A Gold code sequence generator suitable for use in a code division multiple access spread spectrum communication application is designed. A dual, single return shift register configuration is used to generate Gold code sequences. The code sequences are generated by the mod-2 addition of two linear maximal length pseudo-random noise codes, each of which corresponds to a sixth-order primitive polynomial. A computer model of the design is used to generate all 65 possible members of the Gold code sequence family. A tabulation of all sequences and their initial condition “keys” is provided, along with a designation as to which code sequences are balanced. The mathematical basis of maximal length sequence generation is developed, using first the matrix characterization of a shift register generator, and then switching to the alternate treatment of a shift register generator as a polynomial division engine. The link between the matrix representation and the polynomial representation via the characteristic equation, the use of the generating function, and the three mathematical properties required of polynomials which are capable of generating maximal length sequences are described. Gold’s algorithm for selecting preferred polynomial pairs is presented, as is his technique for determining the characteristic phase of a maximal length sequence. The actual Gold code generator is then designed and modeled in software. All Gold code sequences output from the generator are tabulated. The family of sequences is evaluated in terms of its randomness properties. Finally, the results of computer analysis of the auto and cross-correlation characteristics of the family is summarized.
| Identifer | oai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:rtd-5797 |
| Date | 01 January 1985 |
| Creators | Young, Mark W. |
| Publisher | STARS |
| Source Sets | University of Central Florida |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Retrospective Theses and Dissertations |
| Rights | Public Domain |
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