Detection and synchronization of audio transmissions using complex audio signals

A system comprising:

• a processor;
• and
• a memory storing instructions which, when executed by the processor, cause the processor to:
• receive an audio signal that contains an audio transmission, the audio transmission containing (i) a predetermined portion and (ii) data for transmission using the audio transmission;
• compute a first plurality of similarity measures between (i) a real portion of an expected sequence of complex values and (ii) a first plurality of portions of the audio signal, the first plurality of portions of the audio signal beginning at a first plurality of times;
• determine that a first portion of the audio signal from among the first plurality of portions of the audio signal corresponds to the largest of the first plurality of similarity measures, the first portion of the audio signal beginning at a first time from among the first plurality of times;
• compute a second plurality of similarity measures between (i) the real portion of the expected sequence and an imaginary portion of the expected sequence of complex values and (ii) a second plurality of portions of the audio signal, the second plurality of portions of the audio signal beginning at a second plurality of times;
• determine that a second portion of the audio signal from among the second plurality of portions of the audio signal corresponds to the largest of the second plurality of similarity measures, the second portion of the audio signal beginning at a second time from among the second plurality of times;
• and
• determine an arrival time of the audio transmission based on the second time.