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The paper is aimed at building analytical models of signals possessing complex types of digital modulation within the framework of the cyclostationary approach. The proposed analytical approach includes procedures leading to closed-form analytical expressions of spectral correlation functions (SCF), which are functions depending on two arguments: frequency and cyclic frequency. They describe the probabilistic properties of the analyzed signals assuming the signals can be modeled as realizations of second-order cyclostationary random processes (CSRP). The proposed approach of obtaining both normal and conjugate SCFs is based on the modified shaping operator technique, which turns out to be an effective tool applied to CSRP analysis. The technique handles the constructing the variety of the typically used in practice CSRPs in the form of chained transforms applied to one or several independent CSRPs of known characteristics by means of relatively simple operations, widely expressed in signal and systems theory. These operations performed over signals, which are assumed to be realizations of the CSRP, correspond to the transformations of their SCF, whose formulae are presented in the paper. The paper also reveals the exact analytical expressions obtained for the normal and conjugate SCF of OFDM signals with cyclic prefix (CP) whose subcarriers are modulated using BPSK and QPSK methods. By example of OFDM signal with a CP and QPSK subcarrier modulation, a quantitative comparison was carried out between the analytical SCF assembled according to the model formula and its estimate obtained by a numerical simulation using the estimation method based on the mixed two-dimensional fast Fourier transform. It is shown that the SCF estimate converges in root-mean sense to the constructed analytical model with an increase in the duration of the analyzed signal data sample. |
