Article

A high-performance/low-latency vector rotational CORDIC architecture based on extended elementary angle set and trellis-based searching schemes

Dept. of Electr. Eng., Nat. Central Univ., Chung-li, Taiwan
IEEE Transactions on Circuits and Systems II Analog and Digital Signal Processing 10/2003; DOI: 10.1109/TCSII.2003.816923
Source: IEEE Xplore

ABSTRACT The coordinate rotational digital computer (CORDIC) algorithm is a well-known iterative method for the computation of vector rotation. For applications that require forward rotation (or vector rotation) only, the angle recoding (AR) technique provides a relaxed approach to speed up the operation of the CORDIC algorithm. In this paper, we further apply the concept of AR technique to extend the elementary angle set in the microrotation phase. This technique is called the extended elementary-angle set (EEAS) scheme. The proposed EEAS scheme provides a more flexible way of decomposing the target rotation angle in CORDIC operation, and its quantization error performance is better than the AR technique. Meanwhile, to solve the optimization problem encountered in the EEAS scheme, we also proposed a novel search algorithm, called the trellis-based searching (TBS) algorithm. Compared with the greedy algorithm used in the conventional AR technique, the proposed TBS algorithm yields apparent signal-to-quantization-noise ratio (SQNR) improvement. Moreover, in the scaling phase of the EEAS-based CORDIC algorithm, we suggest a novel scaling operation, called Extended Type-II (ET-II) scaling operation. The ET-II scaling operation applies the same design concepts as the EEAS scheme. It results in much smaller quantization error than conventional Type-I scaling operation in the numerical approximation of scaling factor. By combining the aforementioned new schemes, the proposed EEAS-based CORDIC algorithm can improve the overall SQNR performance by up to 25 dB compared with previous works. Also, given the same target SQNR performance, we require only about 66% iteration number in the iterative CORDIC structure, or use 66% hardware complexity in the parallel CORDIC structure compared with conventional AR technique. Hence, high-performance/low-latency CORDIC very large-scale integration architectures can be achieved without degrading the SQNR performance.

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    • "Using this recoding schemes the total number of iterations could be reduced to less than half of the conventional CORDIC algorithm for the same accuracy. Wu et al [7] have suggested an AR scheme based on an extended elementary-angle-set (EEAS), that provides a more flexible way of decomposing the target rotation angle. In the EEAS approach, the set S EAS of the elementary-angle set is extended further to S EEAS = "
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    • "and . The iterations for micro-rotation phase as well as the scaling phase could be implemented in the same architecture to reduce the hardware cost, as shown in Fig. 3. 3) Parallel Angle Recoding: The AR methods [19], [21] could be used to reduce the number of iterations by more than 50%, when the angle of rotation is known in advance. However, for unknown rotation angles, their hardware implementation involves more cycle time than the conventional implementation, which results in a reduction in overall efficacy of the algorithm. "
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