A communications system and method for transmitting digital information includes arranging a modulator to have an input bit stream of binary data and arranging a signal generator to generate four orthonormal hyper phase shift keying (HPSK) basis functions that are periodic functions with a duration T. A bit to symbol mapper is arranged to combine the bit stream and the HPSK basis functions to form a succession of 4-bit HPSK symbols for 16-HPSK, 5-bit HPSK symbols for 32-HPSK or 6-bit HPSK symbols for 64-HPSK, and a transmitter is arranged to transmit signals indicative of the HPSK symbols. A receiver is arranged to receive the signals from the transmitter and the HPSK symbols are demodulated with the HPSK basis functions to reproduce the bit stream of binary data.