Array Faulty Element Diagnostics by Few Phaseless Data and Convex Optimization

The problem of detecting defective turned-off elements in antenna arrays from amplitude-only data is addressed.Commonly used antenna diagnostics methods, such as the back transformation method (BTM) and the matrix method (MM), exploit amplitude and phase field data. Here, instead, the diagnostics is cast as the recovery of a real (binary) signal from few amplitude measurements of the near-field. Therefore, it is basically a phase retrieval problem.Taking inspiration from the recently introduced PhaseMax algorithm, the phase retrieval is formulated as a convex optimization. In particular, PhaseMax is adapted to the faults detection problem by removing the need to estimate a reference solution. Moreover, it is shown that the convex optimization is equivalent to a sparse minimization problem which allows to employ all the powerful tools of compressive sensing realm.Preliminary numerical results are presented to assess the achievable performance as the number of faulty elements increase. Finally, a strategy that reduces the number of measurement points by employing steering diversities is presented and checked.