Handshaking protocol for time-reversal system

A system comprising:

• a first device comprising:
• an input circuit configured to receive a handshake signal transmitted wirelessly from a second device through multiple propagation paths, the handshake signal including a preamble and a training sequence, the training sequence including a sequence of symbols known to the first and second devices;
• and
• a data processor configured to:
• determine a synchronization index based on the preamble;
• identify the training sequence in the handshake signal based on the synchronization index;
• determine a channel response signal based on the received training sequence;
• generate a signature waveform that is a time-reversed signal of the channel response signal;
• and
• generate a transmission signal based on transmit data and the signature waveform, the transmit data being data configured to be transmitted to the second device
• in which the data processor is configured to determine a channel response by calculating =Cq u, in which represents an estimated channel response, Cq represents a conversion matrix, and u represents a portion of the received handshake signal that is estimated to be the received training sequence;
• in which the conversion matrix Cq is determined by calculating Cq=(T′T)−1 T′ in which T is a Toeplitz matrix generated based on sq, which represents an effective training sequence sent by the second device.