The Central Limit Theorem for the Normalized Sums of the MAI for SSMA Communication Systems Using Spreading Sequences of Markov Chains
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E89-A No.9 pp.2307-2314
- Publication Date
- 2006/09/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e89-a.9.2307
- Type of Manuscript
- Special Section PAPER (Special Section on Sequence Design and its Application in Communications)
- Category
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Hiroshi FUJISAKI, Gerhard KELLER, "The Central Limit Theorem for the Normalized Sums of the MAI for SSMA Communication Systems Using Spreading Sequences of Markov Chains" in IEICE TRANSACTIONS on Fundamentals,
vol. E89-A, no. 9, pp. 2307-2314, September 2006, doi: 10.1093/ietfec/e89-a.9.2307.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e89-a.9.2307/_p
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@ARTICLE{e89-a_9_2307,
author={Hiroshi FUJISAKI, Gerhard KELLER, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Central Limit Theorem for the Normalized Sums of the MAI for SSMA Communication Systems Using Spreading Sequences of Markov Chains},
year={2006},
volume={E89-A},
number={9},
pages={2307-2314},
abstract={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.},
keywords={},
doi={10.1093/ietfec/e89-a.9.2307},
ISSN={1745-1337},
month={September},}
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TY - JOUR
TI - The Central Limit Theorem for the Normalized Sums of the MAI for SSMA Communication Systems Using Spreading Sequences of Markov Chains
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2307
EP - 2314
AU - Hiroshi FUJISAKI
AU - Gerhard KELLER
PY - 2006
DO - 10.1093/ietfec/e89-a.9.2307
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E89-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2006
AB - 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.
ER -
English
