Determination of the Propagation Constant From Single-Ended Line Test Data

This paper presents a numerical method, here, called recursive obliquely moving approximation (ROMA), for determining the propagation constant from single-ended line test measurements. The method is based on deriving an equation binding the input impedance of the open-ended transmission line and the characteristic impedance with the line propagation constant. The algorithm solving this equation relies on a recursive Newton-Raphson-type procedure. Initial guesses are generated using oblique least squares on the complex plane for the extrapolation of previous data while moving toward higher frequencies. For residential access, the loops often consist of multiple sections. In those scenarios, the ROMA algorithm gives a less accurate and more difficult-to-interpret estimate of the propagation constant than for single-segment loops. Nevertheless, it still enables a quick and credible estimation of the loop capacity. ROMA provides these estimates without à priori information; it is insensitive to local solutions, and it has low numerical complexity. Moreover, for single-segment loops, common in, e.g., mobile backhaul applications, the algorithm gives a highly accurate estimation of the propagation constant.