The sparse controlled proportionate recursive least square algorithm performs well for the systems with variable sparsity and for systems with fixed sparsity. The algorithm updates each filter weight iteratively with different gain factors to increase the rate of convergence. It uses the degree of sparseness to calculate the gain factor during iterations. The estimated degree of sparseness is calculated for the estimated weight vector. The proportionate matrix assigns independent gain to each filter weight while updating the filter taps. For fixed sparse systems, the degree of sparseness converges to the original degree of sparseness faster than the filter weight vector, which increases the algorithm's convergence rate. The convergence controlling parameter μ is crucial to the SC-PRLS's effectiveness. Therefore, Analysis of both transient and steady-state performance is necessary. This study investigates the performance of the mean square error of the SC-PRLS algorithm. Energy conservation principle is applied to calculate the mean square performance of transient and steady-state stages. Explicit conditions are obtained to ensure better performance of the algorithm. The selection of convergence controlling parameter μ also depends on the number of filter weights. A larger tap length requires higher μ for faster convergence, while lower μ is needed for lower steady-state error. The optimum value is 0.65, and the range of convergence controlling parameter μ is 30-65 for better performance.

Analysis of SC-PRLS, convergence controlling parameter, MSE (mean square error), MMSE.