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The Research of Massive MIMO is an emerging area, since the more antennas the transmitters or receivers equipped with, the higher spectral efficiency and link reliability the system can provide. Due to the limited feedback channel, precoding and codebook design are important to exploit the performance of massive MIMO. To improve the precoding performance, we propose a novel hierarchical codebook with the Fourier-based perturbation matrices as the subcodebook and the Kerdock codebook as the maindoi:10.4108/sis.2.4.e5 fatcat:mdbzlm6t6zfg3exzyuebs4vty4