基于CORDIC的精确快速幅相解算方法

针对传统CORDIC算法进行高精度幅度相位解算时迭代次数过多、时延较长、相位收敛较慢等局限，提出了一种基于最佳一致逼近方法的幅度与相位补偿算法，即利用传统CORDIC算法迭代一定次数后得到的向量信息，采用最佳一致逼近方法对幅度和相位分区间进行一阶多项式补偿，有效提高了计算精度.仿真及实测结果表明，对传统CORDIC算法4次迭代后的结果进行补偿，幅度相对误差可达到10^-5量级、相位绝对误差可达到10^-5度量级，最大输出时延不大于100ns.在使用部分专用乘法器的条件下，寄存器消耗降低了42.5%，查找表消耗降低了15.5%.采用该补偿算法，每多一次CORDIC迭代其相位精度可提高约一个数量级.因此，本文提出的补偿CORDIC算法在迭代次数、计算精度等方面优于传统CORDIC算法，适合于高精度计算的场合.

High Precision & Speed Amplitude and Phase Solving Algorithm Based on CORDIC

An amplitude and phase compensation algorithm based on the best uniform approximation method is proposed.It overcomes the limitations of the traditional CORDIC when used in high-precision calculation of the amplitude and phase,such as too many iterations,long delay time,and slow phase convergence.By utilizing the vector information obtained from several iterations of traditional CORDIC,sectionalized first-order polynomial of best uniform approximation compensating for the amplitude and phase results is constructed,thus efficiently improving the computation accuracy.Simulation and test results show that,by using the proposed algorithm with 4 iterations of traditional CORDIC,the relative error of amplitude can reach 10^-5 level,and the absolute error of phase can reach 10^-5 degree level.At the same time,the maximum delay time is no more than 100 ns.And with the use of some dedicated multipliers,the registers and LUTs are reduced by 42.5% and 15.5% respectively.Moreover,the phase precision can be increased approximately one order with one more iteration.Hence,compared to conventional CORDIC algorithm,the proposed algorithm improves in iterations and computation precision,and is suitable for high-precision computation applications.