Non-linear system identification of a broadband subscriber line interface circuitry using the Volterra approach

Making use of the Volterra approach, black box modeling is applied to a large scale analog circuitry for an ADSL (asymmetric digital subscriber line) central office application. Reducing the number of free parameters through special assumptions on the Volterra kernels, one ends up with the Hammerstein model. Taking the first few taps of the Volterra kernels and approximating the last taps through Hammerstein kernels, the VolterraHammerstein model is obtained. The parametrization of these models is an inverse problem and leads to an ill-conditioned linear equations system, thus regularization techniques are used. Discrete multi tones (DMT) serve as excitation signals. For validation of the presented methods a reference model is constructed. This model consists of full factorable Volterra kernels, where the order of the non-linearity corresponds to that occurring in the circuitry. For the circuitry, data acquisition is done by an analog network simulator. Emphasis was put on the accuracy of the inter-modulation products, described by a generalized signal to noise ratio. The Hammerstein and the Volterra-Hammerstein models are compared with each other and with meassurements from the laboratory.