Dimension Reduction of Channel Correlation Matrix Using CUR-Decomposition Technique for 3-D Massive Antenna System

Millimeter wave (mm-Wave) communications are emerging to meet the increasing demand for high transmission data rate in high user density areas. Meanwhile, the mm-Wave base station (BS) needs to employ a large number of antenna elements to increase the gain as well as serve a huge number of users. However, a vast number of antenna elements causes dimensionality problem in channel correlation matrix (rotation matrix). Therefore, we propose a novel codebook construction design based on CUR-decomposition technique to reduce the dimensionality problem. In this paper, the original correlation matrix is decomposed to the product of three low dimension matrices (<inline-formula> <tex-math notation="LaTeX">$\mathbf {C}$ </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">$\mathbf {U}$ </tex-math></inline-formula>, and <inline-formula> <tex-math notation="LaTeX">$\mathbf {R}$ </tex-math></inline-formula>). The new rotated codebook is then constructed by the new rotation matrix. Moreover, we evaluate the new decomposition matrix with the original matrix in terms of compression ratio and mismatch error. We also provide the achievable sum rate capacities for singular value decomposition, zero forcing, and a matched filter techniques to compare with the proposed method. Furthermore, the system capacity enhancement related to the number of antenna elements and the required feedback bits are analyzed. Simulation results show that the proposed method achieves much better system performance since the dimensionality problem is solved. The proposed method can be applied in the fifth generation massive antenna multi-user system with over a hundred antenna elements.