Computation of the PAR of continuous-time real-value OFDM signal

Computation of the peak-to-average envelope power ratio (PAR) of an orthogonal frequency division multiplexing (OFDM) signal plays a major role in peak reduction methods. A procedure for computing the PAR of a continuous-time real-value OFDM signal which is known as discrete multi-tone, with any PSK or QAM installations, is developed here. It is shown that the derivative of the real-value signal waveform function (RVSWF), whose square is the instantaneous envelope power function (EPF), can be transformed into a linear sum of Chebyshev polynomials of the first kind and the second kind. Consequently, the roots of the derivative of RVSWF can be obtained by solving a polynomial. The procedure may be useful for theoretical studies of PAR distributions and developing the peak reduction methods.