title: Fast estimation of sparse doubly spread acoustic channels.
abstract: The estimation of doubly spread underwater acoustic channels is addressed. By exploiting the sparsity in the delay-Doppler domain, this paper proposes a fast projected gradient method (FPGM) that can handle complex-valued data for estimating the delay-Doppler spread function of a time-varying channel. The proposed FPGM formulates the sparse channel estimation as a complex-valued convex optimization using an [script-l](1)-norm constraint. Conventional approaches to complex-valued optimization split the complex variables into their real and imaginary parts; this doubles the dimension compared with the original problem and may break the special data structure. Unlike the conventional methods, the proposed method directly handles the complex variables as a whole without splitting them into real numbers; hence the dimension will not increase. By exploiting the block Toeplitz-like structure of the coefficient matrix, the computational complexity of the FPGM is reduced to O(LNlogN), where L is the dimension of the Doppler shift and N is the signal length. Simulation results verify the accuracy and efficiency of the FPGM, indicating that is robust to parameter selection and is orders-of-magnitude faster than standard convex optimization algorithms. The Kauai experimental data processing results are also provided to demonstrate the performance of the proposed algorithm.
authors.affiliation: Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China. cengwj06@mails.tsinghua.edu.cn
authors.forename: Wen-Jun
authors.initials: WJ
authors.lastname: Zeng
authors.forename: Wen
authors.initials: W
authors.lastname: Xu