CORDIC Algorithm for WLAN

Mr. Gadekar S. R Int. Journal of Engineering Research and Applications www.ijera.com
ISSN: 2248-9622, Vol. 5, Issue 8, (Part - 2) August 2015, pp.01-04
www.ijera.com 1 | P a g e
CORDIC Algorithm for WLAN
Mr. Gadekar S. R.
(Department of Electronics Engineering, Pune University, Maharashtra)
ABSTRACT
This research aims to implement CORDIC Algorithm for WLAN. The design is coded using VHDL language
and for the hardware implementation XILINX Spartan-3FPGA is used. VHDL implementation is based on
results obtained from Xilinx ISE simulation.
Keywords: CORDIC, FPGA, implementation, WLAN.
I. INTRODUCTION
CORDIC (for COordinate Rotation DIgital
Computer), also called as the digit-by-digit method
and Volder's algorithm. It is a simple and efficient
algorithm to calculate hyperbolic and trigonometric
functions. It is commonly used when no hardware
multiplier is available (e.g., simple microcontrollers
and FPGAs) as the only operations it requires are
addition, subtraction, bit shift and table lookup.
The CORDIC Algorithm calculates the angle of
received vector in a signal constellation by means of
arctangent function and it is used in receivers to find
frequency offset and phase shift.
II. Wireless LAN
A wireless LAN (WLAN) is a wireless computer
network that connects two or more devices using a
wireless distribution method within a limited area
such as a home, school, computer labs, or office
building. By using this WLAN users can move
around within a local coverage area and still be
connected to the network, and can provide a
connection to the wider Internet. Most modern
WLANs are based on IEEE 802.11 standards,
marketed under the Wi-Fi.
III. CORDIC ALGORITHM
3.1 Mode of operation
CORDIC rotator works in two modes: Rotation
& Vectoring [3].
3.1.1 Rotation mode
This explanation shows how to use CORDIC in
rotation mode to calculate the sine and cosine of an
angle and assumes the desired angle is given in
radians and represented in a fixed point format. To
determine the sine or cosine for an angle, the y or x
coordinate of a point on the unit circle corresponding
to the desired angle must be found.
Using CORDIC, we would start with the
vector :
Fig. 1 An example for CORDIC algorithm
In the first iteration, this vector is rotated 45°
counter clockwise to get the vector . Successive
iterations rotate the vector in one or the other
direction by size-decreasing steps, until the desired
angle has been achieved. Step i size is arctan(1/(2i−1
))
for i = 1, 2, 3, ….
More formally, every iteration calculates a rotation,
which is performed by multiplying the vector
with the rotation matrix .
=
The rotation matrix is given by:
=
Using the following two trigonometric identities:
the rotation matrix becomes:
RESEARCH ARTICLE OPEN ACCESS

The expression for the rotated vector then
becomes:
Where and yi-1 are the components of .
Restricting the angles yi so that takes on the
values +/- , the multiplication with the tangent can
be replaced by a division by a power of two, which is
efficiently done in digital computer hardware using a
bit shift. The expression then becomes:
=
Where
and can have the values of −1 or 1, and is used to
determine the direction of the rotation; if the angle
is positive then is +1, otherwise it is −1.
can be ignored in the iterative process and then
applied afterward with a scaling factor:
K (n) = =
which is calculated in advance and stored in a table,
or as a single constant if the number of iterations is
fixed. This correction could also be made in advance,
by scaling and hence saving a multiplication.
Additionally it can be noted that:
K=
to allow further reduction of the algorithm's
complexity.
After a sufficient number of iterations, the
vector's angle will be close to the wanted angle β. For
most ordinary purposes, 40 iterations (n = 40) is
sufficient to obtain the correct result to the 10th
decimal place.
The only task left is to determine if the rotation
should be clockwise or counters clockwise at each
iteration (choosing the value of σ). This is done by
keeping track of how much the angle was rotated at
each iteration and subtracting that from the wanted
angle; then in order to get closer to the wanted angle
β, if is positive, the rotation is clockwise,
otherwise it is negative and the rotation is counter
clockwise.
= - . = arctan
The values of must also be recomputed and stored.
But for small angles,
Arctan ( ) =
In fixed point representation, reducing table size.
As can be seen in the illustration above, the sine
of the angle β is the y coordinates of the final
vector , while the x coordinate is the cosine value.
After a sufficient number of iterations, the
vector's angle will be close to the wanted angle β. For
most ordinary purposes, 40 iterations (n = 40) is
sufficient to obtain the correct result to the 10th
decimal place.
IV. SCHEME OF IMPLEMENTATION

Fig. 2 Block diagram for CORDIC Algorithm.
V. RESULT
VI. CONCLUSION
This paper shows that CORDIC Algorithm is
useful for use in WLAN technology. By the
regularity, the CORDIC based architecture is very
suitable for implementation with pipelined VLSI
array processors.
This paper represents method to calculate
angle in wireless LAN receiver block by using
CORDIC Algorithm.

REFERENCES
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Highly concurrent structure for matrix
arithmetic and signal processing, IEEE
comput. Mag. Vol. 15, 1982, pp. 65-82.
[2] Duprat J., and Mullar J. M., The CORDIC
Algorithm: New results for VLSI
implementation, IEEE Transactions on
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[3] Valls, J., Kuhalmann, M., Parhi K.K.,
Efficient mapping of CORDIC Algorithms
for FPGA Based computers, 1998.
[4] Terry J., Heiskala J., OFDM Wireless
LANs: A Theoretical and practical Guide,
Indianapolis, Ind.: Sams, 2002.
[5] Alfke P., Efficient shift registers, LFSR
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[6] Andraka R. J. Building a high
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[7] Despain A. M., Fourier Transform
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IEEE transactions on computers Vol. 23,
1974, pp.93-1001.
[8] Deprettere E. Dewilde P., and Udo R.,
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proc.ICASSP’84, 1984, pp. 41.A.6.1-
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[9] Nee R., Prasad R., OFDM for Wireless
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Artech house, 2000.
[10] Walther J. S., A unified algorithm for
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[11] Volder J., Binary computation algorithm
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generation, Convair Report IAR-1 148
Aeroelectrics Group June 1956.

CORDIC Algorithm for WLAN

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