Correlation properties of complete code of binary spread spectrum phase-shift keyed signals with polarization coding

Abstract

Problem statement. Investigation of correlation properties of complete code of binary spread spectrum phase-shift keyed signals as the limiting case of large systems is a topical task for building large systems of binary spread spectrum phase-shift keyed signals with polarization coding with optimal correlation properties. Also, this task is of independent academic interest due to the fact that the alphabet of symbols for these signals lacks multicasting properties unlike the familiar cases of complete codes of spread spectrum phase-shift keyed signals. Objective. To accurately define the distribution laws as well as the moments about zero and the mean for the n-th order of presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding. To offer approximations of accurate distribution laws suitable for engineering applications. Results. The accurate distribution laws for presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding were found in the form of the related distribution series. The analytic expressions for the n-th order of presented values of these functions for the complete code of the specified signals were assigned. The calculation example for the distribution series of presented values of aperiodic and periodic correlation functions for the complete code of the specified signals with the length of vector code sequences N=4 was given. The values of the relative frequencies of the correlation functions values for this case were found by the means of direct computing and their exact match with the corresponding predicted probability values was demonstrated. The approximations of the accurate distribution laws were given: for periodic correlation functions case – by Gaussian probability density, and for the aperiodic functions case – by the Pearson curve of VII type. Practical relevance. The found accurate laws for presented values of aperiodic and periodic correlation functions of the complete code of binary spread spectrum phase-shift keyed signals with polarization coding and their approximations allow to assess the correlation properties of large systems of such signals.