The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable ...The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10<sup>-</sup><sup>16</sup>. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.展开更多
传统流水线结构的坐标旋转数字计算(Coordinate Rotation Digital Computer,CORDIC)算法的迭代周期固定,在实现反正切函数运算时存在硬件资源消耗过多、输出时延较长等问题,提出一种基于查找表的改进的CORDIC算法。该方法不仅通过缩减...传统流水线结构的坐标旋转数字计算(Coordinate Rotation Digital Computer,CORDIC)算法的迭代周期固定,在实现反正切函数运算时存在硬件资源消耗过多、输出时延较长等问题,提出一种基于查找表的改进的CORDIC算法。该方法不仅通过缩减有效数据位宽、合并迭代等手段节省了剩余角度Z路径的计算量,而且还消除了的增益因子的影响,有效的减小了硬件资源消耗及电路面积。分别使用matlab以及XILINX ISE进行理论建模分析仿真以及实际验证,结果表明:改进CORDIC算法在保证输出精度前提下,电路工作速度有一定提高,输出时延也有所减少,寄存器消耗节省50.6%,有效的降低了硬件资源消耗,适合实时性强、硬件资源有限的现代通信应用场合。展开更多
为了能够减少算法运算时间、减小稳态误差、提高收敛速度、增强跟踪性能以及增加抗噪性能,提出了1种变步长最小均方误差(least mean square,LMS)算法。针对现有LMS类算法在低信噪比下性能不佳、人为设定参数较多等缺点,基于反正切函数,...为了能够减少算法运算时间、减小稳态误差、提高收敛速度、增强跟踪性能以及增加抗噪性能,提出了1种变步长最小均方误差(least mean square,LMS)算法。针对现有LMS类算法在低信噪比下性能不佳、人为设定参数较多等缺点,基于反正切函数,且利用误差的相关函数动态调整步长。理论上分析了该算法复杂度、稳态失调、收敛速度、跟踪性能以及抗噪性能,并分别设计高信噪比和低信噪比的条件下进行实验仿真比较。理论分析结合实验仿真验证:该算法在高低信噪比时均具有较快的收敛速度和跟踪速度,能获得小的稳态误差和稳态失调,且需要设定的参数变量个数少。展开更多
针对已有的最小均方误差(least mean square,LMS)算法性能方面的缺陷,通过对步长选取问题的研究,提出了一种改进变步长LMS算法。基于原反正切函数引入输入信号反馈因子的二范数项,以实现对输入信号的实时跟踪,提高算法的跟踪能力。用误...针对已有的最小均方误差(least mean square,LMS)算法性能方面的缺陷,通过对步长选取问题的研究,提出了一种改进变步长LMS算法。基于原反正切函数引入输入信号反馈因子的二范数项,以实现对输入信号的实时跟踪,提高算法的跟踪能力。用误差相关值代替原算法中的误差平方项,提高其抗干扰能力,并加入补偿项,以补偿算法趋于稳态时的收敛速度。详细讨论了各个参数对算法收敛性、跟踪性、稳定性的影响及算法的抗干扰性。与已有算法进行的仿真结果对比表明,在高低信噪比情况下,改进算法在收敛速度、稳态误差,以及对时变系统跟踪能力等方面均呈现了优异的性能。展开更多
Frequency lock loops （FLL） discriminating algorithms for direct-sequence spread-spectrum are discussed. The existing algorithms can＇t solve the problem of data bit reversal during one pre-detection integral period....Frequency lock loops （FLL） discriminating algorithms for direct-sequence spread-spectrum are discussed. The existing algorithms can＇t solve the problem of data bit reversal during one pre-detection integral period. And when the initial frequency offset is large, the frequency discriminator can＇ t work normally. To solve these problems, a new FLL discriminating algorithm is introduced. The least-squares discriminator is used in this new algorithm. As the least-squares discriminator has a short process unit period, the correspond- ing frequency discriminating range is large. And the data bit reversal just influence one process unit period, so the least-squares discriminated result will not be affected. Compared with traditional frequency discriminator, the least-squares algorithm can effectively solve the problem of data bit reversal and can endure larger initial frequency offset.展开更多
文摘The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10<sup>-</sup><sup>16</sup>. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.
文摘传统流水线结构的坐标旋转数字计算(Coordinate Rotation Digital Computer,CORDIC)算法的迭代周期固定,在实现反正切函数运算时存在硬件资源消耗过多、输出时延较长等问题,提出一种基于查找表的改进的CORDIC算法。该方法不仅通过缩减有效数据位宽、合并迭代等手段节省了剩余角度Z路径的计算量,而且还消除了的增益因子的影响,有效的减小了硬件资源消耗及电路面积。分别使用matlab以及XILINX ISE进行理论建模分析仿真以及实际验证,结果表明:改进CORDIC算法在保证输出精度前提下,电路工作速度有一定提高,输出时延也有所减少,寄存器消耗节省50.6%,有效的降低了硬件资源消耗,适合实时性强、硬件资源有限的现代通信应用场合。
文摘为了能够减少算法运算时间、减小稳态误差、提高收敛速度、增强跟踪性能以及增加抗噪性能,提出了1种变步长最小均方误差(least mean square,LMS)算法。针对现有LMS类算法在低信噪比下性能不佳、人为设定参数较多等缺点,基于反正切函数,且利用误差的相关函数动态调整步长。理论上分析了该算法复杂度、稳态失调、收敛速度、跟踪性能以及抗噪性能,并分别设计高信噪比和低信噪比的条件下进行实验仿真比较。理论分析结合实验仿真验证:该算法在高低信噪比时均具有较快的收敛速度和跟踪速度,能获得小的稳态误差和稳态失调,且需要设定的参数变量个数少。
文摘针对已有的最小均方误差(least mean square,LMS)算法性能方面的缺陷,通过对步长选取问题的研究,提出了一种改进变步长LMS算法。基于原反正切函数引入输入信号反馈因子的二范数项,以实现对输入信号的实时跟踪,提高算法的跟踪能力。用误差相关值代替原算法中的误差平方项,提高其抗干扰能力,并加入补偿项,以补偿算法趋于稳态时的收敛速度。详细讨论了各个参数对算法收敛性、跟踪性、稳定性的影响及算法的抗干扰性。与已有算法进行的仿真结果对比表明,在高低信噪比情况下,改进算法在收敛速度、稳态误差,以及对时变系统跟踪能力等方面均呈现了优异的性能。
文摘Frequency lock loops （FLL） discriminating algorithms for direct-sequence spread-spectrum are discussed. The existing algorithms can＇t solve the problem of data bit reversal during one pre-detection integral period. And when the initial frequency offset is large, the frequency discriminator can＇ t work normally. To solve these problems, a new FLL discriminating algorithm is introduced. The least-squares discriminator is used in this new algorithm. As the least-squares discriminator has a short process unit period, the correspond- ing frequency discriminating range is large. And the data bit reversal just influence one process unit period, so the least-squares discriminated result will not be affected. Compared with traditional frequency discriminator, the least-squares algorithm can effectively solve the problem of data bit reversal and can endure larger initial frequency offset.
