On Bit Error Probabilities of SSMA Communication Systems Using Spreading Sequences of Markov Chains

Hiroshi FUJISAKI  Yosuke YAMADA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E88-A   No.10   pp.2669-2677
Publication Date: 2005/10/01
Online ISSN: 
DOI: 10.1093/ietfec/e88-a.10.2669
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
Category: 
Keyword: 
SSMA (spread spectrum multiple access) communication systems,  spreading sequences,  Markov chains,  MAI (multiple-access interference),  bit error probability,  CLT (central limit theorem),  SGA (standard Gaussian approximation),  

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Summary: 
We study asynchronous SSMA communication systems using binary spreading sequences of Markov chains and prove the CLT (central limit theorem) for the empirical distribution of the normalized MAI (multiple-access interference). We also prove that the distribution of the normalized MAI for asynchronous systems can never be Gaussian if chains are irreducible and aperiodic. Based on these results, we propose novel theoretical evaluations of bit error probabilities in such systems based on the CLT and compare these and conventional theoretical estimations based on the SGA (standard Gaussian approximation) with experimental results. Consequently we confirm that the proposed theoretical evaluations based on the CLT agree with the experimental results better than the theoretical evaluations based on the SGA. Accordingly, using the theoretical evaluations based on the CLT, we give the optimum spreading sequences of Markov chains in terms of bit error probabilities.