A two-step optimization of the centro-hermitian form in direct data domain least squares approach

This paper presents a new convex solution algorithm for the direct data domain least squares (D3LS) real weight approach that is extensively used during adaptive beam pattern synthesis of smart antenna arrays. The original D3LS approach is reformulated by using centro-hermitian matrix properties as well as convex optimization techniques and solved by using the proposed two-step convex optimization framework that is implemented in linear programming framework. The first convex formulation determines the unknown coefficient that is required during the centro-hermitian matrix manipulations. The second convex formulation solves the D3LS approach to calculate the corresponding optimal real weight coefficients. The numerical beam synthesis results demonstrate that the proposed convex solution based on centro-hermitian matrix manipulations of the D3LS approach effectively solves the real weight coefficients, overcomes possible matrix inversion issues and eliminates complexity, hardware implementation and energy consumption concerns due to complex weight coefficients. Moreover, although traditional beam pattern syntheses with real weights yield symmetric beam patterns, the proposed convex solution approach successfully removes this restriction.