Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027, People's Republic of China.
J Acoust Soc Am. 2012 Jan;131(1):303-17. doi: 10.1121/1.3665992.
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-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.
本文针对双扩展水下声信道估计问题展开研究。通过在延迟-多普勒域上利用稀疏性，本文提出了一种快速投影梯度法（FPGM），该方法可以处理复数数据，用于估计时变信道的延迟-多普勒扩展函数。所提出的 FPGM 将稀疏信道估计表述为使用 script-l-范数约束的复数凸优化问题。传统的复数优化方法将复数变量分解为实部和虚部；与原始问题相比，这会将维度加倍，并且可能破坏特殊的数据结构。与传统方法不同，所提出的方法直接整体处理复数变量，而无需将其分解为实数；因此维度不会增加。通过利用系数矩阵的块 Toeplitz 结构，FPGM 的计算复杂度降低到 O(LNlogN)，其中 L 是多普勒频移的维度，N 是信号长度。仿真结果验证了 FPGM 的准确性和效率，表明其对参数选择具有鲁棒性，并且比标准凸优化算法快几个数量级。还提供了考艾岛实验数据处理结果，以证明所提出算法的性能。
