Statistical Modeling of PAM Signals and Power Spectra

The structure and the statistical properties of the pseudo-random PAM signals are fundamental for the characterization and prediction of the optical fiber transmission performances. Both scalar (ASK and PSK) and complex (QAM) optical modulations are based on PAM signals of the appropriate order to generate the tributaries. In this chapter, we will provide the theory and the modeling of both white noise and pseudo-random PAM signals of any order, obtained combining the corresponding PAM sequence with the appropriate pulse shape, suited for the optical transmission system. In particular, the intersymbol interference and spectral efficiency are two fundamental properties of the transmitted signal that strongly depend on the pulse shape and affect the transmission performances. After introducing the general theory of the pseudo-random PAM signals, the chapter focuses on two fundamental signal models, largely used both in modeling and experimental verification of Terabit optical fiber transmission systems, namely, the Nyquist pulse and the ERF pulse. Both white noise and pseudo-random PAM signals, generated through Nyquist and ERF pulse shapes, are extensively analyzed in the time and frequency domain, deriving complete set of equations and verifying the signal properties with extensive simulations. The third shaping pulse we will consider in this chapter to load the pseudo-random PAM sequences is the delta impulse. Even in this case, the theoretical conclusions are verified through several simulations and compared with the PAM sequences loaded with either Nyquist or ERF pulse.