Stability of the MGS-like elimination method for equality constrained least squares problems

This paper proves that the weighting method via modified Gram-Schmidt（MGS） for solving the equality constrained least squares problem in the limit is equivalent to the direct elimination method via MGS（MGS-elimination method）. By virtue of this equivalence, the backward and forward roundoff error analysis of the MGS-elimination method is proved. Numerical experiments are provided to verify the results.

Separate Least Mean Square Based Equalizer with Joint Optimization for Multi-CAP Visible Light Communication

Visible light communication(VLC) is expected to be a potential candidate of the key technologies in the sixth generation(6G) wireless communication system to support Internet of Things(IoT) applications. In this work, a separate least mean square(S-LMS) equalizer is proposed to compensate lowpass frequency response in VLC system. Joint optimization is employed to realize the proposed S-LMS equalizer with pre-part and post-part by introducing Lagrangian. For verification, the performance of VLC system based on multi-band carrier-less amplitude and phase(m-CAP) modulation with S-LMS equalizer is investigated and compared with that without equalizer,with LMS equalizer and with recursive least squares(RLS)-Volterra equalizer. Results indicate the proposed equalizer shows significant improved bit error ratio(BER) performance under the same conditions. Compared to the RLS-Volterra equalizer, SLMS equalizer achieves better performance under low data rate or high signal noise ratio(SNR) conditions with obviously lower computational complexity.

Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations

In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

一种宽带非线性信道校正方法

针对高速数传解调器接收宽带高阶调制信号时因信道非线性导致的性能恶化问题,提出一种基于两层自适应均衡网络的非线性信道校正方法。该方法先利用递归最小二乘法获得Volterra非线性前置校正系数,再利用自适应基带均衡器消除信道的剩余影响,以提升解调器的捕获跟踪能力,并在高速数传解调器工程应用中实现2.4 Gb/s 16QAM信号的稳定接收。

模分复用系统中盲均衡算法的均衡性能研究

恒模算法(CMA)是一种广泛应用于模分复用系统的算法,可对系统中模式耦合、差分模式群时延和色散等损伤因素进行均衡补偿,进而得到理想信号。为了研究CMA算法在强耦合模分复用系统中的均衡性能,采用功率耦合理论搭建6×6模分复用系统模型,并在接收端使用CMA和修正的恒定模数算法(MCMA)对系统输出信号进行均衡,获得了星座图、均方根误差(RMSE)值和误比特率(BER)。结果表明,在星座图方面,MCMA可以减少散点,使星座点更紧凑;在RMSE方面,MCMA均衡后的信号的RMSE值小于CMA均衡后得到的RMSE值,说明MCMA均衡后的数据离散程度较低;在BER方面,当BER为10-3时,MCMA要求的光信噪比比CMA低1.0 dB,因此,MCMA的均衡效果优于CMA。该研究结果为强耦合模分复用系统中的均衡算法提供了一些参考。

拓扑优化结构中棋盘格式的光滑及等面积处理方法

为了解决拓扑优化后出现的边缘棋盘格式问题,提出了用线性最小二乘法对边缘棋盘格式进行线性化处理。在拓扑优化棋盘格式边界线性化处理后,出现了小梁结构端面面积在长度方向不相等和不均匀等问题,对实际工程应用带来不便。针对此问题提出了首先用常规的单边中心分割等面积处理方法对线性光滑处理后的模型进行优化,使重构模型趋于均匀化、规则化,但是发现单边中心分割等面积法处理后重构模型的小梁中心出现了偏离。为了保证小梁结构端面面积相等、同时保证小梁中心线不偏离,又提出了双边中心分割等面积法,这种方法避免了小梁结构等面积变化后的中心线偏离问题,保证拓扑优化结构的完整性。通过计算对比分析,发现双边中心分割等面积法处理后的重构模型在静力学分析中的性能均优于其他两种方法,验证了双边中心分割等面积法处理的可行性。

变步长CMA和DD-LMS双模式切换盲均衡算法

针对经典盲均衡算法收敛速度较慢和稳态误差较大的问题,提出了一种基于变步长恒模算法(Constant Modulus Algorithm, CMA)和判决引导的最小均方(Decision Directed Least Mean Square, DD-LMS)算法的双模式切换盲均衡算法。在算法收敛初期采用CMA算法,以确保算法可以较快收敛。在收敛之后切换至DD-LMS算法,以进一步降低稳态误差。通过设定阈值来切换算法,取相邻多次迭代误差的平均值作为算法的切换值,以确保算法切换时机的合理性。另外,引入Softsign变步长函数并加入3个参数对该函数进行改进,使得Softsign变步长函数可以依据不同信道环境设定最佳参数,同时提高算法的收敛速度。仿真结果表明,在卫星通用信道条件下,所提算法的收敛迭代次数约为1 000次,稳态误差为-12 dB,在信噪比为15 dB时,误码率为1×10~(-6)。与相关算法对比,所提算法的收敛速度较高,误码率和稳态误差较低。

Ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints

The reasonable prior information between the parameters in the adjustment processing can significantly improve the precision of the parameter solution. Based on the principle of equality constraints, we establish the mixed additive and multiplicative random error model with equality constraints and derive the weighted least squares iterative solution of the model. In addition, aiming at the ill-posed problem of the coefficient matrix, we also propose the ridge estimation iterative solution of ill-posed mixed additive and multiplicative random error model with equality constraints based on the principle of ridge estimation method and derive the U-curve method to determine the ridge parameter. The experimental results show that the weighted least squares iterative solution can obtain more reasonable parameter estimation and precision information than existing solutions, verifying the feasibility of applying the equality constraints to the mixed additive and multiplicative random error model. Furthermore, the ridge estimation iterative solution can obtain more accurate parameter estimation and precision information than the weighted least squares iterative solution.

Application of Equality Test of Coefficients of Variation to the Heteroskedasticity Test

The presence of heteroskedasticity in a considered regression model may bias the standard deviations of parameters obtained by the Ordinary Least Square (OLS) method. In this case, several hypothesis tests on the model under consideration may be biased, for example, CHOW’s coefficient stability test (or structural change test), Student’s t-test and Fisher’s F-test. Most of the heteroscedasticity tests in the literature are based on the comparison of variances. Despite the multiplication of equality tests of coefficients of variation (CVs) that have appeared in the literature, to our knowledge, the first and only use of the coefficient of variation in the detection of heteroskedasticity was offered by Li and Yao in 2017. Thus, this paper offers an approach to determine the existence of heteroskedasticity by a test of equality of coefficients of variation. We verify by a Monte Carlo robustness and performance test that our method seems even better than some tests in the literature. The results of this study contribute to the exploitation of the statistical measurement of CV dispersion. They help technicians economists to better verify their hypotheses before making a scientific decision when making a necessary forecast, in order to contribute effectively to the economic and sustainable development of a company or enterprise.

Enhancement in Channel Equalization Using Particle Swarm Optimization Techniques

This work proposes an improved inertia weight update method and position update method in Particle Swarm Optimization (PSO) to enhance the convergence and mean square error of channel equalizer. The search abilities of PSO are managed by the key parameter Inertia Weight (IW). A higher value leads to global search whereas a smaller value shifts the search to local which makes convergence faster. Different approaches are reported in literature to improve PSO by modifying inertia weight. This work investigates the performance of the existing PSO variants related to time varying inertia weight methods and proposes new strategies to improve the convergence and mean square error of channel equalizer. Also the position update method in PSO is modified to achieve better convergence in channel equalization. The simulation presents the enhanced performance of the proposed techniques in transversal and decision feedback models. The simulation results also analyze the superiority in linear and nonlinear channel conditions.

A Robust Decision Feedback Equalizer for ATSC DTV Receivers

Least mean square (LMS) decision feedback equalizer (DFE) is preferred as an effective solution to coping with inter-symbol interference (ISI) for ATSC digital television (DTV) receivers. In DTV transmission environment, echo delay often covers several hundreds symbols, which leads to very large-scale equalizer. One consequence of the large-scale equalizer is the very slow convergence, which combined with error propagation, inherent drawback of DFE, seriously deteriorates the performance of the receivers, especially in severe channels More working modes and corresponding robust control mechanism were given to help the equalizer converge to the stable state smoothly. Simulation results show that the improved equalizer can perform better, especially in the severe channels.

LOW COMPLEXITY LMMSE TURBO EQUALIZATION FOR COMBINED ERROR CONTROL CODED AND LINEARLY PRECODED OFDM

The turbo equalization approach is studied for Orthogonal Frequency Division Multiplexing (OFDM) system with combined error control coding and linear precoding. While previous literatures employed linear precoder of small size for complexity reasons, this paper proposes to use a linear precoder of size larger than or equal to the maximum length of the equivalent discrete-time channel in order to achieve full frequency diversity and reduce complexities of the error control coder/decoder. Also a low complexity Linear Minimum Mean Square Error (LMMSE) turbo equalizer is derived for the receiver. Through simulation and performance analysis, it is shown that the performance of the proposed scheme over frequency selective fading channel reaches the matched filter bound; compared with the same coded OFDM without linear precoding, the proposed scheme shows an Signal-to-Noise Ratio (SNR) improvement of at least 6dB at a bit error rate of 10-6 over a multipath channel with exponential power delay profile. Convergence behavior of the proposed scheme with turbo equalization using various type of linear precoder/transformer, various inter-leaver size and error control coder of various constraint length is also investigated.

On the Implementation of a Probabilistic Equalizer for Low-Cost Impulse Radio UWB in High Data Rate

This paper treats the digital design of a probabilistic energy equalizer for impulse radio (IR) UWB receiver in high data rate (100Mbps). The aim of this study is to bypass certain complex mathematical function as a chi-squared distribution and reduce the computational complexity of the equalizer for a low cost hardware implementation. As in Sub-MAP algorithm, the max* operation is investigated for complexity reduction and tested by computer simulation with fixed point data types under 802.15.3a channel models. The obtained re-sults prove that the complexity reduction involves a very slight algorithm deterioration and still meet the low-cost constraint of the implementation.

三变量等幂和对称式组三题

利用跨层相等数组和对称式组,将已有的几个等幂和数组推广成含3变量的等幂和对称式组,将其从一个数组推广成无穷多个数组,而且是三维空间的无穷组.

基于四元数的直接判决并行恒模均衡算法

近年来4元数理论成为各界学者研究的热点并被应用到许多领域。该文基于4元数自适应滤波算法对正交极化信道均衡问题进行研究。为了解决4元数恒模(QCMA)算法的相位模糊问题,该文将QCMA算法与4元数最小均方算法(QLMS)相结合提出一种4元数直接判决并行恒模(QCMA+DD-QLMS)算法。基于广义哈密顿实演算(GHR)的梯度运算规则对新的算法做了理论推导并进行MATLAB实验仿真,仿真结果表明该文所提算法不但能够解决QCMA算法相位模糊问题,还具有更小的稳态均方误差(MSE)。

光纤网络多通道数据均衡化分配方法

光纤网络数据动态能力较强,受噪声的影响,易降低数据的分配效率。为此,提出一种新的多通道数据均衡化分配方法。在建立通信模型后,计算节点的负载占比变化,并均衡处理待分配数据节点的负载占比。然后建立传输过程的连续表达函数,并通过最小均方差的约束,保证分配代价的合理性。最后,计算在同时间间隔内数据载波带宽的变化分配相同带宽变化的数据。实验结果表明:应用该方法后,数据分配结果的归一化幅度保持在±0.6之间,不同类型的数据分布规整;该方法的分配误差集中在2.59%~3.51%之间,具有较高的精准度。

采用自适应连续时间线性均衡器和判决反馈均衡器算法的一种16 Gbit/s并转串/串转并接口

该文在体硅CMOS工艺下设计了一种16 Gbit/s并转串/串转并接口(SerDes)芯片,该SerDes由4个通道(lanes)和2个锁相环(PLLs)组成。在接收器模拟前端(AFE)采用负阻抗结构连续时间线性均衡器(CTLE),得到22.9 dB高频增益,利用5-tap判决反馈均衡器(DFE)进一步对信号码间干扰(ISI)做补偿,其中tap1做展开预计算处理,得到充足的时序约束条件。采用最小均方根(LMS)算法自适应控制CTLE和DFE的补偿系数来对抗工艺、电源和温度波动带来的影响。测试结果表明,芯片工作在16 Gbit/s时,总功耗为615 mW。发射器输出信号眼高为143 mV,眼宽43.8 ps(0.7UI),接收器抖动容忍指标在各频点均满足PCIe4.0协议要求,工作温度覆盖–55℃~125℃,电源电压覆盖0.9 V±10%,误码率小于1E-12。

非均匀子带划分的宽带数字阵通道均衡算法

针对通道严重失配情况下,(加权)最小二乘法的频域均衡性能恶化和均匀子带分解的频域均衡占用过多硬件资源的问题,提出一种根据均衡滤波器的幅频特性非均匀划分频带实现均衡的方法。首先,根据幅度改善因子的大小来调整幅度划分的区间;然后,合并频点数小于滤波器阶数的相邻幅度区间,并求出对应的频带;最后,在非均匀划分的频带上实现信号的滤波补偿、合成。仿真结果表明,在通道严重失配情况下,相比均匀子带划分频域均衡方法,所提方法在幅度和相位改善因子上分别提高了8.68 dB和8.58 dB,在滤波器组数和阶数上分别降低了6组和8阶,可以提高子带频域均衡算法的硬件可实现性,改善宽带数字阵列雷达中脉冲压缩和数字波束形成的性能,增强雷达探测能力。

融合非物理模型的改进AM-RetinexNet图像增强算法

针对地下空间低照度图像色彩偏暗、亮度低且分布不均、增强后图像色偏和噪声高等问题,研究提出了融合非物理模型的改进AM-RetinexNet图像增强算法。该算法将RGB图像转换成HSV分量,利用HSV空间相互独立性实现图像亮度增强和色彩增强处理,其中S分量利用V分量提取的相关信息进行自适应调整,V分量采用融合直方均衡化与注意力机制优化的RetinexNet进行照度分量增强处理;将处理后HSV分量转化成RGB图像,并对图像进行自适应色彩恢复,得到照度增强图像。对比实验表明,在图像的细节处理、亮度整体增强处理、图像降噪和色彩视觉修正等方面该方法表现较好,测试指标中平均互信息(MI)、标准差(STD)、结构相似性(SSIM)、平均梯度(AG)、空间频率(SF)和峰值信噪比(PSNR)最佳,均值分别可达到6.18,70.62,0.56,13.29,36.53,39.22。