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EXEX

--OR FUNCTIONOR FUNCTION

001111

110011

111100

000000Y=A BY=A BBBAA

A

B

Y

EX-OR Function Truth Table

EX-OR gate produces HIGH output, if odd numberof inputs or HIGH, in all other cases, the output will be

LOW.

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PN SEQUENCEPN SEQUENCEPN SEQUENCE :PN SEQUENCE :

A Pseudo Random Noise sequence is one inA Pseudo Random Noise sequence is one inwhich the bits appear in a random manner withwhich the bits appear in a random manner with

a specified length and the pattern is repeateda specified length and the pattern is repeated

for subsequent sequences.for subsequent sequences.PN sequence is the best choice as it appearsPN sequence is the best choice as it appears

as noise to all other users excepting the desiredas noise to all other users excepting the desired

receiver.receiver.

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Requirements of a PN sequence:Requirements of a PN sequence:

Be easy to generateBe easy to generate Have random propertiesHave random properties

Have long periodsHave long periods

Be difficult to reconstruct from a shortBe difficult to reconstruct from a shortsegment.segment.

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PN SEQUENCE GENERATIONPN SEQUENCE GENERATION Example :Example : Suppose we have 4 digit words.Suppose we have 4 digit words.

The natural sequence is from 0000 to 1111.The natural sequence is from 0000 to 1111.Purely random sequence could be a series ofPurely random sequence could be a series of15 word sets, with the combination of words in15 word sets, with the combination of words in

each set being randomeach set being randomThe PN sequence is important because, theThe PN sequence is important because, the

receiver needs a replica of the transmittedreceiver needs a replica of the transmitted

sequence to de spread the signals.sequence to de spread the signals.he PN sequence has a random set of wordshe PN sequence has a random set of words

which repeat after a specific sequence length.which repeat after a specific sequence length.

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Example of a PN sequence :Example of a PN sequence :

Consider a 4 bit sequence.. 0001.Consider a 4 bit sequence.. 0001.

EX-OR

1 2 3 4

0 0 0 1

The first 4 bit sequence is 0001.

The next 4 bit sequence will be 1000, 1100, 1110, 1111,0111, 1011, 0101, 1010, 1101, 0110, 0011, 1001, 0100, 0010.

The next 4 bit after this again starts with 0001.

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Example for PN Sequence generator is (SSRG)Example for PN Sequence generator is (SSRG)

SIMPLE SHIFT REGISTER GENERATORSIMPLE SHIFT REGISTER GENERATOR..

A generic form of a simple shift registerA generic form of a simple shift registergenerator is shown below.generator is shown below.

1 2 3 4 5 6 N

Feed back logic-exclusive OR circuits

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Properties of PN sequences:Properties of PN sequences:PN Sequences exhibit the following properties:PN Sequences exhibit the following properties:

The maximal length of the sequence isThe maximal length of the sequence is 22nn--1,1,

where n is the number of stages in the shiftwhere n is the number of stages in the shiftregister.register.

The number of 1The number of 1s will be 2s will be 2(n(n--1)1) and that of 0and that of 0ss

will be 2will be 2(n(n--1)1)

--1. i.e., the number of 11. i.e., the number of 1s will bes will beone more than the number of 0one more than the number of 0s.s.

If a maximal SRG sequence is added to a phaseIf a maximal SRG sequence is added to a phase

shift (time shift) of it, then the resultingshift (time shift) of it, then the resultingsequence is another phase shift of the originalsequence is another phase shift of the originalsequence. This is called thesequence. This is called theshift and addshift and add

property of SSRGs.property of SSRGs.

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Cross CorrelationCross Correlation

Cross Correlation defines the likeness betweenCross Correlation defines the likeness betweentwo different random variables and could betwo different random variables and could be

described by :described by :Cross CorrelationCross Correlation ==x(t) * y(tx(t) * y(t--T) dTT) dT

For a PN sequence, this could be re written as :For a PN sequence, this could be re written as :

Cross correlation =Cross correlation = 00TT CC JJ (t) * C(t) * C kk(t(t--T)dTT)dT..

The cross correlation function will have veryThe cross correlation function will have very

small negative values.small negative values.

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Classification of PN Codes :Classification of PN Codes :PN codes are classified into 2 types.PN codes are classified into 2 types.

1.1. PN Long codePN Long code2.2. PN Short codePN Short code

PN Long Code :PN Long Code : It is used for MobileIt is used for Mobile

Identification in reverse link and dataIdentification in reverse link and data

scrambling in forward linkscrambling in forward link

PN short code :PN short code : It is used for base stationIt is used for base stationidentification in forward link and orthogonalidentification in forward link and orthogonal

modulation in reverse link.modulation in reverse link.

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In forward link, long code is used to encryptIn forward link, long code is used to encryptuser ID, in reverse link long code is used (ESNuser ID, in reverse link long code is used (ESN

Electronic serial number). The code mask isElectronic serial number). The code mask is

done by using ESN.done by using ESN.

Both Base station and respective user haveBoth Base station and respective user haveknowledge of PN sequence at any given instantknowledge of PN sequence at any given instantof time as a specified private code mask isof time as a specified private code mask is

exchanged between them.exchanged between them.

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PN short code :PN short code :

This sequence uses 15 bits and code isThis sequence uses 15 bits and code isgenerated at 1.2288 Mcps. The code repeatsgenerated at 1.2288 Mcps. The code repeats

with a period of 26.67 m sec.with a period of 26.67 m sec.221515 = 32.768X10= 32.768X1033

Chip duration = 1/(1.2288X10Chip duration = 1/(1.2288X1066) = 0.8138) = 0.8138 SecSec

Hence, the code durationHence, the code duration

= 32.768X10= 32.768X1033X 0.8138X10X 0.8138X10--66= 26.67 m sec.= 26.67 m sec.

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The code is used by Base station and isThe code is used by Base station and isused for final spreading of signal in theused for final spreading of signal in theforward channel and is also transmittedforward channel and is also transmitted

as a pilot sequence by Base Station.as a pilot sequence by Base Station.

All the base station use the same shortAll the base station use the same shortcode by distinct offcode by distinct off--set time forset time foridentification.identification.

i.e., PN offsets are used for BTSi.e., PN offsets are used for BTSidentity.identity.

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ORTHOGONAL CODESORTHOGONAL CODES

Two codes are said to be orthogonal, if theTwo codes are said to be orthogonal, if theproduct (Exproduct (Ex--or) of the two codes producesor) of the two codes producesequal number of 1s and 0s.equal number of 1s and 0s.

Ex : if A= 111010 and B=011001, then XoringEx : if A= 111010 and B=011001, then Xoring

A and B gives the answer as 100011, whichA and B gives the answer as 100011, which

has three number of 1s and three number ofhas three number of 1s and three number of0s.0s.

Conventionally, 1 is mapped as +1 and 0 asConventionally, 1 is mapped as +1 and 0 as

--1.1.Example for orthogonal codes areExample for orthogonal codes areWALSHWALSHCODESCODES..

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WALSH CODESWALSH CODES

Most commonly used orthogonal codes inMost commonly used orthogonal codes inCDMA systemsCDMA systems

A set of lengthA set of lengthnnconsists ofconsists ofnnrows ofrows ofnXn Walsh matrix.nXn Walsh matrix.

W1= (0).W1= (0). In general, WIn general, W2n2n= [= [ WWnn, W, Wnn, W, Wnn, W, Wnn ],],wherewherennis the dimension of the matrix.is the dimension of the matrix.

The over score denotes the logical NOT ofThe over score denotes the logical NOT ofthe bits in the matrix.the bits in the matrix.

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The matrix has the property that everyThe matrix has the property that everyrow is orthogonal to every other row androw is orthogonal to every other row andalso to the logical NOT of every other row.also to the logical NOT of every other row.

WW2x22x2 = 0 0= 0 0

0 10 1

WW4x44x4 = 0 0 0 0= 0 0 0 0

0 1 0 10 1 0 10 0 1 10 0 1 1

0 1 1 00 1 1 0

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WW2nx2n2nx2n = w= wnn wwnn

wwnn wwnn

0 0 0

0 1

0 0

0 1

0 0

0 1

0 0

0 1

1 1

1 0

0 0

0 1

0 0

0 1

0 0

0 1

1 1

1 0

0 0

0 1

0 0

0 1

0 0

0 1

1 1

1 0

0 0

0 1

0 0

0 1

0 0

0 1

1 1

1 0

1 1

1 0

1 1

1 0

1 1

1 0

0 0

0 1

Walsh Code Generation :

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