Compressed sensing based underwater acoustic channel estimation using two dimensional frequency characterization

Abstract

Underwater acoustic (UWA) channel estimation in shallow water depths is a challenging problem due to rapidly fluctuating transients in the acoustic channel impulse response. Transmitted signal undergoes nonstationary reflections at the moving sea surface and rough sea bottom before being received via multiple paths at the receiver. These non-stationary reflections along with unpredictable surges of energy due to surface focusing events render the channel delay spread challenging to localize. In this work, we present compressed sensing (CS) based underwater acoustic channel estimation techniques at the intersection of time, frequency and sparsity. Specifically, following are the key contributions of this work.

First, a 2D frequency domain representation of the channel is obtained via a carefully chosen transmitted signal design. This modeling transforms the problem of channel estimation to channel recovery in 2D Fourier domain. Interestingly, this framework is similar to K-space based image reconstruction used in Magnetic Resonance Imaging (MRI) where CS is used extensively for signal recovery. It is observed that the channel is sparser in the 2D Fourier domain in comparison to the channel in time domain. Thus, the proposed frequency domain representation allows CS framework to be inherited naturally. Here, it is pertinent to add that this framework has been proposed for the first time in UWA.

Second, we introduce non-uniform compressing sampling for shallow water acoustic communications. Specifically, techniques presented in this work perform random CS at different sampling rates across different frequency bands in the 2D frequency domain. We propose non uniform CS with prior information and non-uniform modified-CS with the prior information method for channel estimation wherein application domain knowledge is utilized with reference to frequency domain characteristics of the shallow water channel. Thus, this work illustrates the use of CS methods but by appropriately rooting them in this application domain.

We present numerical validation of proposed techniques based on channel estimates from field experiments as well as a public domain channel simulator that has recently been tested against data from different field trials.