A proportionate type block-oriented functional link adaptive filter for sparse nonlinear systems

Nonlinear adaptive filters (NAFs) are used in applications like self-interference cancellation to identify nonlinear systems but at the expense of high computational complexity. When the system response is sparse, NAFs are further combined with proportionate-type algorithms to accelerate system identification which increases the computational complexity further. To alleviate the NAF complexity problem, a block-oriented functional link adaptive filter (BO-FLAF) algorithm, which has lower complexity and filter order than the FLAF was recently proposed. Since proportionate adaptation complexity is directly proportional to the filter order, a proportionate BO-FLAF is more attractive from a computation standpoint than the existing proportionate FLAF (PFLAF). Therefore, we develop a novel proportionate Hammerstein BO-FLAF (PHBO-FLAF) in this paper. Through theoretical complexity analysis we prove that the proposed PHBO trigonometric FLAF (PHBO-TFLAF) has 53.2% lesser multiplications and 7 times less logarithmic operations than the PTFLAF. We also show that the PHBO-TFLAF has faster convergence than the HBO-TFLAF and PTFLAF and models memoryless systems much better than the PTFLAF.