Efficient assessment of the instantaneous power distributions of pulse-shaped single- and multi-carrier signals

We present a new approach for assessing the instantaneous power distributions of the continuous-time transmit signal (i.e., after pulse shaping) in single- and multi-carrier transmission schemes. On the one hand, an efficient calculation of the distribution for single-carrier signals via the fast Fourier transform (FFT) is given. On the other hand, tight approximations for multi-carrier transmission based on orthogonal frequency-division multiplexing (OFDM) are reviewed. Thereby, the effect of non-modulated carriers (guard bands) is taken into account. The impact of the roll-off factor of root-raised-cosine pulse shaping is analyzed and its converse influence on the peak-to-average power behavior of both modulation strategies is discussed. All theoretical derivations match very well with numerical results obtained from Monte-Carlo simulations.