Simulation of DOA Estimation Algorithm Using Sparse Representation of Wideband Signal Covariance Matrix

Direction of Arrival (DOA) estimation for wideband signals is a crucial problem in array signal processing, with the core objective of determining the spatial方位 of signal sources through signals received by sensor arrays. Traditional narrowband DOA estimation methods exhibit performance limitations in wideband signal scenarios, making algorithms based on sparse representation of covariance matrices a research hotspot in recent years. Challenges in Wideband Signal DOA Estimation Wideband signals possess broad frequency spectra, preventing direct application of traditional narrowband algorithms (such as MUSIC and ESPRIT). In wideband environments, the energy distribution across different frequency bands is uneven, making it difficult for conventional methods to fully exploit the directional information of signals, often leading to reduced estimation accuracy. Fundamental Concept of Covariance Matrix Sparse Representation The core idea of this approach involves modeling the covariance matrix of wideband signals with a sparse structure, assuming that the方位 distribution of signal sources is spatially sparse (only a few directions contain active signals). Through optimization algorithms, sparse solutions are sought on spatial angle grids to determine the true signal directions. Algorithm Simulation Workflow 1. Wideband Signal Modeling: Typically employs frequency-domain block processing, decomposing wideband signals into multiple narrowband components. Implementation typically involves using FFT operations and frequency bin partitioning in MATLAB or Python. 2. Covariance Matrix Calculation: Computes covariance matrices for signals in each frequency band, followed by averaging or weighted fusion to enhance robustness. Code implementation usually involves matrix operations and eigenvalue decomposition for each subband. 3. Sparse Regression Optimization: Employs sparse recovery algorithms (such as L1-norm optimization, Orthogonal Matching Pursuit-OMP) to solve for sparse solutions under a given angle dictionary matrix. Key implementation aspects include regularization parameter tuning and convergence criteria setting. 4. DOA Estimation: Determines the true directions of signal sources based on the positions of non-zero elements in the sparse solution. This step involves peak detection algorithms and threshold setting in practical code implementation. Significance of Simulation Verification Simulations can validate algorithm performance in terms of signal-to-noise ratio (SNR), angular resolution, and computational complexity. Common tests include: estimation accuracy under different SNRs, separation capability for multiple signal sources, and computational efficiency comparisons. Furthermore, simulations help optimize algorithm parameters (such as regularization coefficients and grid density) to improve adaptability in practical applications. This algorithm holds significant application value in radar, sonar, wireless communications, and other fields, particularly for wideband signal localization in complex environments. Future research could focus on adaptive sparse dictionary construction in dynamic scenarios to enhance the algorithm's real-time performance and robustness.