Increasing demands for mobile internet access have led to exponential developments in mobile communications technologies. The next generation mobile technology is expected to exploit electronic beam steering and to have a higher operating frequency to facilitate a higher bandwidth. This places a heavy burden on the base station antenna arrays, which should be sparse to accommodate passively cooling the system. Conventional sparse array topologies suffer from undesirable radiation pattern characteristics such as grating lobes. Therefore, this work focused on exploring methods to synthesize the antenna elements' geometrical parameters to enhance the radiation pattern and to explore the limitations that arise due to the array's sparseness. To this end, both a deterministic and a stochastic method were proposed. Starting with an analytical window function as a continuous current distribution and approximating this by adjusting the antenna elements' radial coordinates results in the fact that the desired window's radiation pattern is only approximated in a limited field of view, depending on the sparseness. Full electromagnetic wave simulations are performed to show that downscaling the topology to make it more dense gives rise to increased coupling effects that deteriorate the array's performance. In addition to the deterministic method, a genetic algorithm optimization method is employed to stochastically obtain the optimal current distribution window. Approximating the optimal continuous current distribution again leads to the array factor following the optimal window's radiation pattern in a limited field of view. Furthermore, it is shown that for the conditions used in this work, the optimum continuous current distribution is also the optimum current distribution for finite element arrays, implying that only one optimization needs to be executed when designing such an array. Concluding, the applicability of density tapering to sparse arrays is limited. The inherent undersampling causes a limited realization of the window function's characteristics. Density tapering does improve the absolute performance of a sparse array in terms of peak sidelobe level, but may be useful if the region of interest is concentrated near the main beam. The requirements and in particular the region of interest of the application determine whether density tapering can be effectively employed.