Convex Optimization and Its Application to Antenna Array

Abstract

Antennas are indispensable element in the organization of wireless communication for transmission and reception of information. It is fairly apparent that the information transmitted or received must be best possible. Convex programming has the potential to become a pervasive numerical technology along with least squares, linear programming, and quadratic programming. Convex programming amalgamates and generalizes least squares, linear programming, and quadratic programming. In this thesis, a new modeling software or tool has been introduced that is, Convex Optimization Software (CVX) which uses the methodology called disciplined convex programming (DCP). There are great advantages to recognizing or formulating a problem as a convex optimization problem. The most basic advantage is that the problem can then be solved, very reliably and efficiently, using interior-point methods or other special methods for convex optimization. It has acknowledged significant consideration in recent times for these reasons. Although, this tool uses MATLAB as modeling language but the performance is much finer than MATLAB. In CVX, DCP imposes a set of conventions to follow in order to solve problems. These conventions are straightforward, taken from basic principles of convex analysis. In order to get the solution, problem should follow the rules or else it will not be solved, even if it is convex. In this thesis, prominence is to study the Convex Optimization Software (CVX), to illustrate its performance and to execute the results for antenna arrays. CVX uses the DCP rule set which covers all the existing functions of MATLAB and is further expanded. To illustrate the performance of CVX, Low pass and Chebyshev filters are utilized. In this MATLAB and CVX are compared and the results obtained by CVX are more optimized or close to the theoretical values, which suggests that CVX is better software. Antenna arrays are becoming an attraction in communication systems because of their better-quality performance, as they provide an efficient means to detect and process signals. CVX is implemented to minimize the beam width of antenna array. For the given specifications the results obtained by CVX shows that the problem is feasible at half beam width (in degrees) 12, 13, 14 and 26. This brings to result that the optimum half beam width is 12.