Communicating wirelessly underwater has been an area of interest for researchers, engineers, and practitioners alike. One of the main reasons for the slow rate of progress in this area is that the underwater acoustic channel is in general much more hostile — in terms of multipath, frequency selectivity, noise, and the Doppler effect — than the over-the-air radio frequency channel. In this work a time warp based technique which can be used to model time-varying wideband Doppler shifts (as seen in an UWA channel) in MATLAB is proposed. A corresponding procedure to estimate the parameters from observed data, required for inverting the effect of the time warp, is also proposed. Two different Doppler correction methods are compared; both can be used to undo the Doppler effect in measured data from an experiment subject to the wideband Doppler effect. The techniques presented correct for the wideband Doppler effect as if it changed the time scale of the received signal. The first resampling based technique corrects for the average expansion/contraction over a packet, inherently assuming the relative velocity to be constant over the duration of the packet. The second time warp based technique models time-varying Doppler shift. Sinusoids, added to the beginning and end of each packet, are used to estimate the parameters required to invert the effect of the warp. The time warp based methods are demonstrated using Orthogonal Frequency Division Multiplexing (OFDM) signals, but will in principle work for other kinds of wideband signals also. The presented results — using MATLAB based simulations, and over-the-air experiments performed in such a way as to introduce the Doppler effect in the received signals — emphasize the improvements that can be attained by using the time warp based Doppler modeling and correction method. The thesis concludes with suggestions for future work. / Master of Science

The Underwater Acoustic (UWA) channel has been an area of interest for many researchers and engineers, but also a very challenging area. Compared to the over-the-air radio frequency (RF) channel, the underwater acoustic channel causes multiple distortions – due to multipath, frequency selectivity, noise, and Doppler – some of which are more severe. The increased distortion causes many techniques and assumptions made for typical RF communication systems to break down. One of the assumptions that breaks down is that the Doppler effect that the signal undergoes can be modelled with a simple shift in frequency, since the signals used to communicate in a UWA channel are effectively wideband. In this work the Doppler Effect that a signal undergoes is modelled as a nonlinear time warp. A procedure is developed to estimate the parameters of the time warp from the observed signal. These time warp parameters are then used to reverse the effect of the time warp. Two different methods for estimating the time warp parameters and correcting the Doppler are compared. The first technique uses sinusoids placed at the beginning and end of the signal to estimate the parameters of the warp that the signal undergoes. The second technique uses sinusoids that are present during the signal to estimate and correct for the warp. The frequencies of the sinusoids are outside of the frequency range used for the transmitted data signal, so there is no interference with the information that is being sent. The transmitted data signal uses Orthogonal Frequency Division Multiplexing (OFDM) to encode the data symbols, but the Doppler Correction technique will in principle work for other kinds of wideband signals as well. The results, which include MATLAB based simulations and over-the-air experiments, show that performance improvements can be realized using the time warp correction model. / Master of Science