Decision-Aided Progressive Symbol Phase Equalizer in Sweep Spread Carrier Underwater Acoustic Communications

Sweep spread carrier (S2C) acoustic communication uses wideband chirp waveforms as they are well suited for communicating in an undersea multipath environment. While the gradient heterodyne receivers in the S2C systems can handle the multipath arrivals, we show that they are extremely sensitive to a time scaling of the communication waveform induced by the Doppler effect or carrier frequency offset. The time-scaling can be estimated, and compensated for by re-scaling the received waveform. However, estimation errors leave out a residual timescale even in the re-scaled waveform. We show that even a timescale estimation error of the order of ±10<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">–5</sup> can lead to deleterious variations in the symbol phases within a received S2C frame. We also show the existence of multiple, frequency-dependent, approximately affine symbol phase migration trajectories in a received frame in the presence of small residual time-scales and timing errors. Motivated by this observation, we propose a parallel bank of low complexity decision-aided progressive symbol phase (DAPSP) equalizers to effectively suppress the symbol phase migration in the S2C receiver.