1. A process comprising: receiving a digital input signal; producing a digital pre-distortion signal from the digital input signal in response to a non-linear impairment digital pre-distortion error signal; amplifying the digital pre-distortion signal with a power amplifier to produce a radio frequency output signal; producing from the radio frequency output signal a digital feedback signal that includes linear impairments and non-linear impairments; separating the linear impairments from the non-linear impairments; subtracting the linear impairments from the digital feedback signal to result in a non-linear impairment digital pre-distortion error signal; and updating the producing a digital pre-distortion signal from the digital input signal in response to the non-linear impairment digital pre-distortion error signal from the subtracting.