CORDIC-Based Processor

ECE 734

Project Presentation

05/08/02

Jui-Ning Cheng

Motivation

MAC unit computing is not efficient enough when the DSP algorithm includes more complicated functions, such as trigonometric, exponential, and logarithm.

CORDIC (COordinate Rotation DIgital Computer) is an iterative algorithm to perform vector rotations by arbitrary angles using only shifts and adds.

Algorithm

The basic CORDIC iteration equations at the i-th step are:

m: Coordinate parameter (1, 0, -1) i: Rotation direction (Rotation/Vectoring mode)

S(m,i): Shift sequence m,i: Rotation angle

Km,i: Scaling factor

i

imSiii ymxx ,

1 2

i

imSiii xyy ,

1 2

imiii zz ,1

Architecture

BarrelShifters

X Reg x(n)

BarrelShifters

MUX MUX

+ / -

x

x'

y(n) Y Reg

MUX MUX

+ / -

y

y'

i i

+ / -

Z Reg

z(i+1)

z(i)

i

a(n-1)..a(1)a(0)

generator

sign(xi)sign(yi)sign(zi)

rotation

vectoring

i

Pipelined Structure

Complexity is increased : Arithmetic operators are mapped into a dedicated unit, and also the additional registers between each stage.

Maximum throughput: Clock drives only one CORDIC operation per cycle.

BasicCORDICProcessor

REG

BasicCORDICProcessor

REG

BasicCORDICProcessor

REG

x

y

x'

y'

Implementation Examples

We classify these particular DSP function into three categories:

 

(a)Linear transformations: discrete Fourier transform, Chirp-Z transform, discrete Hartley transform, and fast Fourier transform.

(b)Digital filters: orthogonal digital filters, and adaptive lattice filters.

(c)Matrix based digital signal processing algorithms: QR factorization, with applications to Kalman filtering, eigenvalue and singular value decompositions.

This project will exam one example in each category to illustrate the utilization of CORDIC-based processor array.