A method of feedback for a 4-antenna downlink channel in a Multiple Input Multiple Output (MIMO) system, comprising: detecting a downlink multiple-antenna channel ; determining a first codeword in a first level codebook corresponding to a rank of R according to a long-term broadband channel characteristic estimated from a result of the detection , wherein any codeword in the first level codebook is a diagonal matrix, two same 2×C block matrices exist on a diagonal line, and C column vectors of the 2×C block matrix are selected from Q 1 discrete Fourier transform (DFT) beam vectors; feeding back an index of the first codeword ; determining a second codeword in a second level codebook corresponding to the rank of R according to a short-term channel characteristic estimated from the result of the detection and the first codeword , wherein any codeword in the second level codebook is a 2C×R matrix, and each column of the 2C×R matrix is formed of one C×1 beam selection vector and one C×1 beam selection vector comprising phase offset information; and feeding back an index of the second codeword ; characterised in that : corresponding to the rank of 1, a column vector of any codeword in the second level codebook is configured as selecting a different DFT beam independently for each polarization; and corresponding to the rank of 2, a column vector of any codeword in the second level codebook is configured as selecting a different DFT beam independently for each polarization and selecting a same DFT beam for each layer, or configured as selecting a different DFT beam independently for each polarization and selecting a same or different DFT beam for each layer independently. detecting a downlink multiple-antenna channel ; determining a first codeword in a first level codebook corresponding to a rank of R according to a long-term broadband channel characteristic estimated from a result of the detection , wherein any codeword in the first level codebook is a diagonal matrix, two same 2×C block matrices exist on a diagonal line, and C column vectors of the 2×C block matrix are selected from Q 1 discrete Fourier transform (DFT) beam vectors; feeding back an index of the first codeword ; determining a second codeword in a second level codebook corresponding to the rank of R according to a short-term channel characteristic estimated from the result of the detection and the first codeword , wherein any codeword in the second level codebook is a 2C×R matrix, and each column of the 2C×R matrix is formed of one C×1 beam selection vector and one C×1 beam selection vector comprising phase offset information; and feeding back an index of the second codeword ; corresponding to the rank of 1, a column vector of any codeword in the second level codebook is configured as selecting a different DFT beam independently for each polarization; and corresponding to the rank of 2, a column vector of any codeword in the second level codebook is configured as selecting a different DFT beam independently for each polarization and selecting a same DFT beam for each layer, or configured as selecting a different DFT beam independently for each polarization and selecting a same or different DFT beam for each layer independently. <EOS>