THE CHARACTERISTICS OF LINEAR PSEUDORANDOM SEQUENCE ENSEMBLES FOR A CDMA COMMUNICATION SYSTEM
Keywords:
CDMA, pseudo-random sequence, correlation characteristicsAbstract
Issues of selecting various-size pseudo-random sequence (PRS) ensembles to generate pseudo-noise signals in code-division multiple access (CDMA) communication systems are investigated. Cross interference and auto interference are inherent for CDMA systems. Cross interference occurs when radio signal modulated by an "alien" PRS arrives to the CDMA receiver. Auto interference occurs when a radio signal modulated with PRS arrives to the CDMA receiver with a delay with respect to its copy in the receiver. The interference levels depend on the values taken by cross-correlation functions (CCF) and autocorrelation function (ACF) sidelobes. The PRS ensemble selection criteria were formed so as to minimize cross interference and auto interference levels in the CDMA communication system. The criterion determining the cross interference level seems to be more preferable. In accordance with the selected criteria, PRS having the lowest maximum values of CCF moduli value and the lowest values of ACF modulus sidelobes are included in the ensemble. In the article, Kasami’s (length 1023), Legendre’s (length 1031), Hall’s (length 1051) and Legendre’s and Hall’s subclasses truncated to length 1023 are taken into consideration. For comparison, subclasses of M-sequences and Gold's PRS with length 1023 are considered. According to standards determining CDMA communication systems, M-sequences and Gold’s PRS are widely used in such systems. The authors have analyzed the ACF and CCF of all sequences in these subclasses. The particular PRS of the considered subclasses having the lowest levels of the maximum CCF modulus value and the ACF modulus sidelobes are identified. The upper boundary values for the CCF and PRS ACF sidelobes of the considered subclasses are clarified. The PRS of the Kasami subclass satisfying the chosen criteria are selected based on the obtained results. A few Kasami’s PRS ensembles of different size ensuring the minimal level of cross interference in the system are composed.
References
2. Гантмахер В.Е., Быстров Н.Е., Чеботарев Д.В. Шумоподобные сигналы. Анализ, синтез, обработка. СПб.: Наука и Техника, 2005.
3. Варакин Л.Е. Теория сложных сигналов. М.: Советское радио, 1970.
4. Ипатов В.П. Периодические дискретные сигналы с оптимальными корреляционными свойствами. М.: Радио и связь, 1992.
5. Свердлик М.Б. Оптимальные дискретные сигналы. М.: Советское радио, 1975.
6. Диксон Р.К. Широкополосные системы. М.: Связь, 1979.
7. Ипатов В.П. Широкополосные сигналы. Wiley, 2004.
8. Gold R. Optimal binary sequences for spread spectrum multiplexing // IEEE Trans. Inform. Theory. 1967. V. 13. P. 619 — 621.
9. Xiang Q. On balanced binary sequences with twolevel autocorrelation functions. // IEEE.Trans. Inform. Theory. 1998. V. 44. N 7. P. 975 — 986.
10. Едемский В.А., Антонова О.В. Линейная сложность обобщенных циклотометрических последовательностей с периодом 2mpn // Прикладная дискретная математика. Теоретические основы прикладной дискретной математики. 2012. № 3 (17). C. 5 — 12.
11. Калмыков В.В., Юдачев С.С. Ансамбли составных кодовых последовательностей. // Вестник МГТУ им. Н.Э. Баумана. Сер. Приборостроение. 1994. № 4. C. 101 — 106.
12. Пестряков В.В. Шумоподобные сигналы в системах передачи информации. М.: Советское радио, 1973.
13. Варакин Л.Е. Системы связи с шумоподобными сигналами. М.: Советское радио, 1985.
14. Hall M. A survey of Difference Sets // Proc. Am. Math. Soc. 1956. V. 7. P. 975 — 986.
15. Сdma 2000 m2m numbering recommendations system requirements document. Current. Telecommunications Industry Association (TIA), 2012.
16. Сизякова А.Ю., Семина Ю.В. Алгоритмы формирования ПСП для МДКР // Наука и образование. 2015. № 6 (13). C. 18 — 20.
