Covert acoustic communications through solid propagation channels using spread spectrum coding and adaptive channel pre-distortion

A method of covert acoustic communication between a plurality of nodes including at least N1, N2, N3, . . . Nm, comprising:

• for each node pair,
• determining at each node a channel response H(f) having an amplitude and phase from a transmitted and received wideband channel sounding pulse of bandwidth BWWB propagating as elastic waves along a continuous solid path connecting the node pair, said channel response H(f) having a global average amplitude response over bandwidth BWWB;
• selecting at each node a contiguous narrow frequency bandwidth BWNB<BWWB, center frequency fc from the channel response H(f) over which a local average amplitude response is greater than the global average amplitude response and a spread spectrum rate;
• and
• exchanging the bandwidth BWNB and center frequency fc between the pair of nodes,
• for each transmitting node of a node pair;
• given a spreading factor for a unique spread spectrum code, selecting a rate for a narrowband information signal such that a spread information signal has a bandwidth approximately equal to but not greater than bandwidth BWNB;
• forming the spread information signal, using the unique spread spectrum code;
• modulating the spread information signal onto the transmitting node's center frequency fc to place the spread information signal within transmitting node's bandwidth BWNB;
• pre-distorting the spread information signal with a pre-distortion filter of 1/H(f) of the transmitting node over bandwidth BWNB at center frequency fc of the transmitting node to form a transmit signal;
• and
• transmitting the transmit signal over the continuous solid path,
• for each receiving node of a node pair;
• demodulating a received time signal with the transmitting node's center frequency fc;
• and
• de-spreading the demodulated time signal using the transmitting node's unique spread spectrum code.

A method of covert acoustic communication from at least node N1 to at least node N2, comprising:

• determining a channel response H(f) having an amplitude and phase from a transmitted and received wideband channel sounding pulse of bandwidth BWWB propagating as elastic waves along a continuous solid path connecting nodes N1 and N2, said channel response H(f) having a global average amplitude response over bandwidth BWWB;
• selecting a contiguous narrow frequency bandwidth BWNB<BWWB and center frequency fc from the channel response H(f) over which a local average amplitude response is greater than the global average amplitude response;
• given a spreading factor for a unique direct-sequence spread spectrum (DSSS) code, selecting a rate for an information signal such that a chip rate for a spread information signal has a bandwidth approximately equal to but not greater than bandwidth BWNB;
• at node N1,
• spreading the information signal by the spreading factor, using the unique spread spectrum code, to form the spread information signal;
• pre-distorting the spread information signal with a pre-distortion filter of 1/H(f) over bandwidth BWNB at center frequency fc to form a transmit signal;
• and
• transmitting the transmit signal from node N1 over the continuous solid path to node N2 to covertly communicate the information signal,
• at node N2,
• demodulating a received time signal with center frequency fc;
• and
• de-spreading the demodulated time signal using the spread spectrum code and chip rate unique to node 1.