Methods of Summing Crosstalk From Mixed Sources—Part I: Theoretical Analysis

Digital subscriber lines (DSLs) are fundamentally limited by crosstalk. The case where all crosstalk is from the same type of DSL has been studied over the years and accurate models have been standardized. However, crosstalk from multiple different types of DSLs is a relatively new area of study and models of summing mixed crosstalk have only recently been postulated. As more and more types of DSLs are deployed by multiple service providers, it is imperative to gain confidence in the method of modeling worst-case mixed crosstalk and to understand its limitations in order to enable efficient spectrum management of the loop plant. All known crosstalk summation methods are described here in detail and their properties are compared. This paper also presents a new methodology for deriving sound crosstalk summation methods. This new methodology consists of deriving lower bounds to the worst-case method, which is intrinsically too pessimistic. In particular, it has been ascertained that the Minkowski inequality and, to a lesser extent, the Hölder inequality, yield new crosstalk summation methods that exhibit appealing properties. It is also shown here that the standardized Full Service Access Network (FSAN) method is a particular case of the more general Minkowski-bound method. Finally, the accuracy of known and new summation methods is deeply analyzed and discussed in Part II of this work, where the problem of defining an accurate statistical modeling of the pair-to-pair crosstalk power coupling losses is also addressed.