General form of the power spectral density of multicarrier signals

Abstract

Multicarrier modulation has been adopted in many modern communication systems because of its many appealing properties. Its relatively high out-of-band radiation has spurred many techniques to shape the power spectral density (PSD) of multicarrier signals, including spectral precoding and pulse shaping. We derive a general expression for the PSD which is valid for subcarrier-specific pulses and for spectral precoders operating over multiple blocks. The only statistical assumptions on the vector-valued sequence modulating the active subcarriers are wide-sense cyclostationarity and properness. The applicability of the result to a number of popular multicarrier formats is discussed.