In this paper, the performance of cellular communications based on the ambitious technology of High-Altitude Platforms (HAPs) is discussed when using tapered concentric circular arrays. The coverage cell will be described and designed with an efficient beamforming technique where the Hamming window is proposed as a tapering function and applied to the uniform concentric circular arrays (UCCA) for sidelobe reduction. Based on establishing some mapping curves, this novel tapering window is optimized in its parameters to have the lowest possible sidelobe level that can be 45 dB below the main lobe level. The optimum weights of Hamming window are found to be function of the number of elements of the innermost ring and the number of rings in the array. The cell power pattern is also discussed where the out-of-cell radiation is greatly reduced which in turns reduces the co-channel interference and improves the Carrier-to-Interference Ratio (CIR).