Abstract
An efficient, noniterative Radix-8 (NR-8) coordinate rotation digital computer (CORDIC) algorithm is proposed for low-latency and high-efficiency computation of the functions of sine, cosine, or the phase shift, with which the values of the functions are precisely computed by only using the angle in a narrow range of [0, π/12] rather than in a wide angle range of [0, π/2]. This algorithm is expressed by a formula that simplifies the traditional iterative processes by using a complex multiplier. The results obtained from the simulation and the experiment on an FPGA show that the NR-8 CORDIC algorithm operates well, with which the 16-bit precision output is extremely precise, with only 0.012% of the absolute error for computing the sine or cosine function with a step of 0.001°. Compared with the best conventional CORDIC algorithm, the clock latency of this algorithm significantly decreases down to less than 50%, only needs half of the logic resources and consumes half of the power. This algorithm also takes advantages over other newly improved CORDIC algorithms and requires less than half of the clock latency, even for a 23-bit precision output. Therefore, this algorithm could provide a potential application in real-time systems such as radar digital beamforming.
Highlights
As one of the most common transcendental functions, the sine or cosine function has been widely used in real-time digital signal processing systems, such as radar, ultrasound, robotics, communication and so on [1,2,3,4,5,6,7]
A new noniterative Radix-8 (NR-8) coordinate rotation digital computer (CORDIC) algorithm is proposed for low-latency steps were taken: (1) The NR-8 CORDIC algorithm was derived from the conventional Radix-2 implementation on FPGAs
We propose a noniterative computation structure of the R-8 CORDIC algorithm by iterating the data in a narrow input angle interval, using an explicit formula of solution, simplifying the scale factor and transforming the input variables x0 and y0 to accelerate the convergence of the algorithm
Summary
As one of the most common transcendental functions, the sine or cosine function has been widely used in real-time digital signal processing systems, such as radar, ultrasound, robotics, communication and so on [1,2,3,4,5,6,7]. The CORDIC algorithm often requires many iterations to converge, application to adaptive beamforming [5], and the pipeline level m depends on the m-bit precision. A new noniterative Radix-8 (NR-8) CORDIC algorithm is proposed for low-latency steps were taken: (1) The NR-8 CORDIC algorithm was derived from the conventional Radix-2 implementation on FPGAs. In the process of the development of an NR-8 CORDIC algorithm, CORDIC one. Selected range of the iteration angle and realize a noniterative formula of the CORDIC algorithm; As a result, the algorithm can reduce 7–17 clock latenciesmodule of the readily conventional (16-bit besides, the algorithm can be accelerated by the multiplier available in FPGAs precision) algorithm to a three-clock latency, needs less logic resources and consumes less power. Conclusion is made according to the results obtained from the above sections
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