Channel Estimation in Time-Varying Ocean Environments Using OTFS Modulation

Communication through the ocean is challenging due to its rapidly time-varying nature. Studies indicate that the ocean channel in the delay-Doppler domain displays a sparse structure that remains constant for an extended duration compared to other domains. Recent advancements in orthogonal time-frequency spacing (OTFS) have demonstrated the feasibility of communication within the delay-Doppler domain. Given the context of a sparse 2-D delay-Doppler channel <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H$</tex> E C<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MXN</sup> with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$M$</tex> frequency tones and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$N$</tex> pulses, the algorithm leverages the properties of the cyclic prefix (CP). This characteristic trans-forms the cyclic convolution of the 2-D input, structured using OTFS, with channel <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H$</tex> into an estimation of FFT(Vec(H)). The process results in an ultra-long FFT, providing a precise channel estimate. This method combines long fast Fourier transform (FFT) sequences with the diagonalization method, making our algorithm simple to implement on hardware. We further enhance the algorithm by exploiting the sparsity of the channel matrix through the sparse Bayesian learning (SBL) method.