块稀疏水声信道的改进压缩感知估计

压缩感知信道估计可利用信道稀疏特性提高估计性能,但对于具有典型块稀疏分布的水声信道,经典的l₀或l₁范数无法很好地描述块稀疏特性。利用水声信道块稀疏分布规律特性提出一种能够识别块稀疏结构的块稀疏似零范数,并在稀疏恢复信道估计算法中引入块稀疏似零范数约束项,进一步推导了复数域块稀疏似零范数恢复迭代算法,该算法通过对块稀疏似零范数进行梯度下降迭代并将梯度解投影至解空间来获得水声信道的块稀疏似零范数估计。数值仿真和海上水声通信实验结果表明该算法相对经典的稀疏信道估计算法有较明显的性能改善。通过算法推导、仿真和实验可获取结论:利用水声信道的块稀疏特性进行压缩感知重构可有效提高信道估计性能。 

Improved compressed sensing estimation of block sparse underwater acoustic channel

For sparse underwater acoustic channels, compressed sensing methods can be adopted to improve the estimation performance. The classic l₀ or l₁ norm, however, are limited in describing the block sparse distributed characteristics of the underwater acoustic channel. We introduce the block sparsity identification term, i.e. block sparse approximated l₀ norm (BAL0) to address this problem. By adopting complex projected gradient method and then projecting the gradient solution to a set of the underwater acoustic channel solution space, an iterative algorithm is derived to solve the complex-field BAL0 norm channel estimation. Both the numerical simulation and experimental results show that the proposed algorithm has significant performance improvement compared with classic sparse signal recovery algorithms. By the derivation of the algorithm, simulations and at-sea experiment, one can conclude that the estimation quality of underwater acoustic channel can be improved by exploiting its block sparsity in compressed sensing reconstructions.