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

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 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. Index Terms-Angle recording (AR), coordinate rotational digital computer (CORDIC) algorithm, extended elementary-angle set (EEAS), trellis-based searching (TBS).

Area-energy efficient CORDICs using new elementary-angle-set and base-2 exponent expansions scheme

“…But AR-CORDICs need additional encoders to pre-code the input angle as a linear combination of a set of selected elementary angles of micro-rotation [19 22]. In addition, many AR-CORDICs' input angles are not arbitrary but even needs to be known in advance [23][24][25][26]. High-Radix CORDIC can rotate multiple angles at a time but its rotation factor at each stage is a variable value which requires either a large ROM at the final compensation stage or sophisticated technique at each stage to compensate the vector [27 28].…”