In RF transceivers the complex baseband signal x(t) containing the useful information is up-converted around a carrier frequency fc and frequency down-converted to baseband, in transmission and reception respectively, using a mixer and an LO generally implemented by a PLL (Gardner, 1979). Without phase noise, the RF signal y(t) can be simply written as
Now by taking into account the LO phase noise θ(t), in radians, Equation 2.21 becomes
Like the flicker noise described in Section 2.2.5, the phase noise θ(t) is commonly described in the frequency domain by its PSD in dBc/Hz (or rad2/Hz in linear). It is the ratio between the noise power measured in 1 Hz bandwidth, at a frequency offset fm, and the power of the carrier (Hajimiri and Lee, 1998; Lee and Hajimiri, 2000). It is illustrated in Figure 2.12; ideal oscillators are merely represented by a Dirac function in the frequency domain, whereas real ones present a kind of “skirt” due to the phase noise profile.
Because the output of the LO and the signal are multiplied in the time domain through ...