An original arbitrary waveform generator (AWG) architecture suited for software radio (SR) transmission is presented. A piecewise linear approximation of the wanted signal is generated thanks to a predefined set of slopes. The digital-to- analog (DA) conversion involved in this operation is based on a differential digital coding which drives a custom digital-to-analog converter (DAC), named here the Riemann Pump. This circuit is in charge of outputting the piecewise linear signal by integration of current steps into a capacitive load, potentially being the input impedance of a power amplifier. Simulations have been carried out on a first design, developed in a GaN technology, with a configuration that covers 1 GHz bandwidth with an oversampling ratio (OSR) of 4 and 3 input bits. The generation of concurrent modulated signals is demonstrated, with a rejection of 30 dBr over the whole band. The system exhibits promising performances as for the realization of a multi standard concurrent radio frequency transmitter with moderate hardware complexity