Optimal training design for linearly time-varying MIMO/OFDM channels modelled by a complex exponential basis expansion

Time- and frequency-selective fading of propagating channels degrades the performance of multiple-input multiple-output/orthogonal frequency-division multiplexing (MIMO/OFDM) systems extensively by introducing double convolutions in both time-domain and frequency- domain. The author addresses the problem of linearly time-varying (LTV) channel estimation of MIMO/OFDM systems. First, the time-varying coefficients of the LTV channel are modelled by complex exponential basis expansions. Secondly, the LTV channel is estimated and the optimal pilot symbols are derived following the minimum mean square error criterion. It is shown that the optimal pilot strategy is to group consecutive pilot tones together as a pilot cluster and to distribute uniformly all pilot clusters in frequency-domain. In addition, the LTV channel estimation is further improved by imposing a window function on received signals. Finally, through simulations, it is shown that the new channel estimator can provide a considerable performance improvement in estimating MIMO-LTV channels, especially for the rapidly time-varying channel of a large Doppler frequency.     

基于无迹卡尔曼滤波的MIMO-OFDM系统信道估计算法

基于对现有MIMO-OFDM系统信道估计技术及其理论的分析,提出了一种基于无迹卡尔曼滤波（UKF）的信道估计算法。该算法不需要信道的任何先验统计信息,从频域出发,首先利用最小二乘（LS）算法得到导频处信道的粗略估计值,再在时域运用路径捕获法和UKF算法得到信道的精确估计值。仿真结果表明,与LS算法、最小均方（LMS）算法等相比,该算法在较低运算复杂度下可以获得信道估计性能的明显改善。     

MIMO-OFDM系统中一种新的信道估计方法

提出了多输入多输出-正交频分复用(MIMO-OFDM)系统中一种新的信道估计方法.根据最小均方误差的准则,推导出了求解信道频率响应的方程,方程求解的运算量主要集中在一个矩阵的求逆上.对每一个符号,此矩阵是固定的,所以矩阵的求逆仅需计算一次,整个求解过程的运算量较低.计算机仿真给出了这种方法的归一化均方误差和误码率性能.仿真结果表明,本文方法在多普勒频移为60Hz和360Hz下,其归一化的均方误差值相当,表明本文方法可以在不同的移动环境中良好工作.在不同的数据调制方式和不同的多普勒频移下,本文方法的误码率性能优于最小平方算法,略差于线性最小均方误差算法,但复杂度大大降低.     

Optimal power and subcarriers allocation in downlink OFDMA system with imperfect channel knowledge

Most of existing work on resource allocation in TDMA and OFDMA systems assumes the availability of perfect channel state information (CSI) at the transmitter, which is rarely possible due to feedback delay and channel estimation error. In this paper, we study the effect of feedback delay and channel estimation error on margin adaptive resource allocation in a downlink OFDMA system. By using convex optimization framework, we find an optimal solution to the problem. First, we study the individual effect of feedback delay and channel estimation error on resource allocation by considering them exclusively. Then, we consider the simultaneous presence of feedback delay and channel estimation error and study their combined effect on resource allocation. We derive an explicit close form expression for the users’ transmit power and propose an algorithm for power and subcarriers allocation for each of these three scenarios. The algorithms have polynomial complexities and solve the problem with zero optimality gaps. Simulation results show that the system performance is very sensitive to feedback delay and is affected significantly by imperfect channel estimation. Our proposed algorithms highly improve the system performance in the availability of only imperfect CSI at the transmitter.     

Turbo channel estimation and equalisation for a superposition-based cooperative system

This study investigates the superposition-based cooperative transmission system. In this system, a key point is for the relay node to detect data transmitted from the source node. This issued was less considered in the existing literature as the channel is usually assumed to be flat fading and a priori known. In practice, however, the channel is not only a priori unknown but subject to frequency selective fading. Channel estimation is thus necessary. Of particular interest is the channel estimation at the relay node which imposes extra requirement for the system resources. The authors propose a novel turbo least-square channel estimator by exploring the superposition structure of the transmission data. The proposed channel estimator not only requires no pilot symbols but also has significantly better performance than the classic approach. The soft-in-soft-out minimum mean square error (MMSE) equaliser is also re-derived to match the superimposed data structure. Finally computer simulation results are shown to verify the proposed algorithm.     

Decision-directed channel estimation based on iterative linear minimum mean square error for orthogonal frequency division multiplexing systems

A decision-directed (DD) channel estimation based on iterative linear minimum mean square error (LMMSE) is proposed for orthogonal frequency division multiplexing systems. Existing DD channel estimation is well known to have the problem of error propagation because of symbol-by-symbol detection. The proposed algorithm can estimate the correction term of current channel state information (CSI) according to the error vector of previous CSI by applying the orthogonality principle, and corrects the current CSI with this correction term. Analysis and simulation results have shown that this method has no error propagation problem. The performance of the proposed algorithm is much better than the conventional DD channel estimation, and close to the optimal LMMSE estimator, but with much less computational complexity compared with the optimal LMMSE estimator.     

IEEE802.16e系统信道估计算法研究

针对IEEE802.16e系统下行链路的导频分配模式,提出了一种适用于IEEE802.16e系统下行链路的信道估计方法。该方法采用两个一维信道估计器的级联。首先在时域进行滤波,根据最近原则将前一个符号导频处的信道响应作为下一个符号相同位置子载波处的信道响应,从而得到梳状导频结构;其次在频域进行滤波,采用最大似然算法估计出所有子载波上的信道响应。车速60km/h和车速120km/h信道下的仿真结果表明,采用该信道估计方法可降低系统的误码率,提高高速移动环境下系统的性能。     

OFDM水声通信系统动态OMP信道跟踪算法

针对正交频分复用(Orthogonal Frequency Division Multiplexing, OFDM)水声通信系统中最小二乘(Least Square,LS)信道估计算法和静态压缩感知信道估计算法分别存在估计精度低、导频开销大和计算复杂度高、实时性差的缺点,利用水声信道冲激响应的时域相关性,通过建立动态稀疏观测模型,提出一种动态正交匹配追踪(Dynamic Orthogonal MatchingPursuit,D-OMP)信道跟踪算法。该算法仅在初始时刻进行一次完整的正交匹配追踪(OrthogonalMatching Pursuit, OMP)信道估计获取信道支撑集,之后通过连续跟踪前一时刻信道支撑集的变化来跟踪信道。仿真结果表明,在导频开销相同的情况下,与传统LS算法、经典OMP算法相比,所提算法具有更好的信道跟踪性能和较低的算法复杂度。     

基于差分进化的时变信道最大似然估计算法

研究了隧道环境下的通信信道估计。针对隧道环境的地铁列车与轨旁设备之间无线通信中无线传输信道快速变化的特点,提出了一种采用元胞差分进化(DE)方法实时获取时变信道的有效信道长度的新型最大似然(ML)信道估计算法——DE-ML算法。仿真结果表明该算法在使用较少导频信息的情况下,通过差分进化方法有效估计跟踪有效信道长度,其估计性能优于最小二乘(LS)、线性最小均方误差(LMMSE)、传统ML等经典信道估计算法。该算法能在提高系统传输效率的同时显著提高算法的估计精度,尤其在高速移动情况下也具有了非常良好的性能。     

Semi-blind channel estimation for the uplink of multi-carrier code-division multiple access systems with timing offset

Timing offsets (TO) introduce misaligned interferences and phase errors, which degrade the performance of channel estimation. The authors propose a new semi-blind channel estimator that can cancel the TO effects on channel estimation and work well in the uplink of multi-carrier code-division multiple access systems in the presence of TO. The proposed channel estimator exploits the spreading sequence information instead of pilots to accomplish semi-blind estimation. Since the estimated channel coefficients are affected by the users? transmitted data, the effect of the users? data needs to be reduced. For this purpose, the authors also propose two smoothing algorithms, division smoothing and optimisation smoothing. In addition, to extend the new estimator to the system where the number of active users is too large, channel estimation over multiple symbols is discussed. The simulation results show that the proposed semi-blind estimator works better than a conventional estimator in the presence of TO, and its performance is very close to the conventional estimator in the absence of TO. Besides, the proposed estimator is compared with a sub-space estimator in simulation, and the results indicate that the new proposed estimator can achieve the same mean square error performance over the duration of a single symbol as the sub-space estimator over the duration of several symbols.     

莱斯信道下大规模MIMO系统混合模数转换器的随机向量量化方案

针对大规模MIMO系统用配置单精度模数转换器(ADC)来降低系统能耗会导致系统损失部分性能的问题,提出了一种莱斯信道下大规模MIMO系统的采用混合ADC的随机向量量化(RVQ)改进方案。该方案在频分双工模式下,首先在基站端采用高分辨率ADC和低分辨率ADC混合的接收方案处理信号,使接收的导频信号和有用信号具有较高的转换精度;系统对导频信号进行信道估计后,再对信道状态信息(CSI)进行RVQ处理,以此减小系统的反馈开销;最后运用最小均方误差(MMSE)信号检测算法减轻由量化误差引起的的用户间干扰,从而达到降低能耗并减小系统性能损失的目的。实验结果表明,这种改进的RVQ方案能在降低系统能耗的基础上有效减小系统容量损失,并使其和速率接近传统的高分辨率ADC接收方案。     

一种适用于慢衰落信道OFDM系统的信道估计算法

针对慢衰落信道OFDM系统,提出了一种新的低复杂度的且能对抗定时误差的信道估计器.这种信道估计器是基于导频间隔I=2的特殊梳状导频结构设计的.基于工程实现的考虑,采用了最小平方(LS)算法进行导频信道估计,同时利用了线性内插对非导频信道进行估计.分析了定时误差对非导频子载波估计的影响,并提出了一种相当简单但十分有效的修正算法,仿真结果有力的证明了此算法能有效的抵抗定时误差对非导频信道插值估计的影响.     

Minimum Error Entropy Based EKF for GPS Code Tracking Loop

This paper investigates the minimum error entropy based extended Kalman filter (MEEKF) for multipath parameter estimation of the Global Positioning System (GPS). The extended Kalman filter (EKF) is designed to give a preliminary estimation of the state. The scheme is designed by introducing an additional term, which is tuned according to the higher order moment of the estimation error. The minimum error entropy criterion is introduced for updating the entropy of the innovation at each time step. According to the stochastic information gradient method, an optimal filer gain matrix is obtained. The mean square error criterion is limited to the assumption of linearity and Gaussianity. However, non-Gaussian noise is often encountered in many practical environments and their performances degrade dramatically in non-Gaussian cases. Most of the existing multipath estimation algorithms are usually designed for Gaussian noise. The I (in-phase) and Q (quadrature) accumulator outputs from the GPS correlators are used as the observational measurements of the EKF to estimate the multipath parameters such as amplitude, code delay, phase, and carrier Doppler. One reasonable way to obtain an optimal estimation is based on the minimum error entropy criterion. The MEEKF algorithm provides better estimation accuracy since the error entropy involved can characterize all the randomness of the residual. Performance assessment is presented to evaluate the effectivity of the system designs for GPS code tracking loop with multipath parameter estimation using the minimum error entropy based extended Kalman filter.     

Precoded orthogonal frequency division multiplexing with hidden pilots for ultrawideband wireless communications

The authors propose a new hidden pilot scheme equipped with precoding and its application to orthogonal frequency division multiplexing-ultra-wideband (OFDM-UWB) systems. The proposed scheme can be thought of as an improvement over conventional hidden pilot schemes. By carefully designing precoder and hidden pilot from the view point of frequency diversity, channel estimation and the peak-to-average power ratio (PAPR), more frequency diversity gain and reduced PAPR can be achieved. In addition, the authors can support more pilots to estimate a channel providing mitigated self-interference between data symbol and hidden pilot with almost no loss of bandwidth efficiency in OFDM-based UWB communication systems. The authors show improved performance of the proposed scheme over the multiband OFDM scheme through simulations in a realistic UWB channel environment.     

Joint ML time-frequency synchronisation and channel estimation algorithm for MIMO-OFDM systems

The maximum-likelihood (ML) time-frequency synchronisation algorithm combined with channel estimation for multiple input multiple output-orthogonal frequency division multiplexing (MIMO-OFDM) systems in frequency selective fading channels is addressed. In the proposed algorithm, the authors use two steps to maximise an ML metric to obtain first the frequency offset and then timing. A fast Fourier transform algorithm is used to estimate the frequency offset. Using these two estimates, the channel is identified. A simple iterative algorithm is proposed to improve the frequency offset estimation. The performance of the proposed synchronisation approach, in terms of timing failure probability and mean square error of the estimated frequency offset and bit error rate, is compared with others in the literature. Comparison of simulation results with the Cramer-Rao lower bound clearly illustrates the accuracy of the proposed algorithm, which outperforms the state-of-the-art synchroniser devices in the open literature.     

基于深度学习的OFDM半相干水声通信方法

针对正交频分复用(Orthogonal Frequency Division Multiplexing, OFDM)水声通信中常用的相干和非相干通信分别面临的对多普勒敏感和频谱效率低的问题,提出一种高阶幅度键控调制的半相干通信技术,将OFDM符号时频帧结构中全部频点采用高阶幅度键控调制方式,并利用信号幅度信息完成半相干信道估计。通过两种基于深度学习的算法优化半相干信道估计这一非线性过程,较非相干通信有效提高了频谱效率,较一定信噪比下的相干通信提高了鲁棒性,降低了误比特率和系统复杂度,并利用元学习算法降低深度学习算法对训练数据的依赖。最后,提取海试信道数据,完成OFDM半相干水声通信系统仿真,验证了所提方法在频谱效率和系统误比特率性能方面较非相干和相干通信的优势,当信道长度改变时,基于元学习的算法依然可以获得较好的性能。     

一种改进LS信道估计算法在稀疏多径水声信道中的应用

为了消除水声正交频分复用调制(Orthogonal Frequency Division Multiplexing,OFDM)系统中噪声对稀疏多径信道估计的影响,提出了一种改进的最小二乘(Least-Square,LS)信道估计算法。该方法在传统基于离散傅里叶变换(Discrete Fourier Transform,DFT)插值的信道估计结构上进行了改进,得到了基于阈值探测的DFT插值信道估计方法,该方法将小于阈值的时域信道响应置零,探测最有效信道抽头,有效消除噪声干扰的影响。仿真结果验证了DFT插值在稀疏多径水声信道估计中的实用性;得到了当循环前缀长度与信道长度越接近时信道估计性能(Bit Error Rate,BER)越好的结论;确定了在两种调制方式下算法的阈值系数范围;且该新算法与已有算法所需的信噪比可低约2 d B,解决了用循环前缀长度来近似信道真实长度的实际问题。     

适用于OFDM系统的改进的信道估计算法

针对实际系统中的信道冲激响应(CIR)泄漏问题,提出了一种适用于梳状导频正交频分复用(OFDM)系统的改进的最小二乘(LS)信道估计算法.该算法基于分数抽头延时信道近似(FTCA)的参数化信道模型,此信道模型采用一个抽头间隔为分数倍采样间隔的抽头延时线结构的有限冲激响应(FIR)滤波器表示.此算法首先通过FTCA信道模型来近似实际信道,然后再估计该信道模型中的某些参数来获取实际的信道信息;该算法利用了FTCA信道模型中所有的延时抽头,从而很好地抑制了CIR泄漏.仿真与分析表明,FTCA信道模型能够有效地近似实际信道,同时降低信道自相关矩阵的维数,从而提高信道估计的性能.     

Error estimation and h adaptive boundary elements

This paper deals with error estimation of the boundary element method (BEM) and the h adaptive boundary elements. The various error sources in the BEM are discussed, and the upper bound of the BEM solution error is derived by means of the interpolation error of the BEM solution. A new error estimator is presented in the paper by using post-processing data from the standard BEM solutions. Two adaptive algorithms, the standard h adaptive and the h-hierarchical adaptive, are implemented based on direct boundary element method for two-dimensional elasticity problems. A few numerical examples are used to compare the accuracy of the proposed adaptive algorithm, as well as the error estimator. The stability of the BEM system matrix, which may deteriorate due to the introduction of h-hierarchical interpolation functions, has also been studied.     

Generalized wave-front reconstruction algorithm applied in a Shack-Hartmann Test

A generalized numerical wave-front reconstruction method is proposed that is suitable for diversified irregular pupil shapes of optical systems to be measured. That is, to make a generalized and regular normal equation set, the test domain is extended to a regular square shape. The compatibility of this method is discussed in detail, and efficient algorithms (such as the Cholesky method) for solving this normal equation set are given. In addition, the authors give strict analyses of not only the error propagation in the wave-front estimate but also of the discretization errors of this domain extension algorithm. Finally, some application examples are given to demonstrate this algorithm.