Abstract

In this thesis, the problem of modeling a Digital Subscriber Line (DSL) network is investigated. Any changes made to the DSL network such as addition or relocation of customers may affect the performance of the overall network. Therefore, it is very useful to have a laboratory model to test the effect of every change made to the network easily. The model can also be used by service providers to test the quality of service before assigning a line to a new customer, reducing the trouble-shooting cost. The modeling consists of extracting the magnitude response of a particular DSL channel, fitting the data to a discrete-time finite dimensional LTI model and reducing its order reasonably. The resultant filter will be a suitable model for laboratory implementations. The magnitude response of the DSL network can be computed numerically using general and small-scale models available for transmission lines. The computation can be generalized to the distributed networks. Digital filter approximation can be accomplished using the conventional methods. A gradient-based method is also proposed in order to generate a FIR filter. The model order reduction is performed using Balanced Realization technique which is applicable to all stable finite dimensional LTI models. It is also accomplished by minimizing either mean-squared error or infinity norm of error. The performance of each method is evaluated using standard test loops. A reasonable range of model order for each test loop is also discussed based on the configuration of each loop, which can be used as a general guide for any wired transmission network.