Compressed Sensing of Delay and Doppler Spreading in Underwater Acoustic Channels

The measurements of delay and Doppler (DD) spreading in underwater acoustic channels (UACs) have multiple applications, including communications as well as the development of a dynamic UAC simulator. However, these measurements suffer from the difficulties of fast time variations and large data sets. This paper addresses an efficient compressed sensing (CS) method to solve these problems. First, the DD spreading in UACs is studied by using a doubly spread model; second, the least-square criterion is implemented and its limit is analyzed. Subsequently, the matching pursuit (MP) method is applied to the problem by exploiting the sparsity of the DD model-based UACs. Although the MP method improves the performance of the LS method, it has unavoidable deficiencies, e.g., the redundant selections of bases that lead to a limited measurement of DD spreading. Thus, this paper proposes an improved version by inserting a projection matrix. The projected MP (PMP) method adopts QR decomposition for an efficient computation. Finally, at-sea data-based comparisons among the above mentioned three methods are conducted to verify the superiority of the PMP method.