适用于通信信号盲源分离的 分离条件数学建模方法研究

针对使用盲源分离技术分离卫星通信信号的数学假设工程实施问题，重点对分离条件中的数学假设混合矩阵列满秩展开研究。根据最优化理论，提出了一种适用于通信信号盲源分离的分离条件数学建模方法。首先，介绍了盲源分离的分离模型与基本假设；其次，选择矩阵条件数来衡量混合矩阵的正定性，并结合阵列天线接收模型，以矩阵条件数为目标函数，建立最优化模型，寻找最优天线间距；最后，以两个信号源、两个接收天线为例进行仿真。仿真结果表明：所建立的优化模型可以有效找到最优天线间距，通过设计合适的天线间距可以有效满足混合矩阵列满秩条件。最优天线间距与载波频率成反比。该建模方法有效将抽象的数学假设转化为具体的天线间距设计，加强了盲源分离技术的可实施性，为大规模的盲源分离天线阵列设计提供技术支撑。

Research on mathematical modeling method of separation conditions for blind source separation of communication signals

Aiming at the engineering implementation problem of separating satellite communication signals using blind source separation technology, the mathematical assumption of the full rank of the mixed matrix column in the separation conditions is emphatically studied. Based on the optimization theory, a mathematical modeling method of separation conditions for blind source separation of communication signals is proposed. Firstly, the separation model and basic assumptions of BSS are introduced; Then, the condition number of the matrix is selected to measure the positive definiteness of the mixed matrix, and combined with the array antenna receiving model, the optimization model is established with the condition number of the matrix as the objective function to find the optimal antenna spacing; Finally, two signal sources and two receiving antennas are simulated. The simulation results show that the optimization model can effectively find the optimal antenna spacing, and the full rank condition of the mixed matrix column can be effectively satisfied by designing appropriate antenna spacing. The optimum antenna spacing is inversely proportional to the carrier frequency. The optimization model effectively translates abstract mathematical assumptions into specific antenna spacing design, providing technical support for large-scale BSS antenna array design.