This paper presents an original agile all-digital feedback loop receiver system for power amplifier (PA) linearization using digital predistortion (DPD). The proposed feedback loop is based on a radio-frequency pulse-width modulation analog-to-digital converter. For proof of concept, the system was implemented using a single field programmable gate array chip. Additionally, the system is also presented in a remote version, suitable for future centralized radio access network, in which the DPD can be performed in a central unit, far from the PA. Measurement results of important DPD metrics, such as adjacent channel power ratio (ACPR) and error vector magnitude (EVM), are presented and evaluated to verify the correct functioning of the proposed feedback loop. The obtained results demonstrate the system's agility and high analog input bandwidth from a few megahertzes up to almost 4 GHz, while maintaining the LTE ACPR and EVM requirements.