Praise for Fundamentals of WiMAX

136 Chapter 4 • Orthogonal Frequency Division Multiplexingx[n]+x[n]γ = 5dBAntipeakGeneratorc[n]Figure 4.15 A peak cancellation as a model of soft limiter whenγ =5dBwherecn [ ]is the clipping signal defined bycn [ ]=⎧⎨⎩jθ[ n]| A−| x[ n]|| e , if | x[ n]|>A0, if | x[ n] | ≤ Afor n =0,..., NL −1−3pt(4.33)where θ[ n]= arg( −x[ n]); that is, the phase of cn [ ] is out of phase with xn [ ] by 180° , and A isthe clipping level, which is defined asγ ≜A=2E{| x[ n] | }Aεx. (4.34)In such a peak-cancellation strategy, an antipeak generator estimates peaks greater than clippinglevel. The clipped signal ̃x[ n] can be obtained by adding a time-shifted and scaled signal cn [ ] tothe original signal xn [ ]. The exact clipping signal cn [ ] can be generated to reduce PAR, using avariety of techniques.Obviously, clipping reduces the PAR at the expense of distorting the signal by the additivesignal cn [ ]. The two primary drawbacks from clipping are (1) spectral regrowth—frequencydomainleakage—which causes unacceptable interference to users in neighboring RF channels,and (2) distortion of the desired signal. We now consider these two effects separately.4.5.3.1 Spectral RegrowthThe clipping noise can be expressed in the frequency domain through the use of the DFT. Theresulting clipped frequency-domain signal ̃X isX̃= X + C , k = 0, …, L−1,k k k(4.35)where C krepresents the clipped-off signal in the frequency domain. In Figure 4.16, the powerspectraldensity of the original (X), clipped ( ̃X ), and clipped-off (C) signals are plotted for differentclipping ratios γ of 3 dB, 5 dB, and 7 dB. The following deleterious effects are observed.First, the clipped-off signal C kis strikingly increased as the clipping ratio is lowered from 7 dBto 3 dB. This increase shows the correlation between X kand C kinside the desired band at lowclipping ratios, and causes the in-band signal to be attenuated as the clipping ratio is lowered.