General Form of the Power Spectral Density of Multicarrier Signals

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.