Evaluation of Power Pattern of Antenna Arrays With Elements Position Errors Using Quadratic Relaxation Programming

This letter presents a new method to accurately and reliably evaluate the bounds of the antenna array power pattern in the presence of elements position errors. The erroneous array power pattern is approximated by its second-order Taylor series expansion, from which a box-constrained quadratic programming problem for tolerance analysis is formulated. This problem is a general mixed convex and nonconvex optimization problem, and the convex surrogate version is designed by introducing semidefinite relaxation. Subsequently, convex optimization is adopted to solve the proposed problem. The representative results are reported to give more advanced solutions in comparison to two existing methods.