Non-linear system identification of a broadband subscriber line interface circuit for ADSL-Lite 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 Volterra-Hammerstein 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. Data acquisition is done by the analog network simulator SABER. 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. 1 Motivation Non-linear distortions are limiting the performance of the overall ADSL system. Therefore, performance estimations of the system in the design period are desired to schedule necessary redesigns. A fast method to map the non-linear dynamics of an analog circuitry to a black box model is needed. The discussed ADSL transceiver utilizes DMT multicarrier modulation [6]. The number of bits being allocated to each single carrier determines the overall bit-rate. A proper quantity to describe the possible bit-allocation is the MTPR value (multi tone power ratio), a generalized SNR (signal to noise ratio). The MTPR is defined for each carrier as MTPRi = 10 log ( Si Ni + ∑ j Dij ) in dB, (1) where the index i denotes the i-th carrier. Si stands for the transmitted power of the i-th carrier, which has to be related to the sum of the noise Ni and all the inter-modulations Dij , produced from the other j carriers of the DMT signal