The Central Limit Theorem for the Normalized Sums of the MAI for SSMA Communication Systems Using Spreading Sequences of Markov Chains

Hiroshi FUJISAKI  Gerhard KELLER  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.9   pp.2307-2314
Publication Date: 2006/09/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.9.2307
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Sequence Design and its Application in Communications)
Category: 
Keyword: 
sliding block code,  Markov chain,  αN-mixing,  central limit theorem (CLT),  bit error probability,  spread spectrum multiple access (SSMA) communication system,  

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Summary: 
We extend the sliding block code in symbolic dynamics to transform J (≥2) sequences of Markov chains with time delays. Under the assumption that the chains are irreducible and aperiodic, we prove the central limit theorem (CLT) for the normalized sums of extended sliding block codes from J sequences of Markov chains. We apply the theorem to the system analysis of asynchronous spread spectrum multiple access (SSMA) communication systems using spreading sequences of Markov chains. We find that the standard Gaussian approximation (SGA) for estimations of bit error probabilities in such systems is the 0-th order approximation of the evaluation based on the CLT. We also provide a simple theoretical evaluation of bit error probabilities in such systems, which agrees properly with the experimental results even for the systems with small number of users and low length of spreading sequences.