Study of Multistate PN Sequences.
Abstract
The present work has been successful in extending the fundamental concepts and results of the theory of binary sequences to the multistate case. Substantial progress and new results have been achieved in the following areas: Generation of Maximal Linear Multistate Sequences; Implementation of Multistate Sequences with Binary Logic Elements; Special Properties of Multistate Sequences; Definition and Computation of the Autocorrelation Function of Multistate Sequences; and Computation of the Power Spectral Density of Maximal Linear Multistate Sequences. In Section 1 the multistate encoded signal and its analytical representation is reviewed to ensure that the properties of the multistate sequences which have the greatest impact on the resultant signals were emphasized during the current study. In Section 2 the concept of a linear multistate sequence is discussed. The multistate alphabet (finite fields over GF(2k)) and the polynomial corresponding to a feedback shift register are described. A method for implementing multistate sequences with binary logic elements is presented in this section. The concept of a maximal multistate sequence is discussed, and a method for determining maximal multistate polynomials is given. A table of irreducible polynomials of degree 2 for the 8-state case is constructed and presented in Section 2.5. The autocorrelation function of multistate sequences is defined in Section 3, and the autocorrelation function of maximal linear multistate sequences is determined. The result is essentially independent of the period of the sequence and depends only on the number of states of the sequence.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 06, 1981
- Accession Number
- ADA103061