Beamforming Design Based On The Asymptotic Analysis For High Band 3D Massive MIMO Systems

Compared with conventional lower band signals,high band signals have a shorter wavelength.By using high band signals,a smaller physical size of the antenna array can be achieved,which is more conducive to antenna integration.Thanks to the small wavelength at high band,it is promising to combine 3-Dimension Massive multiple-input multipleoutput(3D Massive MIMO)with high band communications.In particular,high band 3D Massive MIMO differs from the conventional MIMO in array structure and radio propagation.In this paper,the optimum beamforming transmission for downlink high band3 D Massive MIMO systems with a compact planar array at the base station(BS)is investigated for the asymptotic case where the BS has unlimited antenna elements.Based on the law of large numbers,the effect of noise and multi-user interference vanish and the channel characteristics tend to be stable in the asymptotic regime with unlimited antenna elements.These asymptotic properties are beneficial to the design of the actual communication systems.Thus,we analyze the high band sparse channel asymptotically.Based on the results of asymptotic analysis,an optimal beamforming algorithm for high band3 D Massive MIMO systems is proposed,and the closed-form expression of the optimal weight vectors is also given,by applying matrix theory.The specific contributions of this paper lie in the following aspects:(1)In this paper,we derive the asymptotic approximation of the high band sparse channel correlation matrix by analyzing the steering vectors of the compact planar array in the vertical and horizontal dimensions asymptotically,and reveal the asymptotic characteristics of the 3D Massive MIMO systems.Through the relevant mathematical deduction,we prove that: the eigenvectors of the single-path line-of-sight(LOS)channel correlation matrix can be approximated by Discrete Fourier Transform vectors;in the high band communication scenario,users with different elevation angles have orthogonal vertical LOS components,and users with different azimuth angles have orthogonal horizontal LOS components.The asymptotic approximation is verified to be accurate even for the finite regime by simulations.Note that the single-path model considering only the LOS path is chosen for the sake of simplicity purposes and our scheme is applicable to the Rician fading channel as well.(2)Based on the results of asymptotic analysis,we propose an optimum beamforming transmission scheme for high band 3D Massive MIMO systems,which provides a closedform solution that maximizes the minimum SINR of all users.Through the relevant mathematical deduction,we prove that: in the high band communication scenario,the multiuser interference vanishes when the vertical or horizontal LOS channel components of different users are orthogonal,and the users can achieve the maximum received signal-tointerference and noise ratio(SINR)and the maximum information transmission rate.Simulation results verified the effectiveness of the proposed algorithm.On the one hand,the proposed algorithm based on the asymptotic analysis is verified to be applicable to the finite regime communication scenarios with a large number of antenna elements by simulations.On the other hand,the proposed scheme has better performance and is more robust to mutual coupling effect compared to the conventional MMSE and MRT schemes.