In this work we consider the one-dimensional (1D) inverse scattering problem of super-resolving the location of discrete point scatters satisfying the 1D Helmholtz equation. This inverse problem has important applications in the detection of shunt faults in electrical transmission lines and leaks in water pipelines where usually only low frequency spectral information is available from measurements. We formulate the inverse scattering problem as a sparse reconstruction problem and apply convex optimization to super-resolve the location of point scatters. We extend previous results and prove that we can super-resolve up to 4 points and 5-18 points with infinite precision if the points are separated by 1/(2fc) and 1/fcrespectively (fcis the maximum frequency we can measure). This is over 4 times closer than previous results. Simulation results are used to demonstrate the effectiveness of the approach.

We propose the use of subcarrier delay spread based adaptive orthogonal frequency division multiplexing (OFDM) for communication through wideband waveguide channels. The technique has important communication applications when robots or vehicles are traveling inside waveguide channels such as tunnels or pipes. The delay spread in these mobile wideband waveguide channels varies significantly across subcarriers because propagation occurs in modes whose characteristics change significantly with frequency. Using knowledge of the delay spread in each subcarrier can then be used to adaptively select and avoid subcarriers with delay spread exceeding the cyclic prefix length. With this approach it is possible to create an OFDM system that is more efficient than systems satisfying the delay spread of all subcarriers. In this paper, we therefore propose subcarrier delay spread based adaptive OFDM to enhance the performance of OFDM systems operating in mobile wideband waveguide channels. To identify the delay spread of individual subcarriers we propose two methods. Using these methods, we provide simulation results to demonstrate the effectiveness of the technique. We also make use of experimental waveguide channel measurements to demonstrate the technique in realistic settings. Results show that performance can be significantly improved by using the proposed approach.