This paper proposes optimal beam patterns of analog beamforming for SU (Single User) massive MIMO (Multi-Input Multi-Output) transmission systems. For hybrid beamforming in SU massive MIMO systems, there are several design parameters such as beam patterns, the number of beams (streams), the shape of array antennas, and so on. In conventional hybrid beamforming, rectangular patch array antennas implemented on a planar surface with linear phase shift beam patterns have been used widely. However, it remains unclear whether existing configurations are optimal or not. Therefore, we propose a method using OBPB (Optimal Beam Projection Beamforming) for designing configuration parameters of the hybrid beamforming. By using the method, the optimal beam patterns are derived first, and are projected on the assumed surface to calculate the achievable number of streams and the resulting channel capacity. The results indicate OBPB with a spherical surface yields at least 3.5 times higher channel capacity than conventional configurations.

This paper proposes a new methodology to design optimal antennas for MIMO (Multi-Input Multi-Output) communication systems by using spherical mode expansion. Given spatial channel properties of a MIMO channel, such as the angular profile at both sides, the optimal MIMO antennas should provide the largest channel capacity with a constraint of the limited implementation space (volume). In designing a conventional MIMO antenna, first the antenna structure (current distribution) is determined, second antenna directivity is calculated based on the current distribution, and thirdly MIMO channel capacity is calculated by using given angular profiles and obtained antenna directivity. This process is repeated by adjusting the antenna structure until the performance satisfies a predefined threshold. To the contrary, this paper solves the optimization problem analytically and finally gives near optimal antenna structure (current distribution) without any greedy search. In the proposed process, first the optimal directivity of MIMO antennas is derived by applying spherical mode expansion to the angular profiles, and second a far-near field conversion is applied on the derived optimal directivity to achieve near optimal current distributions on a limited surface. The effectiveness of the proposed design methodology is validated via numerical calculation of MIMO channel capacity as in the conventional design method while giving near optimal current distribution with constraint of an antenna structure derived from proposed methodology.