New Dichotomous Implementation Approach for Doppler-Shift Estimation and Compensation in an Underwater Acoustic Modem

As a renewed interest in ocean exploration emerges, mainly driven by a much broader autonomous presence, under-water acoustic communications have become essential. But as acoustic waves are most effective only at ranges greater than hundred meters, a number of problems arise in operational conditions, such as low throughput, long propagation delay, multi-path effect and last but not least the impact of Doppler shift. In order to compensate for Doppler effect in the decoding stage, the Doppler shift must be accurately estimated at the receiver side. Several methods can be invoked, however the use of filter banks is known to be one of the most accurate method in the state of the art. In this paper, we propose an FPGA implementation of Doppler estimation based on correlation between the received signal (which contains a known sequence) and numerous dopplerized versions of this known sequence. We take advantage of FPGA technology to run 2 comparisons in parallel, and iterate following a dichotomy approach in order to converge towards the actual Doppler value. Compared to a solution that iteratively searches for the maximum correlation with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> values, our approach only needs to make <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\log_{2}n$</tex> comparisons, in only <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\log_{2}n/2$</tex> as much time, to achieve the same precision. This makes our implementation well suited for real-time applications while still keeping the resource footprint fairly low.