Abstract: A compensator compensates for the distortions of a power amplifier circuit. A power amplifier neural network (PAN) is trained to model the power amplifier circuit using pre-determined input and output signal pairs that characterize the power amplifier circuit. Then a compensator is trained to pre-distort a signal received by the PAN. The compensator uses a neural network trained to optimize a loss between a compensator input and a PAN output, and the loss is calculated according to a multi-objective loss function that includes one or more time-domain loss function and one or more frequency-domain loss functions. The trained compensator performs signal compensation to thereby output a pre-distorted signal to the power amplifier circuit.