Minimizing the Dimensionality Problem in mm-Wave with Large Number of Antenna Elements Using Fast CUR-Decomposition

Millimeter wave (mm-Wave) communications is a key technology to meet the increasing demand for high data rate. Meanwhile, the mm-Wave base station (BS) needs to employ a large number of antenna elements to increase the gain as well as to serve a huge number of users. However, the integration of a vast number of antenna elements will cause dimensionality problem due to large dimension of channel correlation matrix. Therefore, we propose a novel codebook construction design based on Fast CUR-decomposition to minimise this problem. The proposed method represents the original correlation matrix as the product of three very low dimension matrices compared to the original. Then the new rotated codebook is constructed by the new rotation matrix. Moreover, we evaluate our method with the original matrix regarding compression ratio (CR) and mismatch error between the two matrices. Additionally, we provide the ergodic sum-rate capacities for the conventional methods such as singular value decomposition (SVD) technique, zero-forcing (ZF), and a matched filter (MF) to compare with our proposed method. Furthermore, we analyse the enhancement of the system capacity regarding the number of antenna elements and the required feedback bits. The simulation results show that the proposed method can achieve good results after minimising dimension problem. This work it can be extended in the future to be applied to a 5G system with over 100 antenna elements.