RLS Linear Array Algorithm Based on Recursive Principle

The Recursive Least Squares (RLS) algorithm is an efficient adaptive filtering technique particularly suitable for linear array signal processing scenarios. This algorithm recursively updates weight coefficients through iterative computations, enabling rapid tracking of signal variations and demonstrating excellent performance in real-time systems. In code implementation, the RLS algorithm typically maintains a covariance matrix P and weight vector w that update with each new input sample using matrix recursion formulas.

The core advantage of RLS lies in its recursive computation that avoids direct matrix inversion operations. Traditional least squares methods require repetitive inverse matrix calculations, where computational complexity increases dramatically with data volume. RLS algorithm introduces a forgetting factor λ and gain vector k to achieve linear growth in computational load, maintaining efficiency even when processing long data sequences. Code implementations often feature a key update step: w(n) = w(n-1) + k(n)*e(n), where e(n) represents the prediction error and k(n) is the Kalman gain calculated from the covariance matrix.

In linear array applications, RLS algorithm is commonly employed for beamforming and interference suppression. After each sensor in the array receives signals, the algorithm adaptively adjusts channel weights through gradient-based updates, enhancing desired signals while suppressing interference. This adaptive characteristic makes RLS valuable in wireless communications, radar, and sonar systems. Implementation typically involves initializing weight vectors and designing update loops that process array element inputs sequentially.

RLS algorithm implementation requires careful consideration of key parameters: the forgetting factor controls the algorithm's memory of historical data, while the regularization parameter δ influences numerical stability. Proper parameter setting is crucial for algorithm performance, requiring balance between convergence speed and steady-state error. Code implementations often include parameter tuning mechanisms and stability checks, such as monitoring matrix condition numbers to prevent numerical divergence.