A low cost high-efficiency all-digital transmitter using all-digital power amplifiers (“DPA”) and various mapping techniques to generate an output signal, which substantially reproduces a baseband signal at a carrier frequency. A baseband signal generator generates a baseband signal which is quantized by a signal processor using a quantization map. A DPA control mapper outputs control signals to phase selectors using the quantized signal and a quantization table. Each phase selector receives one of the control signals and outputs a waveform at a carrier frequency with a phase corresponding to the control signals, or an inactive signal. Each DPA in a DPA array has an assigned weight, receives one of the waveforms from the phase selectors, and outputs a power signal according to the weight of the DPA and the phase of the received waveform. The combined power signal substantially reproduces the baseband signal at the carrier frequency.