The simulation of the steady state and the non-linear stability of a load modulated power amplifier (LMPA) driven by a random modulated generator, fully performed in the frequency domain by harmonic balance (HB) techniques, is presented. The non-linear microwave circuit and the driving pseudo-random modulated (PRM) generator are integrally defined in the frequency domain. The simulation is implemented and performed using commercially available circuit simulation software. The demodulation of the output signal of the LMPA is implemented with optimally matched filters as software-defined demodulation. The simulated dynamic results of a Quasi-MMIC GaN Doherty power amplifier (DPA) are shown and compared to the measured results with a 16-QAM driving signal at 10 MS/s. The time-domain measurement allows the validation of the new simulation technique through the comparison of both the measured and the simulated error vector magnitude (EVM), the left and right adjacent channel power ratios (ACPRs) versus the average output power. This new simulation is then called pseudo-random modulated harmonic balance (PRM-HB) simulation. The full PRM-HB simulation of an LMPA driven by a random modulated signal, performed in the frequency domain at the design circuit level, results in an advanced simulation tool in the frame of the design of RF circuits and subsystems for telecommunication applications.