CDISE Seminar: Benjamin Fuchs

Monday, 11 July 2016

11:00 – 12:00 in Room 407
Benjamin Fuchs, Institute of Electronics and Telecommunications
of Rennes (IETR), CNRS, France

Application of Convex Relaxation to Array Synthesis and Antenna Selection Problems

The synthesis of antenna arrays is a very long standing field in electromagnetism because of its many applications (e.g. radar, radio astronomy, sonar, communications, direction-finding, seismology, medical diagnosis and treatment). A host of methods have been proposed since the 40’s to solve increasingly difficult synthesis problems. These techniques range from analytical methods (fast but limited to very specific problems) to global optimization approaches (comprehensive but limited in performances due to their computational burden). Convex optimization has been shown to be a good trade-off in efficiency/generality between analytical and global optimization techniques in a number of relevant cases.
The purpose of the talk is to show that a variety of difficult antenna array synthesis problems can be approximated as convex optimization ones and therefore be efficiently solved. More specifically, the application of the semidefinite relaxation technique to approximate the quadratic constraints arising in many synthesis problems is described. The synthesis of shaped beams, phase-only excitations or reconfigurable arrays are instances shown to highlight the practical relevance of the proposed strategy.
In addition, the combinatorial problem of selecting antennas from among a set of possible radiators in order to optimize the performances of the array is addressed. A convex relaxation of the Boolean constraints followed by a probabilistic interpretation of the solution enables to quickly obtain bounds on the best achievable array performances and to make a good antenna selection. Numerical representative examples, such as the selection of quantized array excitations, antenna types and antenna’s locations to optimize the array performances are shown to illustrate the interest of the proposed approach.