Multi-Carrier and Spread Spectrum Systems: From OFDM and MC ...

RF Issues 195s(t)r(t)e jf(t)White noiseFilterH( f )+f(t)e j(.)White noiseEquivalent phase noise modelFigure 4-56Phase noise modelFor brevity but without loss of generality, it is assumed that the transmitted signal is onlyaffected by phase noise ϕ N (t). The oscillator output can be written asr(t) = s(t) e jϕ N (t) . (4.83)The signal at the FFT output corresponding to sub-carrier n is given byN∑c −1R n = S n I 0 + S m I n−m , (4.84)m=0m≠nwhereI n = 1 T s∫ Ts0e j2πf nt e jϕ N (t) dt. (4.85)According to Equation (4.84), the effects of phase noise can be separated into twoparts [74]. The component I 0 in the first term in Equation (4.84) represents a commonphase error due to phase noise that is independent of the sub-carrier index and is commonto all sub-carriers. The sum of the contributions from the N c − 1 sub-carriers given bythe second term in Equation (4.84) represents the ICI caused by phase noise. The ICIdepends on the data and channel coefficients of all different N c − 1 sub-channels suchthat the ICI can be considered as Gaussian noise for large N c .The effects of the common phase error and ICI are shown in Figure 4-57, where themixed time/frequency representation of the total phase error E of the sub-carriers perOFDM symbol is shown for an OFDM system with an FFT size of 2048. The mixedtime/frequency representation of the total phase error shows in the frequency directionthe phase error over all sub-carriers within one OFDM symbol. The time direction isincluded by illustrating this for 30 subsequent OFDM symbols. It can be shown thateach OFDM symbol is affected by a common phase error and noise like ICI. The autocorrelationfunction (ACF) of the common phase error between adjacent OFDM symbolsis shown in Figure 4-58.