Power Gain Optimization Method for Wide-Beam Array Antenna via Convex Optimization

This paper focuses on the problem of maximizing the minimum power gain in a wide main lobe for an array antenna. To obtain the desired power gain pattern, current literatures solve the problem known as shaped beam pattern synthesis (SBPS) by setting the beam pattern expression as the cost function. The power gain in a certain direction of the array antenna is comprehensively decided by the array radiated power density and the total radiated power. Both these two parameters are affected by the selection of array elements' weights. However, the SBPS-based methods do not take the total radiated power into account. Therefore, the SBPS-based methods cannot obtain the power gain pattern directly, and the optimal power gain pattern, consequently, cannot be guaranteed. To overcome this deficiency, this paper maximizes the minimum power gain in the desired wide main lobe by directly setting the power gain expression as the cost function. Aiming at optimizing the cost function, this paper first sets up a power gain optimization problem which has concave form. Termed this optimization problem as the power gain pattern synthesis (PGPS) problem. The concave PGPS problem is then converted to a series of convex subproblems and an iterative algorithm is proposed to solve it efficiently. Solution to the PGPS problem is proven to be able to achieve higher minimum power gain in a desired wide main lobe than the results from the SBPS-based algorithms. Simulations are carried out with both linear array antenna and planar array antenna. Comparisons with the existed SBPS-based algorithms validate the effectiveness and advantages of the proposed PGPS-based algorithm. In addition, further improvement on suppressing the sidelobe level for the PGPS problem is discussed.