Closed-form approximations to the out-of-band emission due to nonlinear power amplifier

The total out-of-band emission (OOBE) from the secondary users (SU) is determined not only by the baseband signaling waveforms, but also by the design of the transmitter chain, which includes the nonlinear power amplifier (PA). The increase in OOBE due to a nonlinear PA has been well-observed, but its characterization involves complicated analysis. In this paper, we present a closed-form approximation to the power spectral density (PSD) of a signal at the output of a nonlinear PA, or more specifically, the solid-state power amplifier (SSPA). The SSPA´s response can be approximated using a third order nonlinear model (TONM) which has been proposed in literature. Using the TONM, we proposed a statistical approximation, together with a piecewise linear model, to determine a closed-form estimate to the OOBE of the PA output signal. Simulation results show a close fit between the theoretical expression for the derived PSD and the simulated model. Since the nonlinear PA increases the OOBE due to spectral regrowth, the ability to characterize this behavior is of particular importance to the application of TV band devices (in television broadcast frequency bands) that need to fulfill certain OOBE limits.