In RF transceivers the complex baseband signal *x*(*t*) containing the useful information is up-converted around a carrier frequency *f*_{c} 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 rad^{2}/Hz in linear). It is the ratio between the noise power measured in 1 Hz bandwidth, at a frequency offset *f*_{m}, 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 ...

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