Design of Cascaded CORDIC Based on Precise Analysis of Critical Path

Abstract

A conventional coordinate rotation digital computer (CORDIC) has a low throughput rate due to its recursive implementation of micro-rotations. On the contrary, a fully-pipelined cascaded CORDIC provides a very high throughput rate at the cost of high complexity and large area. In this paper, possible design choices of cascaded CORDIC are explored over a wide range of operating frequencies, throughput rates, latency, and area complexity. For this purpose, we present a fine-grained critical path analysis of the cascaded CORDIC in terms of bit-level delay. Based on the propagation delay estimate, we propose an algorithm for determining the required number of pipeline stages and locations of the pipeline registers in order to meet the time constraint in a particular application. A hybrid cascaded-recursive CORDIC is also proposed to increase the throughput rate, and to reduce the latency and energy per sample (EPS). From synthesis results, we show that the proposed pipelined cascaded CORDIC with only four pipeline stages requires 31.1% less area and 29.0% less EPS compared to a fully-pipelined CORDIC. An eight stage pipelined recursive cascaded CORDIC provides 18.3% less EPS and 40.4% less area-delay product than a conventional CORDIC.