Turbo receivers for single-input single-output underwater acoustic communications

A method for estimating, using a Bi-SDFE having a SDFE on a first leg in parallel with a time-reversed SDFE on a second leg, a transmitted symbol encoded on a received signal, the method comprising:

• feeding an input signal to each of the first leg and the second leg of the Bi-SDFE;
• calculating a covariance matrix to obtain an estimated covariance;
• updating a feedforward filter and a feedback filter of the SDFE with the estimated covariance and updating a feedforward filter and a feedback filter of the time-reversed SDFE with the estimated covariance;
• filtering, with the SDFE, the input signal communicated to the first leg and determining a first set of bit extrinsic LLRs;
• filtering, with the time-reversed SDFE, the input signal communicated to the second leg and determining a second set of bit extrinsic LLRs;
• combining the first set of bit extrinsic LLRs and the second set of bit extrinsic LLRs to obtain a combined bit extrinsic LLRs;
• and
• estimating the transmitted symbol encoded on the received signal using the combined bit extrinsic LLRs.

An improved single-input single-output (“SISO”) underwater acoustic (“UWA”) modem comprising:

• an acoustic receiver comprising at least one acoustic sensor configured to receive SISO UWA transmissions;
• a memory;
• and
• a signal processing unit in communication with the acoustic receiver, the signal processing unit configured to jointly perform channel equalization and decoding of the SISO UWA transmissions in an iterative fashion using a bidirectional soft-decision feedback turbo equalizer (“Bi-SDFE”) and a maximum a posteriori probability (“MAP”) decoder.