Метод формирующего оператора для моделирования циклостационарных случайных процессов

Abstract

The paper proposes the shaping operator technique for modelling cyclostationary random process (CSRP) which belong to the class of second-order processes being described by the parametric pulse train model. Generating CSRP is expressed as the propagation result of the specially chosen elementary CSRP through the linear time-invariant system with a known impulse response. The paper describes the approach to forming the elementary CSRP based on the train made of Dirac delta-function uniformly following in time domain with constant step and defining the desired structural periodicity of the process being modelled. The analytical expressions for the main characteristics used for describing cyclostationary properties of the elementary process, including two-dimensional, cyclic and spectral corelation functions, were obtained. In addition to the case of the elementary CSRP with correlated weighting coefficients of delta-functions, the case of statistically independent coefficients was considered. It was shown that utilization of the spectral correlation function (SCF) for describing the cyclic property reveals the explicit analytical relation between characteristics of the elementary and modelled CSRPs provided the filter frequency response is known. The paper presents the comparative example which describes the modelling of two CSRPs: one of them was chosen as the train of rectangle pulses which is pulse amplitude modulated by stationary random time series, while the other is considered as a signal formed by the method of direct sequence spread spectrum. The chosen short-length Barker sequence as the code allowed performing visual comparison between absolute value of SCF components taken at the cyclic frequencies multiple of the chip frequency and cyclic frequencies multiple of the symbol frequency. The future development of the methods proposed in the paper opens the road to improving the performance of modern radar and telecommunication systems by means of utilizing cyclic frequencies which are non-random parameters describing the structural properties of signals under processing.