Differences between passive-phase conjugation and decision-feedback equalizer for underwater acoustic communications

Passive-phase conjugation (PPC) uses passive time reversal to remove intersymbol interferences (ISIs) for acoustic communications in a multipath environment. It is based on the theory of signal propagation in a waveguide, which says that the Green's function (or the impulse-response function) convolved with its time-reversed conjugate, summed over a (large-aperture) vertical array of receivers (denoted as the Q function) is approximately a delta function in space and time. A decision feedback equalizer (DFE) uses a nonlinear filter to remove ISI based on the minimum mean-square errors (mmse) between the estimated symbols and the true (or decision) symbols. These two approaches are motivated by different principles. In this paper, we analyze both using a common framework. We note the commonality and differences, and pros and cons, between the two methods and compare their performance in realistic ocean environments, using simulated and at-sea data. The performance measures are mean-square error (mse), output signal-to-noise ratio (SNR), and bit-error rate (BER) as a function of the number of receivers. For a small number of receivers, the DFE outperforms PPC in all measures. The reason for poor PPC performance is that, for a small number of receivers, the Q function has nonnegligible sidelobes, resulting in nonzero ISI. As the number of receivers increases, the BER for both processors approaches zero, but at a different rate. The modeled performance differences (in mse and SNR) between PPC and DFE are in general agreement with the measured values from at-sea data, providing a basis for performance prediction.