On the Sparsity-Based Identification and Compensation of Hammerstein Systems

This letter investigates blind identification and compensation of Hammerstein systems, whose inputs are sparse in the frequency domain. In our analysis, the Hammerstein system comprises an antisymmetric invertible polynomial nonlinear curve followed by a minimum-phase linear system. We show analytically in a simple scenario and empirically in more complex situations that the Hammerstein system is identifiable with high probability, provided that the nonlinear component of the system reduces the sparsity of the input by a sufficiently large amount. Moreover, we propose a practical compensation procedure in the form of the Wiener system that provides a maximally sparse output when cascaded with the given Hammerstein system. Monte Carlo experiments show that the procedure is effective for Hammerstein systems with sufficiently strong nonlinearities submitted to inputs within a wide range of sparsity levels.