基于压缩感知联合稀疏重构的宽带阵列信号处理技术

CS(Compressive-Sensing)-based wideband array signal processing techniques using the framework of sparse reconstruction can avoid the main drawbacks of subspace-based methods. However, current CS-based approaches still suffer from a few limitations, such as lacking of suitable sparse representation models, undesirable reconstruction performance in enviroments with low signal-to-.noise ratio, sensitivity to the array and model errors and so on. In this project, suitable joint sparse representation models will be built for wideband array signals. The assumption about same sparsity structure shared by all narrowband components in existing algorithms will be broken to improve the reconstruction performance. Some novel and effective joint sparse reconstruction algorithms belonging to the greedy iteration, non-convex optimization and Bayesian methods will be developed to meet the requirments of array processing on computational complexity, reconstruction efficiency and convergence tendency respectively. Besides, the deterministic and stochastic models will be built for basis mismatch caused by practical errors. The joint sparse reconstruction methods performing error calibration and sparse signal reconstruction alternatively will be investigated to improve the robustness. The main contents are as follows: the investigations for joint sparse representation models and joint sparse reconstruction algorithms in wideband arrays, the exploration on basis mismatch and robust joint sparse reconstruction algorithms, the theoretical studies on the conditions for direction identification and waveform recovery, and the theoretical and simulation analysis for the performance of the proposed algorithms. By building models, designing algorithms and proposing theories, this project will promote CS-based wideband array signal processing techniques further and provide original research achievements for this field.

基于压缩感知稀疏重构框架的宽带阵列信号处理技术可以避开子空间方法的主要缺陷，但是现有技术仍存在稀疏表达模型不完善、低信噪比环境下重构性能不理想、对阵列及建模误差敏感等问题,本项目为宽带阵列信号建立恰当的联合稀疏表达模型，突破所有窄带分量共享相同稀疏结构的假设从而改善已有算法的重构性能，采用贪婪迭代、非凸优化和贝叶斯的联合稀疏重构方法从不同角度满足阵列处理对复杂度、重构效率、收敛性能等方面的要求；建立确定性和随机性的基不匹配模型，通过误差校准和稀疏信号联合交替更新来改善稳健性。主要内容有：宽带阵列联合稀疏表达模型和联合稀疏重构算法的研究，基不匹配模型和稳健的联合稀疏重构算法的研究，对方向可辨识条件和波形可恢复条件的理论研究以及对算法性能的理论和仿真分析验证。本项目的研究将从建模、算法和理论三个方面推动和完善基于压缩感知联合稀疏重构的宽带阵列信号处理技术的研究，为该领域提供具有原创性的成果。

近几年国内外对压缩感知稀疏重构框架下的宽带阵列信号处理技术非常关注，本项目针对现有算法存在的问题展开了研究，获得了一系列具有原创性的成果，主要包括：1）针对稀疏表达模型不完善的问题，我们设计了频域的联合稀疏表达模型、 网格外目标波达方向估计模型以及对阵元位置误差稳健的稀疏表达模型；2）针对低信噪比条件下重构性能不理想的问题，我们设计了多字典（包括多字典多测量矢量）的聚焦欠定系统解（MSM-FOCUSS）的联合稀疏重构算法以及基于块耦合（Pattern-Coupled）的稀疏重构算法；3）针对稀疏重构对阵列误差和建模敏感性高的问题，提出了基于协方差的稳健稀疏重构（Robust CovSR）算法，基于噪声子空间拟和（NSF）的网格外目标波达方向估计算法，以及基于时间块的网格不匹配联合稀疏贝叶斯算法；4）另外，在多字典联合稀疏重构算法和基于协方差的稳健稀疏重构算法中，我们对方向可辨识条件和方向估计的克拉美罗下界（CRLB）进行了理论分析。