier frequency domain equalizer is proposed and amplify-and-forward protocols are employed. Fast Fourier transform and use of cyclic prefix are also proposed to simplify these algorithms when compared to time-domain equalization. As precise channel data is difficult to capture in underwater communications, the adaptive implementation of FDE is proposed as a solution that can be employed when the channel experiences a fast doppler shift. The two adaptive detectors are based on the least mean-square and recursive least square principles. Numerical simulations show that the performance of the bit error rate performance of the proposed detectors is close to that of the ideal minimum mean square error.

     

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     

基于导频的OFDM信道估计方法及分析

对OFDM系统中基于导频的信道估值器进行了比较分析,分析了DVB-T系统中导频的分布,在DVB-T系统基础上结合最大似然准则和最小均方误差准则,提出了信道估计的方法,并在Reyleigh信道模型下,运用Matlab实现仿真.     

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.     

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.     

Linear expansions for frequency selective channels in OFDM

Modeling the frequency selective fading channels as random processes, we employ a linear expansion based on the Karhunen–Loeve (KL) series representation involving a complete set of orthogonal deterministic vectors with a corresponding uncorrelated random coefficients. Focusing on OFDM transmissions through frequency selective fading, this paper pursues a computationally efficient, pilot-aided linear minimum mean square error (MMSE) uncorrelated KL series expansion coefficients estimation algorithm. Based on such an expansion, no matrix inversion is required in the proposed MMSE estimator. Moreover, truncation in the linear expansion of channel is achieved by exploiting the optimal truncation property of the KL expansion resulting in a smaller computational load on the estimation algorithm. The performance of the proposed approach is studied through analytical and experimental results. We first exploit the performance of the MMSE channel estimator based on the evaluation of minimum Bayesian MSE. We also provide performance analysis results studying the influence of the effect of SNR and correlation mismatch on the estimator performance. Simulation results confirm our theoretical results and illustrate that the proposed algorithm is capable of tracking fast fading and improving performance.     

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.     

快速时变信道下的OFDM信道估计方法

为解决正交频分复用(OFDM)系统在快速时变信道下引入的子载波间干扰(ICI)导致性能急剧下降的问题,提出一种基于带状矩阵的数据辅助型信道估计算法。通过分析由多普勒频偏引入的子载波间干扰矩阵,运用线性模型对信道冲击响应算法进行建模,对每个子载波设计带状补偿矩阵以最大程度消除ICI。数值仿真结果表明,该信道估计算法较最小均方误差(MMSE)算法复杂度大大减小,便于实现,满足快速时变信道下的估计精度需要。     

Performance analysis of channel estimation for OFDM systems with residual timing offset

The authors present an analysis of the effect of timing offset on channel estimation for comb-type pilot-aided orthogonal frequency division multiplexing (OFDM) systems. Residual timing offset does not negatively affect the channel estimation of the pilot subcarrier, but does corrupt the channel information obtained via interpolation. This paper provides the mean square error (MSE) channel estimation performance when a linear interpolation technique is used in a comb-type pilot-aided OFDM system. Analysis shows that the performance degradation of the channel estimator due to imperfect frame synchronization is dependent on the frequency correlation of the channels and the amount of timing offset     

Low complexity channel estimation for space-time coded wideband OFDM systems

In this article, channel estimation for space-time coded orthogonal-frequency division multiplexing (OFDM) systems is considered. By assuming that the channel frequency response is quasi-static over two consecutive OFDM symbols, we develop channel parameter estimators based on the use of space-time block coded (STBC) training blocks. Using an STBC training pattern, a low-rank Wiener filter-based channel estimator with a significant complexity reduction is proposed. A simplified approach for the optimal low-rank estimator is also proposed to further reduce the estimator complexity while retaining an accurate frequency domain channel estimation. Numerical results are provided to demonstrate the performance of the proposed low complexity channel estimators for space-time trellis coded OFDM systems.     

Multiuser Detection in SDMA–OFDM Wireless Communication System Using Complex Multilayer Perceptron Neural Network

The space division multiple access–orthogonal frequency division multiplexing (SDMA–OFDM) wireless system has become very popular owing high spectral efficiency and high load capability. The optimal maximum likelihood multiuser detection (MUD) technique suffers from high computational complexity. On the other hand the linear minimum mean square error (MMSE) MUD techniques yields poor performance and also fails to detect users in overload scenario, where the number of users are more than that of number of receiving antennas. By contrast, the differential evolution algorithm (DEA) aided minimum symbol error rate (MSER) MUD can sustain in overload scenario as it can directly minimizes probability of error rather than mean square error. However, all these classical techniques are still complex as these do channel estimation and multiuser detection sequentially. In this paper, complex multi layer perceptron (CMLP) neural network model is suggested for MUD in SDMA–OFDM system as it do both channel approximation and MUD simultaneously. Simulation results prove that the CMLP aided MUD performs better than the MMSE and MSER techniques in terms of enhanced bit error rate performance with low computational complexity.     

Low-complexity nonlinear least squares carrier offset estimator for OFDM: identifiability, diversity and performance

Orthogonal frequency division multiplexing (OFDM) transforms frequency-selective channels into multiple low-rate flat-fading subchannels. Carrier frequency offset between transmitter and receiver local oscillators must be estimated and compensated at the receiver to maintain orthogonality of these subchannels. In this paper, we derive the nonlinear least squares (NLS) estimator for carrier frequency synchronization that exploits receiver diversity and known OFDM signal subspace structure due to the placement of unmodulated (virtual) subcarriers. The resulting estimator benefits from the high-resolution subspace method without the computational overhead associated with subspace decomposition. Fundamental estimator performance relationships against parameters such as signal-to-noise ratio (SNR), frequency-selective fading, and diversity branch correlation are derived. In particular, we derive the Cramer-Rao bound (CRB) for the mean square error (MSE) of the carrier frequency offset estimator. Numerical studies are presented to verify the results.     

Subspace Projection-based OFDM Channel Estimation

In this paper, we investigate the benefits of pre-processing received data by projection on the performance of channel estimation for orthogonal frequency division multiplexing (OFDM) systems. Projecting data onto its signal subspace will reduce the additive noise energy in the data. Least square (LS) estimation is a low-complex algorithm for training-based OFDM systems and the lower bound on the mean-square error of it is proportional to the noise variance. So, after the received data is pre-processed (projected onto its signal subspace), LS channel estimation on the pre-processed data will increase the performance of channel estimation. This method can also work in multiple-input and multiple-output (MIMO) case. Performance analysis and simulation results show that the proposed algorithm has a considerably smaller complexity than the linear minimum mean square error estimation while having almost the same performance.     

在OFDM系统中用导频符号进行信道估计的新方法

对信道的准确估计是提高相干解调的正交频分复用（OFDM）系统性能的关键，利用在OFDM系统中信道的频域响应是过采样的特性，提出了在频域内用均匀梳状分布的导频符号和导频符号数相同点的傅里叶变换相结合扒道估计方法，在16QAM OFDM系统中将其与带低通滤波器的Isi(sin(x)/x) 插值法，cubic插值法和Winner插值法进行了信道估计的均方误差和无编码的误比特率捻 真结果进行了比较，其结果表明本方法的估计性能优于si和cubic插值法，并接近优化的Win-ner插值法但其计算复杂度与Winner插值法相比却大大降低。