| Summary: | Two-tier massive multiple-input multiple-output (MIMO) systems achieve high sum spectral efficiency by simultaneously serving large numbers of users. However, as the number of service antennas and users tend to infinity, the performance is limited by directed inter-cell and intra-cell interferences. Handling these interferences are challenging due to the large channel dimensionality and the high complexity associated with implementing large precoding/combining matrices. Moreover, two-tier massive MIMO is computationally demanding, as the high antenna count results in high-dimensional matrix operations when conventional MIMO hybrid precoding is applied. In this paper, a manifold learning two-tier beamforming (MLTB) scheme is proposed to enable efficient and low-complexity operation in large scale dimensional MIMO systems. Users of multi-cell are clustered into several regions of user groups by manifold learning. Most of the high-dimensional channels are embedded in the low-dimensional subspace by manifold learning, while retaining the potential spatial correlation of the high-dimensional channels. The nonlinearity of high-dimensional channel is transformed into local linearity to achieve dimensionality reduction. Through proper user clustering, the beamformers are split into outer beamformers and inner beamformers. The outer beamformers can minimize inter-cell interference and the inner beamformers can minimize multi-user interference of intra-groups. The high signal to interference plus noise ratio (SINR) is achieved and the computational complexity is reduced by avoiding the conventional schemes to deal with high-dimensional channel parameters. Performance evaluations show that the proposed MLTB scheme can obtain near-optimal sum-rate and considerably higher energy efficiency than the conventional schemes.
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