Mixed-scaling-rotation CORDIC (MSR-CORDIC) algorithm and architecture for high-performance vector rotational DSP applications

Abstract

The coordinate rotational digital computer (CORDIC) algorithm is a well-known iterative arithmetic for performing vector rotations in many digital signal processing (DSP) applications. However, the large number of iteration is a major disadvantage of this algorithm for its speed performance. Many researchers have proposed schemes to reduce the number of iterations. Nevertheless, in performing the existing CORDIC algorithms, the norm of the vector is usually enlarged so that extra scaling operations are required to deliver the normalized output. In this paper, we merge the two operation phases (microrotations and scaling phases) and propose a new vector rotational scheme called mixed-scaling-rotation coordinate rotational digital computer (MSR-CORDIC) algorithm. It can eliminate the overhead of the scaling operations that are inevitable in existing CORDIC algorithms; hence, it can significantly reduce the total iteration number so as to improve the speed performance. The proposed MSR-CORDIC can be applied to DSP applications, in which the rotational angles are known in advance [e.g., twiddle factor in fast Fourier transform (FFT) processor designs]. Moreover, most CORDIC algorithms generally suffer from the roundoff noise in the fixed-wordlength implementations. We also propose two schemes to control and reduce the impairment. Our simulation results show that the MSR-CORDIC algorithm can enhance the signal-to-quantization-noise ratio (SQNR) performance by controlling the internal dynamic range. We also investigate the first- and second-order statistical properties, including the mean and variance of the SQNR. Simulation results show that the MSR-CORDIC can enhance SQNR performance of both first- and second-order statistical properties. At the VLSI architecture level, we proposed a generalized MSR-CORDIC engine for the tradeoff between hardware complexity and quantization error performance. It can further reduce the hardware complexity when compared with the newly proposed extend elementary angle set CORDIC algorithm . The MSR-CORDIC scheme has been applied to a variable-length FFT processor design , and results in significant hardware reduction in implementing the twiddle factor operations.