Systems and methods are directed to phase modulation of polar coordinates in a transmitter of wireless signals, to achieve high transmit power levels while meeting spectral mask and EVM requirements. An input signal is mapped to a sequence of modulation frequency (e.g., O-QPSK to MSK) to generate a mapped signal. A digital frequency shaping filter is applied to the mapped signal to generate a shaped signal. An adaptive rounding algorithm is applied to the shaped signal to generate a reduced bit-width signal. A digital frequency synthesizer is applied to the reduced bit-width signal to generate an analog waveform for transmission.