Abstract
We design 4-ary codebooks using Reed-Muller codes for multiple-input-multiple-output (MIMO) beamforming systems. An upperbound on the maximum correlation magnitude metric of a 4-ary codebook is derived from the minimum Hamming distance of the corresponding binary linear block code. The 4-ary MIMO beamforming codebooks for the number of transmit antennas equal to 4, 8, 16, and 32 are tabulated. We show that the 4-ary codebook using Reed-Muller codes provides the same symbol error probability (SEP) as the Long-Term Evolution (LTE) codebook when the number of transmit antennas is 4 and when the number of feedback bits is 4.
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