Weighted Subspace Fitting (WSF) for DOA Estimation with Sparse Uniform Circular Arrays

Weighted Subspace Fitting (WSF) is a high-resolution Direction of Arrival (DOA) estimation algorithm particularly suitable for sparse uniform circular array (UCA) configurations. This method estimates signal arrival directions by optimizing a subspace fitting problem, effectively improving estimation accuracy while reducing computational complexity. In code implementation, the WSF algorithm typically involves constructing covariance matrices from received signals and performing eigenvalue decomposition to separate signal and noise subspaces.

Sparse uniform circular arrays consist of antenna elements uniformly distributed along a circular perimeter. Due to physical constraints or cost considerations, these arrays typically have fewer elements, making WSF methodology ideal for maximizing performance with limited data. The core concept of weighted subspace fitting involves constructing a cost function based on projection differences between signal and noise subspaces, then solving for DOA through optimization. Code implementation would require careful matrix operations for subspace projection and orthogonal complement calculations.

The optimization process typically employs the steepest descent method, an iterative optimization technique. This algorithm updates parameters along the gradient direction of the cost function at each step, gradually approaching the optimal solution. Compared to second-order optimization methods like Newton's algorithm, steepest descent requires less computational overhead, making it suitable for real-time systems. However, step size selection requires careful consideration to avoid slow convergence or oscillation issues. In programming terms, this involves implementing gradient calculation routines and adaptive step size control mechanisms.

The combination of WSF with sparse uniform circular arrays offers significant advantages in sidelobe interference suppression and angular resolution enhancement. Its performance surpasses traditional beamforming and MUSIC algorithms, particularly in challenging scenarios involving low signal-to-noise ratios or multipath environments for DOA estimation tasks. The algorithm can be implemented using matrix computation libraries like NumPy or MATLAB, with key functions focusing on covariance matrix estimation, eigenvalue decomposition, and iterative optimization routines.