On the training of MIMO-OFDM channels with least square channel estimation and linear interpolation

The effect of pilot arrangement is investigated on the performance of trained MIMO-OFDM channels where fading is time-flat in a block of coherence-time duration but frequency-selective. The MIMO-OFDM channel is considered to be trained by using least square channel estimation on pilot subcarriers and by applying linear interpolation on data subcarriers. The achievable rate of such a system is derived employing the generalized mutual information approach. Numerical examples are presented examining the optimal density of pilots in the two-dimensional time-frequency domain.     

在OFDM系统中采用余弦变换的信道估计

提出在OFDM通信系统中采用余弦变换(DCT)实现信道内插估计,同时讨论离散傅氏变换(DFT)、离散哈特莱(DHT)、Hadamard变换等数学方法用于采用导引信号下的信道估计。无需知道信道阶数、噪声功率、多谱勒频移等信道统计特性仍能达到较好的信道估计性能,计算简单。仿真结果表明,余弦变换算法的信道估计在多径干扰、多谱勒频移较大时,仍能正常工作,性能稳定,达到较好的信道估计效果。     

MC-CDMA系统基于子空间跟踪的导频辅助信道估计

基于导频辅助的MC-CDMA系统信道估计方法通过在确定的时频位置发送已知的导频符号来获取信道参数,通常包括导频位置的最小二乘估计和内插滤波两步。为了提高导频位置信道频域特性的估计精度,使得后续内插滤波的精度相应得到提高,本文利用基于Givens旋转的子空间跟踪方法构成了对信道的时变参数的估计和跟踪,得到了较为准确导频信道估计。仿真表明,我们给出的基于子空间跟踪的信道估计方法具有更好的稳定性和更高的估计精度。     

Reducing ICI effect in OFDM system using low‐complexity Kalman filter based on comb‐type pilots arrangement

In OFDM systems, time‐varying channels destroy orthogonality between subcarriers causing Inter‐Carrier Interference. To reduce this effect, a Kalman filter, as a benchmark, is used for channel estimation, based on comb‐type pilot arrangements of the OFDM system. An advantage of comb‐type pilot arrangements in channel estimation is the ability to track the variation of the channel caused by Doppler frequency. Kalman method has been proposed to estimate the channel frequency response (CFR) at the pilot locations, then CFR, at data subchannels, is obtained by means of interpolation between estimates at pilot locations. The low‐complexity Kalman method is introduced to reduce the complexity of the system while achieving the same BER/SNR. Different types of interpolations have been also compared such as Low‐pass, Spline‐cubic and Linear interpolation methods. The BER/SNR performance of BPSK modulation schemes are considered for time varying Rayleigh fading channels. Our results has shown that the low‐complexity Kalman estimation, used with the pilot arrangement and a suitable interpolation method, gives almost the same performance as that of the Kalman method specially for low SNR values and hence the effect of Doppler shift effect is controlled. Copyright © 2010 John Wiley & Sons, Ltd.     

Performance comparisons of channel estimation techniques in multipath fading CDMA

The problem of pilot-symbol-aided estimation of multipath fading channels in up-link code-division multiple-access (CDMA) systems is considered. The transmitted symbol streams of each user are divided into time-slots; and each time-slot contains a number of pilot-symbols followed by information data symbols. Channel estimation is based on interpolation of the channel values corresponding to the pilot symbols in adjacent time-slots. Existing channel estimation techniques, including the weighted multislot average method and the wavelet expansion method, are studied. Two new channel estimation methods, namely, the robust channel interpolator, and the polynomial channel interpolator, are developed and are compared with these techniques. It is seen that the two new channel estimation methods significantly outperform the existing methods in multipath fading CDMA systems, for a wide range of Doppler values, and under various receiver schemes (with single or multiple receive antennas), such as the RAKE receiver, the interference cancellation receiver, and a receiver which performs iterative channel estimation and interference cancellation.     

Channel Estimation Based on a Time-Domain Threshold for OFDM Systems

Channel estimation for OFDM systems is usually carried out in frequency domain by the least-squares (LS) method using known pilot symbols. The LS estimator has a merit of low complexity but may suffer from noise because it does not consider any noise effect in obtaining its solution. To enhance the noise immunity of the LS estimator, we consider the estimation noise in time domain named discrete Fourier transform (DFT)-based channel estimation. Residual noise existing at the estimated channel coefficients in time domain could be reduced by reasonable selection of a threshold value. To achieve this, we propose a channel-estimation method based on a time-domain threshold which is a standard deviation of noise obtained by wavelet decomposition. Computer simulation shows that the estimation performance of the proposed method approaches to that of the known-channel case in terms of bit-error rates after the Viterbi decoder in overall SNRs.      

AoA-Based Channel Estimation for Massive MIMO OFDM Communication Systems on High Speed Rails

Channel estimation is a well-known challenge for wireless orthogonal frequency division multiplexing(OFDM)communication systems with massive antennas on high speed rails(HSRs).This paper investigates this problem and design two practicable uplink and downlink channel estimators for orthogonal frequency division multiplexing(OFDM)communication systems with massive antenna arrays at base station on HSRs.Specifically,we first use pilots to estimate the initial angle of arrival(AoA)and channel gain information of each uplink path through discrete Fourier transform(DFT),and then refine the estimates via the angle rotation technique and suggested pilot design.Based on the uplink angel estimation,we design a new downlink channel estimator for frequency division duplexing(FDD)systems.Additionally,we derive the Cramér-Rao lower bounds(CRLBs)of the AoA and channel gain estimates.Finally,numerical results are provided to corroborate our proposed studies.     

MIMO-OFDM系统导频辅助的信道估计

以MIMO—OFDM系统为研究对象，通过设计正交导频进行导频辅助信道估计，对数据点的信道响应进行线性内插、三次样条插值和二次曲线拟合算法，并通过Matlab进行计算机仿真，对这些算法的BER性能进行比较。结果表明：随着信噪比（SNR）的增加，三次样条（Spline）内插和线性内插性能要远好于二次曲线拟合导频估计方法。     

Comb type pilot aided channel estimation in OFDM systems with transmit diversity

Transmit diversity can be applied to OFDM systems by adopting space time code. Since the received signal is the overlapped signals transmitted from different transmit antennas, channel estimation is a rather challenging task for space time coded OFDM (ST-OFDM) systems. Pilot structure can help the receiver to effectively separate the overlapped signals and perform accurate channel estimation. In this paper, we propose three different channel estimation algorithms based on specially designed comb type pilots inserted in frequency domain. One of our proposed algorithms is performed in frequency domain and the other two are performed in time domain. Such comb type pilot based algorithms can provide higher bandwidth efficiency than common significant-tap-catching algorithm using training block pilots. Numerical analyzes and computational simulation show that our proposed estimation schemes have the same good performance while the time domain methods have relatively simple structure.     

基于DFT-BEM模型的LOFDM系统双散射信道最大多普勒扩展估计

栅格正交频分复用（Lattice Orthogonal Frequency Division Multiplexing, LOFDM）系统凭借特殊的网格时频结构和更大的欧式距离特性,在快速移动环境下展现了卓越的抗时变、抗多径能力。最大多普勒扩展作为LOFDM系统自适应策略的重要参数之一,准确的最大多普勒扩展估计对于LOFDM系统发送信号设计以及自适应策略实现十分重要。本文针对LOFDM系统的特殊信号结构以及双散射信道的快时变特性,采用DFT-BEM信道模型近似快时变信道响应,结合快时变信道下LOFDM系统块传输接收实现,利用梳状导频辅助估计多普勒域平均信道频率响应,在此基础上利用信道响应估计值的时间相关函数实现基于F范数的信道最大多普勒扩展估计;并提出基于子空间的最大多普勒扩展估计算法,降低了噪声对最大多普勒扩展估计性能的影响,在低信噪比条件下有效改善了估计性能。      

A time-domain estimation method of rapidly time-varying channels for OFDM-based LTE-R systems

This paper addresses the performance of fast doubly selective fading channel estimation combined with Inter-Carrier Interference (ICI) cancellation for Long Term Evolution (LTE) communication platform in the High Speed Railway (HSR) environment. We consider the Channel Impulse Response (CIR) coefficients with a critical Doppler frequency shift and multi-path fading that were taken from the WINNER II channel model and the D2a propagation scenario, where the conditions of HSR are analyzed. As multi-path fading increases and the channel varies in the order of the symbol period, we first propose a novel approach for designing a pilot symbol structure in the time domain. Then, we describe the deployment of the proposed pilot symbol structure to estimate the channel in the time domain. Channel information corresponding to the data positions is obtained by linear interpolation. In each OFDM symbol, the slope and the initial value for establishing an interpolation function are estimated to adapt to the time variation of the channel. An accurate estimate of channel state information is used for the purpose of ICI cancellation. The simulation results show that the channel estimated by our proposed method can follow the real channel well, even in a very high Doppler frequency. The estimation method in terms of Mean Squared Error (MSE) significantly outperforms the state-of-the-art methods. The combination of our channel estimator with several interference cancelers provides a considerably better system performance than that achieved when frequency channel estimation is used.     

基于部分数据的叠加序列慢时变信道估计

针对OFDMA通信系统,提出了一种基于部分数据的叠加序列慢时变信道估计算法,并在接收端给出了数据恢复的方法。时变信道采用复指数基扩展模型来描述,对OFDMA系统的导频序列进行了精心设计。提出在频域减去一个基于部分数据的序列,从而使发送数据经过反傅里叶变换后,特定位上的数据能量变低,进而大大减少了数据在信道估计时产生的误差。由于在发射端信号已经产生了畸变,在接收端采用特定的方法对数据进行补偿,消除了这种影响。实验仿真证明该方法在一定程度上提高信道估计的性能。     

基于导频信号的LTE系统高移动性信道估计算法

在长期演进(Long Term Evolution, LTE)系统中,精确的信道估计是均衡和相干解调的前提。在高速移动信道下,由于LTE下行链路离散非均匀的导频模式,传统的时间方向信道估计方法性能较差。为了提高信道估计精度,首先利用离散傅里叶变换(Discrete Fourier Transform, DFT)的信道估计方法提高导频处的估计精度。然后根据LTE系统的导频结构,设计了两种时间方向信道估计方法:1) 当信道的统计特性未知时,把不等间隔的导频分布转换为等间隔的导频分布,并利用三阶样条内插估计出数据处的信道频域值;2) 当信道的统计特性已知时,基于最小均方误差准则,设计高性能的自适应内插器,以准确获得信道估计所需系数。仿真和分析表明,相对于传统的线性内插算法,这两种信道估计算法利用更多的导频信息,可大大提高信道估计的精度,同时提升系统的解调性能。      

The BER analysis of OFDMA and SC‐FDMA under pilot‐assisted channel estimation and pilot jamming in rayleigh slow‐fading channel

In this paper, the authors derived the analytical bit error rate expressions for orthogonal frequency division multiple access and single‐carrier frequency‐division multiple access (SC‐FDMA) in Rayleigh slow‐fading channel for binary phase‐shift keying/quadrature phase‐shift keying/16‐quadrature amplitude modulations under pilot jamming and pilot symbol‐assisted channel estimation. Beginning with the bit error rate analysis from the general case of pilot symbol‐assisted channel estimation technique in Rayleigh slow‐fading channel, the expressions are first modified for different modulations and then further customized to account for the Zero‐Forcing equalization in frequency or time direction with application respectively to orthogonal frequency division multiple access or SC‐FDMA without and with pilot jamming. Piecewise‐linear interpolation is used for its simplicity. The simulation results match perfectly with the theoretical predictions except for some discrepancies with SC‐FDMA, which imply that the generalized equations developed here have to be further modified to account for system‐specific features like discrete Fourier transform precoding for SC‐FDMA. Copyright © 2016 John Wiley & Sons, Ltd.     

Efficient Channel Estimation for MIMO Single-Carrier Block Transmission With Dual Cyclic Timeslot Structure

We investigate channel estimation for timeslot-structured single-carrier block transmission (SCBT) over space-, time-, and frequency-selective fading multiple-input multiple-output (MIMO) channels. A MIMO-SCBT with a dual cyclic timeslot structure is presented first. Then, an optimal channel estimation in the minimal mean square error (MMSE) sense on the timeslot basis is investigated. It is shown that the optimal pilots for the timeslot-based MMSE channel estimation are related to the statistical channel state information in eigenmode. Under the assumption that the transmit correlation is unknown at the transmitter, the optimal pilots satisfy the same condition as reported for the block-based least-square (LS) channel estimation in literature, and the channel estimation can be simplified to initial block-based LS channel estimation followed by space-time postprocessing. Particularly, for spatially uncorrelated channels, the space-time postprocessing can be reduced to pathwise processing. A new design of the pilot sequences is given, which leads to an efficient implementation of the channel estimation. Later on, a more efficient implementation for the initial channel estimation is obtained by using the structure of the pilot sequences, and discrete cosine transform (DCT)-based implementation is developed for the space-time postprocessing to approximate the optimal solution with low implementation complexity. Finally, the performance of the proposed channel estimation is verified via simulations.     

基于宽深超分辨率网络的信道估计方法

在正交频分复用(Orthogonal Frequency Division Multiplexing,OFDM) 系统中由于快衰落导致信道特征不连续,常规的信道插值方法无法准确反应导频与整个信道之间的关联性。针对这一问题,提出了一种基于宽深超分辨率（Wide Deep Super-resolution,WDSR）网络的信道估计方法,把导频值通过最小二乘估计（Least Squares,LS）初步插值,再通过WDSR网络再次放大重构整个信道的响应。将信道估计插值上采样替换成初步插值和图像超分辨率上采样两步。仿真结果表明,与超分辨率卷积神经网络(Super-resolution Convolutional Neural Network,SRCNN)信道估计算法相比,在不同种类的信道以及导频数下WDSR信道估计方法均方误差性能提升约4.6 dB。     

多普勒域上稀疏的双向中继信道估计

信道估计技术作为获得信道衰落信息的方法,是提高无线信道传输接收性能的关键技术。本文针对放大转发双向中继系统的时间选择性平坦衰落信道,利用信道在多普勒域的稀疏性进行压缩信道估计。相比于传统的线性估计方法,压缩信道估计考虑了信道的固有稀疏性,降低了导频的开销,改善了信道估计性能,提高了频谱利用率及系统吞吐量。文中通过对双向中继信道进行多普勒域的稀疏建模,仿真分析了信道估计性能随着导频数量增加、信噪比增加,得到不断改善;而不同的导频分布将影响观测矩阵的相关度,从而对信道估计产生影响。仿真表明,当导频随机分布时,信道估计效果最佳。同时,文中还仿真分析了最大多普勒频移对信道估计性能的影响。      

A Robust SFO Estimation Scheme for OFDM-Based DRM with Non-Symmetric Distributed Pilots

This paper proposes a robust sampling frequency offset (SFO) estimation scheme in an orthogonal frequency division multiplexing based digital radio mondiale system with non-symmetrically distributed pilots. In particular, a post fast Fourier transform SFO estimation method is suggested to provide an unbiased estimate of SFO in the presence of frequency selectivity of the channel as well as non-symmetrically distribution of pilot symbols. In order to verify the performance of the proposed frequency-offset estimation scheme, a closed-form expression for the mean square error (MSE) is derived. We show via simulations that the proposed estimation scheme achieves a remarkable robustness against frequency selectivity fading and the theoretical MSE analysis is proven accurate.     

基于导频的信道估计算法的研究

为了解决在恶劣信道条件下,信道插值算法的性能与灵活性问题,给出一种应用于工程实现的三次样条插值的简便算法。通过对三次样条插值仿真算法和其它基于插值估计算法的仿真比较,结果表明：三次样条插值在对复杂信道的估计方面,与其它基于插值的估计算法相比,具有更好的性能;同时,它不需要导频等间隔,在工程应用中更具灵活性。另外还对基于导频的信道估计中常用的插值算法的性能、特点进行了系统的分析和比较。     

OFDM system channel estimation using time-domain training sequencefor mobile reception of digital terrestrial broadcasting

A channel estimation technique using time-domain training sequence is investigated. It is demonstrated that this technique can estimate the channel status more accurately, under low C/N situations, than the conventional frequency domain technique using in-band pilots. A novel channel estimation and compensation scheme for a fast fading channel is developed for an OFDM system using time-domain training sequence. It is compared with the frequency domain pilot channel estimation scheme