Systems and methods for communicating by modulating data on zeros in the presence of channel impairments

A communication system, comprising:

• a transmitter, comprising:
• an encoder configured to receive a plurality of information bits and output a plurality of encoded hits in accordance with a cycling register code (CRC);
• a modulator configured to modulate the plurality of encoded bits to obtain a discrete-time baseband signal, where the plurality of encoded bits are encoded in the zeros of the z-transform of the discrete-time baseband signal;
• and
• a signal generator configured to generate a continuous-time transmitted signal based upon the discrete-time baseband signal;
• a receiver, comprising:
• a demodulator configured to down convert and sample a received continuous-time signal at a given sampling rate to obtain a received discrete-time baseband signal, where the received discrete-time baseband signal includes at least one of a timing offset (TO) and a carrier frequency offset (CFO);
• a decoder configured to decode a plurality of bits of information from the received discrete-time baseband signal by:
• estimating a TO for the received discrete-time baseband signal to identify a received symbol;
• determining a plurality of zeros of a z-transform of the received symbol;
• identifying zeros from the plurality of zeros that encode a plurality of received bits;
• and
• decoding a plurality of information bits based upon the plurality of received hits using the CRC.