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This paper presents a method for achieving high-efficiency linear transmitters by codesign of the RF power amplifier (PA), dynamic supply, and signal processing. For varying amplitude signals, the average efficiency of the PA is improved by adding a supply modulator with requirements derived from nonstandard PA modeling. The efficient PA and supply modulator both introduce signal distortion. A targeted linearization procedure is demonstrated with reduced complexity compared to standard digital predistortion. Experimental results on a 2.14-GHz 81% efficient 40-W peak power GaN PA illustrate the codesign method by achieving 52.5% composite power-added efficiency with high linearity for a W-CDMA signal with a 23-MHz supply modulator bandwidth.