  Sparse adaptive filtering has gained much attention due to its wide
applicability in the field of signal processing. Among the main algorithm
families, sparse norm constraint adaptive filters develop rapidly in recent
years. However, when applied for system identification, most priori work in
sparse norm constraint adaptive filtering suffers from the difficulty of
adaptability to the sparsity of the systems to be identified. To address this
problem, we propose a novel variable p-norm constraint least mean square (LMS)
algorithm, which serves as a variant of the conventional Lp-LMS algorithm
established for sparse system identification. The parameter p is iteratively
adjusted by the gradient descent method applied to the instantaneous square
error. Numerical simulations show that this new approach achieves better
performance than the traditional Lp-LMS and LMS algorithms in terms of
steady-state error and convergence rate.
