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Power amplifiers (PAs) are inherently nonlinear devices that introduce intermodulation to the amplifier output, which can exceed regulatory frequency mask limits and degrade demodulated constellation quality. One solution is to operate the PA in a highly backed-off state to achieve quasi-linear performance. A more effective, low-cost solution is to apply digital predistortion which pre-compensates for the harmful nonlinear effects. This technique is frequently researched with accessible, i.e. ground-based, PAs in mind. This article instead pertains to the many nonlinear PAs on-board orbiting communication satellites that could significantly benefit from such compensation, but are not accessible. We propose a remote version of digital predistortion, which is based upon the indirect learning architecture. Several additional complications arise in the remote version including uplink/downlink additive noise, signal accessibility, time-varying satellite round-trip delay, and predistorted uplink signal restrictions. A monostatic and bistatic remote predistortion architecture are shown to address these issues and provide significant in-band improvement.