Performance Analysis of TPSK in CDMA System

1. Performance Analysis of TPSK in CDMA System Ng Chee Kyun Department of Computer and Communication Systems Engineering, Faculty of Engineering, Universiti Putra Malaysia, Malaysia.

2. CDMA 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}

3. Walsh-Hadamard Code A Hadamard matrix of order 4 where each row represents a Walsh-Hadamard sequence

4. The auto-correlation property of Walsh-Hadamard sequences.

5. The cross-correlation property of Walsh-Hadamard sequences.

6. 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.

7. 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

8. Pulse positions of

9. The arrangement of 16sequences

10. The auto-correlation property of LA sequence C2.

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

12. 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

13. Construction of LAS Sequences

14. The auto-correlation property of LAS sequence.

15. The cross-correlation property of LAS sequence.

16. Probability 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, ….} 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

17. Constellation Diagram for BPSK Signals Since then In BPSK signalling each symbol in spreading sequence corresponds to one chip in data pulse, therefore

18. Constellation Diagram for TPSK Signals Since and then In TPSK signalling each symbol in spreading sequence corresponds to one chip in data pulse, therefore

19. Constellation Diagram for QPSK Signals Since then In QPSK signalling each symbol in spreading sequence corresponds to two chips in data pulse, therefore

20. 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 Pulse positions of

21. The arrangement of 16sequences

22. LA Sequences • For mapping two chips into one symbol, there are nine combinations: •  9-ary PSK LAS-ET Sequences • For mapping two chips into one symbol, there are three combinations: •  TPSK

23. SER Performances

24. CER Performances

25. 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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