Closed-form expressions for the spectral regrowth of CDMA signal passing through a nonlinear amplifier with a digitally modulated carrier are derived using the power series and statistical methods of high-order cumulant. The technique yields an analytical expression for the autocorrelation function of the output signal as a function of the statistics of the input signal transformed by a behavioral model of the amplifier. The third-order nonlinearity is expressed in terms of to include the memory effects of the circuit in-band and out-of-band reactance. The analysis is based on a time-domain model of the signal and the model is used to derive the power spectrum density and other statistical properties of the CDMA signal. Such analytical results are useful in finding optimal operating conditions of the power Amplifier.