Phaseless Array Faulty Diagnostics via Convex Optimization

In this paper, the problem of detecting defective turned-off elements in antenna arrays from nearfield phaseless measurements is addressed. The diagnostics is cast as the recovery of a real (binary) signal from amplitude-only measurements. Such problem falls into the realm of phase retrieval one. 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 asses 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.