Super-Resolution of Discrete Point Faults in Transmission Lines

The 1-D inverse scattering problem of superresolving the location of discrete point shunt conductance or point impedance faults along transmission lines is considered. The results have applications to determine the structure of faults in transmission line components, such as connectors, when the available spectral information is not sufficient to obtain the spatial resolution required. The 1-D inverse scattering problem considered is formulated as a sparse reconstruction problem and convex optimization is applied to super-resolve the profile of discrete point faults in transmission lines. We extend previous results for super-resolution and prove that point faults can be super-resolved exactly with infinite precision in location when there are up to 4 point shunt conductance faults and 5-18 point shunt conductance faults if the faults are separated by λ
_c
/2 and λ
_c
, respectively, where λ
_c
is the minimum wavelength available in the system. This infinite precision is achieved for separations four times smaller than previous results. In addition, it is demonstrated that the location of up to 3 point impedance faults can be super-resolved exactly with infinite precision if they are separated by λ
_c
/2. Simulation and experimental results are used to demonstrate the effectiveness of the approach.