Spectral Characteristics of Digitally Modulated Signals

This lecture first introduces the standard representation of complex baseband signal of digital modulated signal and its power spectral density (PSD). Then it shows how the PSD of bandpass signals can always be obtained by its complex baseband envolope. Finally, two important modulation schemes OFDM and PSK are introduced and the spectral characteristics of these two modulated signals are discussed. I. PSD of Modulated Bandpass Signal As we know that bandwidth efficiency is a very important factor for choosing a modulation scheme. To learn the bandwidth efficiency of one modulation scheme, we need to get the power spectral density of the corresponding modulated signal. Generally, a digitally modulated signal can be written as } ) ( Re{ ) ( ) 2 ( T ct f j e t v t s φ π + = ,where v(t) is the baseband equivalent complex envolope and T φ is the random phase. To calculate the PSD of s(t), we can rewrite it as: } ) ( ) ( { 2 1 ) ( ) 2 ( * ) 2 ( T c T c t f j t f j e t v e t v t s φ π φ π + − + + = Then the PSD of s(t) can be derived by: )] ( ) ( [ ) ( t s t s E ss τ τ φ + = ] ) ( * ) ( * ) ( * ) ( ) ( ) ( * ) ( ) ( [ 4 1 ) 2 2 4 ( 2 2 ) 2 2 4 (