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Abstract

Embodiments include methods for beamforming using an antenna array. Such methods include, for each pair of beamforming vectors (bk,bl) of a codebook comprising a plurality of beamforming vectors corresponding to orientations (1 . . . N), determining at least one corresponding pair of tapering vectors (tk,tl) based on minimizing at least one function f(δ,ϵ), such that when tapered beamforming vectors (tk-bk, tl-bl) are applied to the antenna array for transmitting concurrent beams of orientations (k,l), k≠l, radiated power in orientations (k,l) are at least (1−ϵ) of peak radiated powers in orientations (k,l) of beams formed by (bk,bl); and the beams of orientations (k,l) have sidelobes that are lower than δ in respective orientations (l,k). Such methods also include transmitting data concurrently in orientations (i,j), i≠j, based on weighting the antenna array by tapered beamforming vectors (ti-bi, tj-bj) corresponding to orientations (i,j). Embodiments also include nodes configured to perform such methods.

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First Claim