Beamforming in Coupled-Oscillator Arrays
In this chapter, convex optimization and other global optimization techniques are used to demonstrate the beamforming capabilities of coupled-oscillator arrays and to optimize the stability of the coupled-oscillator array steady-state solution. An introduction to convex optimization is presented followed by several optimization problems showing the beamforming capabilities of such arrays, such as pattern-nulling, difference-beam generation, and multiple-beam generation [96,118,150,151,152]. A global optimization algorithm is also presented that permits one to optimize the stability of the steady-state solution, and therefore it leads to more robust solutions and maximizes the obtained stable beam-scanning limits . Finally, the operation of a coupled-oscillator array as an adaptive beamforming system is demonstrated .
9.1 Preliminary Concepts of Convex Optimization
Convex optimization is a class of optimization problems that has enjoyed an increased scientific interest in the recent years due to the development of very efficient algorithms essentially rendering their solution as easy as the solution of linear programs . As a result, convex optimization problems have found wide application in fields such as control and signal processing and, among these, in the problem of antenna array beam-steering and beamforming. Due to this fact, in this chapter we first present a brief introduction to convex optimization and ...