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# orothogonal codes

gaurav purohit
by

## GAURAV PUROHIT

on 14 December 2013

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#### Transcript of orothogonal codes

photo credit Nasa / Goddard Space Flight Center / Reto Stöckli
Gaurav Purohit
Presented By
contd..
In this paper, the use of Walsh function for the generation of 64-orthogonal set, is investigated and a prototype circuit has been built through a MATLAB simulator to add validity to the theoretical results.
WALSH FUNCTION GENERATION
using
Rademacher functions of order N are set of 1+log2 N orthogonal functions consisting of N = 2^k rectangular pulses. These pulses assume alternately the values +1 and -1 in an interval of (0, T).
contd..
After generating walsh functions using equation 2, we have rectangular pulses as shown in Figure
Walsh sequences
The second step mapping from (+1->0 and -1->1).
contd..
The final step is producing Walsh sequences and is exactly formed as the modulo-2 sum of R0 and the Rademacher sequences {RJ}.
Implementation of 64-Orthogonal Walsh Functions for 3G
Software Defined Application

Gaurav Purohit, Satish Mohanty and Divya Vyas
CONTENTS
Introduction
Implementations
Results
Conclusion
References
Introduction
The paper aims to presents a simulation based study on the theory which replaces a general Sine and cosine function by set of orthogonal functions such as Rademacher functions and Walsh functions i.e. concept of sequence by that
of frequency.
Walsh codes are perfectly antipodal block codes
that found their use in many popular applications like software define radio including multiuser communications such as CDMA and WCDMA.
Walsh functions : A set of Walsh functions of order N=2^k represents an N set of time functions, having the period T, given by
where k = 0,1,,,n and
1) WN, j(t) can take the only values {-1,1}
2) WN, j (0)=0, for any value of j;
....... eq. 1
.....eq. 2
The third step is Walsh sequences are generated as a modulo-2 sum of Rademacher functions.This process is based on Walsh function index sequence conversion into the Gray code.
The result of this operation is formed as set of N Walsh sequences of order N.
walsh function n=6
Generation of Walsh sequences and functions using Rademacher function
M. F. Ghanim, "Multi-user MC-CDMA using Walsh code for Rayleigh and Gaussian channel," IEEE Student Conference on Research and Development (SCOReD), pp.- 58-63, Dec. 2011.

Physical Layer Standard for cdma2000 Spread Spectrum Systems.
Available: [online]
http://www.3gpp2.org/public_html/specs/c.s0002-d_v1.0_021704.pdf, Mar.-2013.

J. L. Walsh, "A closed set of normal orthogonal functions," AJM. Vol. 45. Pp. - 5-24, 1923.

walsh function -The Tutorial Program,
Available: [Online]
http://www.feec.vutbr.cz/EEICT/2005/sbornik/03- Doktorske_projekty/01-Elektronika/20-xruzic20.pdf , Mar.-2013.

Ruziicka, Z.: Elektrorevue: Walshovy funkce a způsoby Jericho generování.
Available: [Online]
http://www.elektrorevue.cz/clanky/04065/index.html#1 , Mar.-2013.

Lee, J. S., Miller, L. E.: CDMA System Engineering Handbook. London: Artech House, 1998.
References
Conclusion
we describe the generation of 64-ary orthogonal codes using Rademacher functions which are used for CDMA and 3G wireless communication for SDR.
The simulated results are validated with the analytical methods using Matlab Simulink and both are found in a close agreement.
THANK YOU
Results
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