双扩展水声信道的时延多普勒域稀疏估计

利用双扩展水声信道在时延-多普勒域存在的稀疏结构,将信道估计转化为压缩感知框架下的稀疏恢复问题可改善估计性能。但是,稀疏恢复经典方法如l_1范数、近似l₀范数无法适应水声信道时延-多普勒域稀疏度的动态变化,而匹配追踪(Matching pursuit,MP)、正交匹配追踪(Orthogonal Matching Pursuit,OMP)等贪婪类算法则存在着易进入局部最优解、二维搜索导致运算复杂度高等问题。提出在时延-多普勒域稀疏恢复的目标函数中引入非均匀范数约束(Non-uniform Norm Constraint,NNC),即在时延-多普勒域信道响应中根据每个时延-多普勒域位置的幅值分别分配为l₀或l₁范数约束,因而可通过不同范数约束组合的方式适应不同的时延-多普勒域稀疏度;同时,通过对非均匀范数代价函数进行梯度下降迭代求解并将梯度解投影至解空间推导了非均匀范数稀疏恢复的迭代求解方法,从而实现双扩展水声信道时延-多普勒估计。数值仿真和实验数据处理表明该算法相对经典方法有较明显的性能改善。通过仿真、海上水声通信实验结果可获取结论,利用时延-多普勒域稀疏特性的信道估计方法结合均衡器可有效提高双扩展信道条件下的水声通信性能。 

Estimation of doubly-spread sparse underwater acoustic channels

In view of the Delay-Doppler (DD) domain sparse structure, estimation of doubly-spread UWA channel can be converted to the problem of sparse recovery under the framework of compressed sensing to achieve performance gain. Although the classic sparse recovery methods such as 11 norm, or approximated l₀ norm algorithms are subject to performance degradation at the presence of various sparsity pattern of the UWA channels, greedy methods including MP (matching pursuit) and OMP (orthogonal matching pursuit) suffer from the drawbacks of local minima traps. A newly defined non-uniform norm constraint (NNC) is proposed to assign into the two dimension objective function of the DD domain sparse recovery, i.e., sparse components in the DD domain are uniformly formulated as 11 norm or l₀ norm constraint according to relative magnitude, to enable sparsity adaptability at the form of different 11 norm or 10 norm mixture. Meanwhile, the iterative method for NN domain sparse recovery is derived by the gradient descent recursion and projecting the solution of which to feasible set. Numerical simulation validates the performance improvement of the proposed algorithm compared to the traditional methods. Furthermore, the UWA communication experimental results demonstrate the superiority of the proposed method in the form of an equalizer driven by channel estimator.