A unified view for vector rotational CORDIC algorithms and architectures based on angle quantization approach

Vector rotation is the key operation employed extensively in many digital signal processing applications. In this paper, we introduce a new design concept called Angle Quantization (AQ). It can be used as a design index for vector rotational operation, where the rotational angle is known in advance. Based on the AQ process, we establish a unified design framework for cost-effective low-latency rotational algorithms and architectures. Several existing works, such as conventional COordinate Rotational DIgital Computer (CORDIC), AR-CORDIC, MVR-CORDIC, and EEAS-based CORDIC, can be fitted into the design framework, forming a Vector Rotational CORDIC Family. Moreover, we address four searching algorithms to solve the optimization problem encountered in the proposed vector rotational CORDIC family. The corresponding scaling operations of the CORDIC family are also discussed. Based on the new design framework, we can realize high-speed/low-complexity rotational VLSI circuits, whereas without degrading the precision performance in fixed-point implementations.