A system for communicating includes a transmitter that has an encoder and baseband modulator that encodes and modulates a sequence of data symbols as a payload data constellation to be communicated. A PN sequence generator and baseband modulator form a pilot signal as a training sequence with a periodically repeating spread spectrum sequence. A circuit superimposes the pilot signal over the sequence of data symbols to form a composite communication signal that is transmitted. A receiver receives the composite communication signal and extracts the pilot signal from the composite communication signal.