APAN ‘06, 17 - 21 July, 2006 Ng Chee Kyun 1

Performance Analysis of TPSK in CDMA Performance Analysis of TPSK in CDMA SystemSystem

Ng Chee KyunDepartment of Computer and Communication Systems

Engineering,Faculty of Engineering, Universiti Putra Malaysia,

Malaysia.

APAN ‘06, 17 - 21 July, 2006 Ng Chee Kyun 2

CDMA SequencesCDMA Sequences

• Traditional CDMA sequences~ m-sequence, Gold code, Walsh-Hadamard code.

~ Binary sequence {+1,-1}.

• Large Area Synchronized (LAS) CDMA sequences ~ Large Area (LA) code and Loosely Synchronous (LS) code.

~ Ternary sequence {+1,0,-1}

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Walsh-Hadamard Code

A Hadamard matrix of order 4

111111111111

1111

4H

where each row represents a Walsh-Hadamard sequence

11110 w 11111 w 11112 w 11113 w

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The auto-correlation property of Walsh-Hadamard sequences.

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The cross-correlation property of Walsh-Hadamard sequences.

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LAS Sequences

• The family of Large Area Synchronized (LAS) sequences is formed by the combination of Large Area (LA) code [Li 99] and Loosely Synchronous (LS) code [Staňczak 01].

• Li in [Li 99] studied various LA code construction schemes and their application to CDMA system.

• Staňczak in [Staňczak 01] investigated the construction of various schemes designed for the generation of various LS codes.

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LA Code• Ternary codes: {+1,0,-1}

• Three parameters: N is the number of non-zero pulses, is the minimum pulse interval, and L is the length or period of LA code.

• There are certain numbers of zeros padding between the pulses interval.

• For instant, the construction of code has been proposed in [Li 99]. The 16 pulse positions, are given by

LKNLA ,, 0

0K

847,38,16LA

nP}808,732,660,592,530,470,414,360,308,258,210,164,120,78,38,0{nP

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Pulse positions of 847,38,16LA

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The arrangement of 16 sequences 847,38,16LA

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The auto-correlation property of LA sequence C2.

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The cross-correlation property between LA sequences C2 and C10.

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LS Code• LS codes can be denoted as by applying a P x P dimensional Walsh-Hadamard matrix to an orthogonal complementary set of length M, while inserting number of zeros padding at the center of the code.

• Then, the total length of the code is given by

• The four 2 x 2 sequences can be formed as

0,, WPMLS

0W

0,, WPMLS02 WMP

4,2,5LS

1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1)(1 zLS 1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1)(2 zLS

1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1)(3 zLS 1,1,1,1,1,1,1,1,1,1,0,0,0,0,1,1,1,1,1,1,1,1,1,1)(4 zLS

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Construction of LAS Sequences

00 ,,;,, WPMLKNLAS

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The auto-correlation property of LAS sequence.

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The cross-correlation property of LAS sequence.

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where is the Euclidean distance or minimum distance between signal points in the I-Q constellation, and is the complementary error function or simply Q-function which defined by

Probability of Error over PSK SystemsProbability of Error over PSK Systems

• Chip Error Rate (CER) is used (instead of BER)~ Binary Phase Shift Keying (BPSK) Binary sequence {+1,-1}.~ Ternary PSK Ternary sequence {+1,0,-1}.

• Symbol Error Rate (SER) – A symbol more than one chip. ~ Quadrature PSK (QPSK) Symbol sequence {+1+1, -1+1, ….}

0

2min

2NdQSER

mind

)(xQ

dxxxQx

2exp

21)(

2

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Constellation Diagram for BPSK Signals

Ed 2min

0

2NEQSERSince then

In BPSK signalling each symbol in spreading sequence corresponds to one chip in data pulse, therefore

0

2NEQSERCER c

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Since and then

In TPSK signalling each symbol in spreading sequence corresponds to one chip in data pulse, therefore

Constellation Diagram for TPSK Signals

Edd 32min

023NEQSER

023NEQSERCER c

23Ed

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Since then

In QPSK signalling each symbol in spreading sequence corresponds to two chips in data pulse, therefore

Constellation Diagram for QPSK Signals

0NEQSER

0

2NEQCER c

Ed 2min

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LAS Even Ternary (LAS-ET) Sequences

• An additional constraint is imposed to original LA code. The pulse interval between two adjacent non-zero

pulses, must be even. The minimum pulse interval, must also be even. compared to

nd0K

818,38,16ETLAS 847,38,16LA

Pulse positions of 818,38,16LA

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The arrangement of 16 sequences 818,38,16LA

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• For mapping two chips into one symbol, there are nine combinations:

9-ary PSK

LA Sequences

]1,1[],1,1[],0,1[],1,1[],1,1[],0,.1[],1,0[],1,0[],0,0[)( ts

• For mapping two chips into one symbol, there are three combinations: TPSK

LAS-ET Sequences

]0,1[],0,0[],0,.1[)( ts

0

3NE

QCER c

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SER Performances

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CER Performances

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Concluding Remarks

• Better CER performance in TPSK signalling can be achieved when two chips in the LAS-ET sequence are mapped in one symbol period.

• At the same time, the spectrum efficiency of this LA sequence is also increased.

• The sequence length in LAS-ET sequence is decreased compared to original LA sequence while maintaining the original size of IFW.

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Thank YouThank You