A method, an electronic device with a memory configured to store a hierarchical codebook with a processor operably connected to the memory to perform the method, and a non-transitory computer-readable medium storing instructions that when executed by a processor of an electronic device cause the electronic device to perform the method. The method identifies input data including at least one of an array size, an antenna element spacing, a phase-shifter resolution, a specified coverage region, or an antenna element pattern. The input data is processed by putting an initial beam through a non-decreasing concave utility function which uses a cyclic coordinate descent algorithm that generates a wide beam meeting one or more design specifications. A codebook is produced that includes the wide beam.