Equations(2)and(6)and the corresponding discussion in the paper[Chin.Phys.Lett.42,056301(2025)]have been corrected.These modiffcations do not affect the results derived in the paper.
The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ...The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.展开更多
第五代移动通信技术(5th-generation mobile communication technology,5G)网络对高速率、低时延、高可靠性的移动通信处理需求不断增加,对终端基带信道估计算法的高性能和低复杂度设计、矩阵处理动态范围提出挑战。针对上述问题,本文...第五代移动通信技术(5th-generation mobile communication technology,5G)网络对高速率、低时延、高可靠性的移动通信处理需求不断增加,对终端基带信道估计算法的高性能和低复杂度设计、矩阵处理动态范围提出挑战。针对上述问题,本文提出一种基于相关矩阵托普利兹(Toeplitz)特性的信道估计算法。依据信道的相干带宽特性计算信道相关矩阵并保留必要的较低矩阵阶数;基于相关矩阵的Toeplitz特性设计低复杂度的递归求逆算法,并针对加权矩阵乘法的元素重复性将矩阵乘法化简为矩阵点乘,简化加权矩阵运算;同时引入跟踪信噪比变化的缩放补偿因子对计算过程和结果分别进行缩放和补偿。理论分析和仿真结果显示,本文所提算法可在达到优异的信道估计性能条件下,有效降低运算复杂度,并极大降低算法矩阵处理的动态范围。展开更多
文摘Equations(2)and(6)and the corresponding discussion in the paper[Chin.Phys.Lett.42,056301(2025)]have been corrected.These modiffcations do not affect the results derived in the paper.
文摘The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.
文摘第五代移动通信技术(5th-generation mobile communication technology,5G)网络对高速率、低时延、高可靠性的移动通信处理需求不断增加,对终端基带信道估计算法的高性能和低复杂度设计、矩阵处理动态范围提出挑战。针对上述问题,本文提出一种基于相关矩阵托普利兹(Toeplitz)特性的信道估计算法。依据信道的相干带宽特性计算信道相关矩阵并保留必要的较低矩阵阶数;基于相关矩阵的Toeplitz特性设计低复杂度的递归求逆算法,并针对加权矩阵乘法的元素重复性将矩阵乘法化简为矩阵点乘,简化加权矩阵运算;同时引入跟踪信噪比变化的缩放补偿因子对计算过程和结果分别进行缩放和补偿。理论分析和仿真结果显示,本文所提算法可在达到优异的信道估计性能条件下,有效降低运算复杂度,并极大降低算法矩阵处理的动态范围。
