Implementation of Cordic Algorithm Using

7/25/2019 Implementation of Cordic Algorithm Using

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IMPLEMENTATION OF CORDIC

ALGORITHM USING MATLAB & VHDL FOR

WLAN RECEIVER

Mr. Sandeep Bidwai1, Prof. Dr. S.P. Patil2and Mr. Saylee S. Bidwai3

[email protected]

Abstract:

This paper is focused on the CORDIC algorithm for wireless LAN.The primary task is to create a VHDL description for CORDIC

vector rotation algorithm. The basic work has been carried out inMATLAB. The VHDL implementation of the CORDIC algorithm isbased on the results obtained from the MATLABs simulationenvironment. The accuracy of vector value in the receiver dependson its number of bits. The main task is to make the calculated anglevalue point the vector to the same constellation point, not to nearestone. This is the cause that determines the required accuracy of theangle calculation. The program in MATLAB calculates the first 20

steps of the CORDIC algorithm and displays how accurate eachstep is. It takes the closest vectors in the signal constellation asinput. CORDIC moduld to which the calculated angle theta is givenas input to comput the sine and cosine functions using Simulink.Last Step includes the VHDL implementation of CORDIC and thesimulation results.

Key Words: CORDIC, MATL AB,VHDL, OFDM , WLAN,

I INTRODUCTION:The CORDIC (COordinate Rotation DIgital

Computer) algorithm was developed by Volder in 1959. Itrotates the vector, stepbystep, with a given angle.Additional theoretical work has been done by Walther in

1971. The main principle of CORDIC are calculations basedon shiftregisters and adders instead of multiplications, whatsaves much hardware resources.All trigonometric functions

can be computed using vector rotation. CORDIC is used for

polar to rectangular and rectangular to polar conversions and

also for calculation of trigonometric functions, vectormagnitude and in some transformations, like discrete Fourier

transform (DFT) or discrete cosine transform (DCT). In

particular case, the CORDIC algorithm is used in wireless

LAN (WLAN) by receivers.

This paper is organized in following five steps. Step

first contains the CORDIC algorithm, its architecture andWLAN with OFDM system. Step second deals with the

implementation of OFDM system in WLAN using FFT/IFFTin MATLAB. Step third includes the implementation of

CORDIC algorithm in MATLAB for the WLAN receiver in

order to find out the angle of incomming vectors fromtransmitter. Step four deals with CORDIC moduld to which

the calculated angle theta is given as input to comput the sine

and cosine functions using Simulink. Step five includes the

VHDL implementation of CORDIC and the simulation

results.

II. CORDIC algorithm for Sine and cosine

1 . Arithmatics

Figure 1 represents the block diagram of conventionalCORDIC algorithm , based on ripple carry adders or sub

tractors

Fig.1 Block diagram of cordic

An adder/subtractor (A/S), depending on a selection input,

performs an addition or a subtraction. This input indicates

whether an operand is negative. The basic cell of A/S is

decomposed by two functions with 4 bits input each. One ofthem is for calculating the output and another to transmit thecarry. According to this an Nbit A/S can fit in (2N+1)/2CLBs (configurable logic block). The additional half CLB isrequired for introducing the least significant bit (LSB) one in

case of the substraction. The critical path here is indicated bythe ripple carry propagation and the routing delay of the A/S

wire. This net has a fanout of 2N in this case. It decreasesthe performance of the circuit and it is the main disadvantage

of conventional CORDIC implementations. As the solution

to this, redundant arithmetic could be used to increase the

speed of the CORDIC. Implementation avoids the carry

propagation from the LSB to the most significant bit (MSB),due to its carryfree property. Redundant arithmetic is goodto accelerate those operations, which have a long propagation
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delay. On the other hand redundant arithmetic also has some

disadvantages. For example, it is impossible to detect the

sign of a redundant number without checking all the digits

which expects a propagation from the MSB to the LSB.

Another problem, that the redundant arithmetic uses digit set{1,0,1}, and needs more hardware resources to executesimple tasks, than the conventional one which uses digit set{1,1}.According to results of the research, the redundantarithmetic is more accurate, but it needs much morehardware than the conventional arithmetic and for this reason

conventional arithmetic has been used in this work. [2]

III. CORDIC module design

Fig. 2 CORDIC module to implement Sine and Cosine

Above fig. shows the CORDIC module forimplementating Sine and cosine Trignometric function using

Embedded MATLAB function block.

The basic equations for vector rotation are [4]x = cos()[x-ytan()]

y = cos()[y+xtan()] = Rotation angle. (1)where x and y are original coordinates before rotation and xand y are the coordinates after rotation. This equatationcan

be simplified by assuming that the tangent is a power of 2.

Tan() = + 2^(-n) (2)Then any angle of rotation can be obtained by performingsuccessive smaller rotations. This assumption help us to

write equation (1) in the form of iterative operations.

Xn+1 = Kn [xn-yndn 2^(-n)]

Yn+1 = Kn [yn+xndn 2^(-n)]

Zn+1 = zndnatan 2^(-n)Kn = cos(atan 2^-n)) = 1 + 1+ 2^(-2n)

Dn = +1 (3)These equations can be used in two different modes: rotation

mode and vector mode. In rotation mode, the input vectorrotates by a specific angle. In vector mode, the input vector

rotates to the x axis.In rotation mode the following equations are used:

Xn+1 = Kn [xnyndn 2^(-n)]Yn+1 = Kn[yn + xndn 2^(-n)]

Zn+1 = zndnatan2^(-n)]

Dn =-1 if zn


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maintained 24 bits. The inputs are applied in the CORDIC

formats in 1QN format. And the respective output is

observed in 2 QN format by performing the simulation of

test benches of the module in Modelsim simultor.

Figure 4 CORDIC module in VHDL

The inputs given to module in terms of Z0 is in the CORDIC

data format. The output is observed in x(n) and y(n) i.e.

cosine and sine functions as discussed previously.

Fig. 5 output wave forms for Main CORDIC module

CONCLUSIONThe CORDIC module designed in MATLAB

simulink has more flexibility to operate for the

implementation of the trignometric function Sine and

Cosine. The CORDIC rotations can be used to perform the

operations on the given input angle to rotate it to the desired

direction and magnitude and phase can be computed. Finnaly

the VHDL module varifies the performance of CORDIC

module with the help of Modelsim simulator.

REFERENCES

[1]

Valls. J. Kuhmann. M. Parhi, K.K. Efficient Mapping of CORDICAlgorithm on FPGA, Signal processing systems 2000 . IEEEworkshop, pp336-343, 11-13 oct. 2000.

[2] Anastasia Lashko, Oleg Zakaznov, CORDIC implementation usingVHDL for WLAN receiver,

[3] Benjamin Heyne, Jurgen Gotze ,A pure cordic based FFT forreconfigurable digital signalprocessing

[4] Volder J.E.: "The CORDIC Trigonometric Computing Technique", IRETrans. Electronic Computers, vol. EC8, pp 330334, 1959.

BIO DATA OF AUTHOR(S)

Mr. Sandeep S. Bidwai

Working as a lecturer in E & TC Dept, at ADCETAshta, Dist- Sangli (MS- INDIA). Completed his

BE (E & TC) from BAM University Aurangabad (MS)

Currently doing ME (Electronics)from Sivaji UniversityKolhapur (MS). He has 3 Yrs of teaching experience

& field of interestVLSI design

Prof.Dr. S. P. PatilPresently working as Principal ADCET Ashta, Dist-

Sangli (MS- INDIA). He has completed his BE, ME(Electronics) & PhD from Shivaji University, Kolhapur

& He has 21Yrs of experience & his areas of interest are

Signal processing & biomedical engineering.

Mrs. Saylee S. Bidwai

Working as a lecturer in E & TC Dept, at ADCETAshta, Dist- Sangli (MS- INDIA). Completed her

BE (Electronics) from SRT University Nanded (MS)

Currently doing ME (Electronics)from Sivaji UniversityKolhapur (MS). She has 3.5 Yrs of teaching experience

& field of interestVLSI design.

Implementation of Cordic Algorithm Using

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