基于FPGA的CORDIC算法实现

针对传统CORDIC算法延时大,消耗资源多的缺点,在平行CORDIC算法的基础上提出了一种优化的平行算法,利用二进制转两极算法和微旋转角度编码对低部和高部的旋转方向进行预测,并在高部旋转中利用正反旋转抵消的策略来进一步减少旋转次数,提高运算速度。采用FPGA对提出的算法进行了硬件设计和验证,结果表明,计算迭代次数少,资源消耗少,精度较传统算法来说都有了明显改善。     

基于改进CORDIC算法的数字预失真实现

针对传统CRODIC算法存在的角度扩展、迭代复杂度等问题,在旋转模式下提出一种改进型CORDIC算法。对于旋转角度范围的扩展,采取将向量限制在第一和第四象限,旋转最后再根据输入向量符号判断旋转角度值;对于迭代复杂度,采用跳跃旋转方式来减少迭代次数。最后在Quartus软件上实现了该改进算法,并且将改进后的CORDIC算法应用于数字预失真技术,在FPGA上设计实现。仿真与实验结果表明:与传统的CORDIC算法相比,改进算法减少了硬件的开销,运算速度和精度都有很大改进,能够快速提取预失真参数,显著提高功率放大器的线性度。     

基于CORDIC算法的高速高精度NCO的FPGA设计

介绍一种利用矢量旋转的CORDIC(Coordination Rotation DIgital Computer)算法,相比较传统NCO采用的查找表算法,证明查找表算法运算速度已不适用于高速宽带数字接收机以及扩频通信的应用,为了实现高速正交数字混频器中的数控振荡器(NCO),采用CORDIC算法产生正余弦信号的实现过程,给出采用ALTERA的stratix系列FPGA中设计数控振荡器的顶层设计结构以及仿真结果,证明基于此算法采用FPGA的可行性设计.     

CORDIC算法的一种补码实现结构设计

根据CORDIC算法原理,分析了该算法角度旋转范围缺陷,提出360°覆盖的角度旋转算法结构;推导出利用补码实现CORDIC算法的迭代运算单元结构,并根据该补码运算原理设计了CORDIC补码迭代运算单元和方向向量发生器的实现结构.     

高性能HPOR CORDIC算法及实现

CORDIC算法在通信和图像处理等各个领域有着广泛的应用,但是浮点CORDIC由于迭代延时大且实现复杂没有得到很好的应用,本文提出了一种修正浮点CORDIC算法：高精度顺序迭代HPORCORDIC。该算法以接近定点的运算代价完成浮点运算迭代,运算速度和硬件实现规模与定点CORDIC相当,运算精度与浮点CORDIC相当,克服了定点CORDIC运算精度差,浮点CORDIC迭代延时大、实现复杂的问题。该算法既可用于通用微处理器的设计,也可用于高性能DSP的设计。     

基于CORDIC旋转器的基-3 FFT算法高效设计

设计出一种可以用于FPGA高效实现的基-3 FFT算法,采用改进的三端前馈延迟转换器结构,优化了延迟和运算过程。针对蝶形运算中复数乘法器占据大量内存的问题,引入了CORDIC旋转器实现输入与旋转因子相乘的运算,可以降低乘法运算的复杂度,该CORDIC旋转器采用改进的高基CORDIC算法,解决了传统的CORDIC算法迭代次数多、延迟大的问题,从而达到高吞吐率要求。该基-3 FFT算法以寻址变序、流水处理的方式,可以满足最高运行频率为404 MHz的FFT处理要求。与基于传统复数乘法器的基-3 FFT算法相比,基于CORDIC旋转器的基-3 FFT算法使功耗平均减少了22%,使总延迟平均减少了29%。     

高速高精度固定角度旋转CORDIC算法的设计与实现

固定角度旋转的CORDIC(Coordinate Rotation Digital Computer)算法已经广泛的应用于高速数字信号处理、图像处理、机器人学等领域.针对固定角度旋转CORDIC算法在相位旋转过程中,存在数据吞吐率较高、占用硬件资源较多且资源消耗量大等缺点,提出了利用混合CORDIC算法,将角度旋转分为单向角度旋转和一次角度估计旋转两部分.本文根据欠阻尼理论,将固定角度旋转采用单向旋转CORDIC算法实现,减少了流水线的级数和迭代符号位的判决,然后通过对角度估计旋转的二进制表示,修正常数因子,再根据角度映射关系进行相关处理,完成高速高精度坐标旋转.最后在硬件平台上进行了仿真实验.实验结果表明,在误差范围一定的前提下,混合算法进一步的减少了迭代次数,并且资源消耗较低,提高了数据吞吐率.     

免缩放因子双步旋转CORDIC算法

集成电路设计中经常使用CORDIC算法实现高效的向量旋转操作.当前对该算法的研究热点集中在减少该算法的迭代次数、扩展其收敛范围以及降低缩放因子补偿操作的代价等问题上.本文提出免缩放因子的双步旋转CORDIC算法使用双步旋转策略,减少了免缩放因子CORDIC算法的迭代次数,将收敛区间扩展到了整个圆周区间.实验结果表明,该算法保持高计算精度的同时减少了迭代次数和面积消耗.     

M倍降速流水线技术实现正切余切

随着超大规模集成电路（VLSI, Very Large Scale Integrated circuites）技术的飞速发展,经常需要用硬件快速精确地进行三角函数的计算,而坐标旋转算法（CORDIC, Cordinate Rotational Digital Computer）能够将多种难以用硬件电路直接实现的复杂三角函数运算分解为统一的加减、移位操作,极大地降低了硬件设计的复杂性。这里在Circular CORDIC和Linear CORDIC的基础之上,搭建了正切余切模块的计算。介绍了M倍降速递归流水线技术,以及在保证车交II夹运算速度的前提下,如何尽可能减少系统的逻辑资源占用。     

OFDM系统中同步算法的FPGA 实现

给出了一种用于 OFDM 系统中可同时完成帧起始位置估计和载波频偏估计／补偿的同步算法及其 FPGA 实现方法。采用量化的方法对该不需要额外同步序列的估计算法进行了改进,提高了载波频偏的估计精度,并在数字域进行了频偏校正。在硬件实现上,利用 CORDIC 算法能够有效计算三角函数的特点,把频偏估计和频偏校正过程中的反正切运算和角度旋转操作转化成加法和移位操作,实现了计算精度、运算速度和硬件资源利用三方面性能的兼顾。     

A programmable CORDIC chip for digital signal processingapplications

A chip implementing the coordinate rotation digital computer (CORDIC) algorithm is described. It contains a 10-MHz 16-b fixed-point CORDIC arithmetic unit, 2-kb RAM, a controller, and input/output (I/O) registers. A modified data-path architecture allows cross-wire free data flow. The chip design involved development of optimized carry-select adders and a modified programmable-logic-array (PLA) cell layout, which allows speed increase in single-layer metal technology. The authors designed, fabricated, and tested a general-purpose fully parallel programmable CORDIC chip in CMOS technology and developed optimal iteration sequences     

FPGA实现基于施密特正交化的自适应算法

在自适应波束形成算法理论基础上,将修正施密特正交化算法运用在基于三角分解的样本矩阵求逆算法中,提出了基于修正施密特正交化算法的三角分解矩阵求逆算法,并给出了具体的可编程门阵列硬件实现结构。该硬件结构的实现采用了坐标旋转数字计算机代替该算法中的除法运算,有效地节约了硬件资源消耗和结构时延。通过硬件仿真对计算结果进行分析研究,实验证明该硬件结构不仅有良好的数值稳定性,能对干扰有效抑制,且硬件资源消耗少,高度模块化。     

IS-CORDIC: a fixed-point inverse recoded single iteration CORDIC architecture

This paper presents a novel modified Coordinate Rotation Digital Computer (CORDIC) architecture that computes values of sine and cosine in a single cycle. The proposed method utilises angle-recoding technique to design a modified CORDIC algorithm. Multiple iterations are merged in the modified algorithm using memory storage for initial iterations and employing inverse recoding to generate constant multiplication factors for the remaining iterations. Scale factor of the algorithm remains constant, as these factors are independent of intermediate directions of rotation. In addition, the architecture is mapped onto a single CORDIC computation element that requires only a single cycle to compute the result. These multiplications are implemented using dedicated hardware multipliers in Field Programmable Gate Arrays and customised fixed-point multiplication techniques for Application Specific Integrated Circuits. Implementation results show that the proposed IS-CORDIC architecture is 7.9 times more efficient than basic CORDIC and has reduced area-delay product than current state of the art implementations.     

A Modified CORDIC FPGA Implementation for Wave Generation

This paper presents a modified coordinate rotation digital computer (CORDIC) algorithm implemented in parallel architecture to generate sine and cosine waveform. Since CORDIC is a combination of only additions and shifts, it can be efficiently implemented in hardware. The proposed algorithm further approximates the way of computing rotation angle based on Taylor series in order to reduce the usage of Read-Only-Memory (ROM) table. Thus area and power is reduced due to partial usage of ROM storage. The precision remains the same as the original algorithm. The modified 32-bits pipeline CORDIC are implemented in Spartan XC3S500E device using Xilinx ISE 12.3 design suite. The result is compared with original CORDIC and Xilinx coregen in device utilization. It is shown that the logic usage is 31 FFs and 285 FFs less than the original design and Xilinx core, respectively. When compared with the original design, the signal power and total power reduction at 40 MHz clocks are 7.69 % and 1.35 %, respectively. The bit error remains at 10^?8 dB level. The SNR of modified CORDIC is about 2 dB lower, which is acceptable in wave generation.     

基于CORDIC算法的Hough变换及其FPGA实现

为了既能提高Hough变换的计算速度,同时能保持精度以及不大的存储量,讨论了Hough变换和CORDIC算法各自的特点,论证了用CORDIC算法实现Hough变换的可行性。研究了采用流水线构架的CORDIC算法,提出了一种基于CORDIC混合基算法的特殊处理器来计算Hough变换,使迭代次数减少1/4,并可显著改善迭代的速度。这种方法占用资源面积比较小,并且结构规则简单,适合于FPGA设计实现,具有较高应用价值。     

采用CORDIC算法的直接数字频率合成器的设计

为了实现CORDIC（Coordinate Rotation Digital Computer）算法在DDS（Direct Digital Frequency Synthesis）中的应用,文章介绍了CORDIC算法的一般法则和DDS的基本结构,提出了一种流水线型的CORDIC算法,并应用于FPGA（Field Programmable Gate Array）设计中,最后给出了基于ModelSim的仿真结果。     

Modified CORDIC algorithm with reduced iterations

Presents a modified CORDIC algorithm that offers a considerable latency time reduction and chip area savings when compared with the original CORDIC method. The operations used are adds, shifts, and multiplication or division.<>     

Ultra Low Power CORDIC Processor for Wireless Communication Algorithms

We designed and implemented an ultra low power CORDIC processor which targets the implementation of advanced wireless communications algorithms based on Givens rotations and Householder reflections. We propose a modified CORDIC algorithm and architecture, and we elaborate on the low power architectural and algorithmic techniques for minimizing its power consumption. Our CORDIC implementation consumes, in rotate mode, on average 50 W @ 10 MHz under 1 V supply voltage in a .25 m technology.