Blind compensation of nonlinear distortions via sparsity recovery

In this work, we address the problem of compensating a nonlinear memoryless system in a blind fashion, i.e., without considering a set of training points. Our proposal works with the assumption that the input signal admits a sparse representation in a transformed domain that should be known in advance. By assuming that the nonlinear distortion function makes the observed signal less sparse (this is observed in frequency transforms), the proposed method aims at estimating the original signal via a sparsity recovery procedure. Our approach is based on an approximation of the ℓ₀-norm and on the use of polynomial functions as compensating structures. In order to assess the viability of the developed method, we perform a representative set of experiments on synthetic data.