Incoherent Subspace Method (CSM) Source Code Implementation

The Incoherent Subspace Method (CSM) represents an advanced technique for broadband signal processing, particularly excelling in Direction of Arrival (DOA) estimation. This algorithm effectively addresses the limitations of traditional subspace methods in broadband scenarios by constructing broadband focusing matrices, thereby enhancing the accuracy and robustness of signal source localization.

### Core Algorithm Concept Broadband Signal Processing Challenge: Narrowband algorithms (e.g., MUSIC) exhibit performance degradation in broadband environments due to inconsistent subspace structures across different frequency components. Focusing Matrix Function: CSM designs focusing matrices to project multi-frequency band signals onto the subspace of a reference frequency, achieving consistent frequency-domain alignment. Incoherent Processing: Independently processes data from each frequency band before fusion, avoiding strong assumptions about signal models inherent in coherent methods, thus adapting to more complex real-world scenarios.

### Implementation Workflow Frequency Domain Partitioning: Performs segmented FFT on broadband signals to extract multi-frequency point data (implemented using MATLAB's fft() function with appropriate windowing). Subspace Projection: Computes covariance matrices for each frequency point and maps them to the signal subspace of the reference frequency using focusing matrices (key operations include eigendecomposition via eig() function and matrix inversion). Incoherent Fusion: Applies weighted averaging to subspace information from all frequency points after projection, followed by spectral peak search for final DOA determination (typically implemented through peak-finding algorithms on spatial spectra).

### Advantages and Extensions Strong Anti-interference Capability: Suitable for multipath and low Signal-to-Noise Ratio (SNR) environments. Extensibility: Can be integrated with sparse reconstruction techniques and deep learning approaches to further enhance resolution.

This algorithm holds significant value for high-precision localization in radar, sonar, and related fields. Its core methodology can be adapted to other frequency-domain non-uniform data processing tasks through appropriate modifications to the focusing matrix calculation and fusion weighting schemes.