Computation of the continuous-time PAR of an 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 continuous-time PAR of an OFDM signal, with any PSK or QAM constellations, is developed here. It is shown that the derivative of 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 EPF can be obtained by solving a polynomial. The procedure may be useful for theoretical studies of PAR distributions and developing the peak reduction methods.