Design of Channel Estimation for Hybrid Beamforming Millimeter-Wave Systems in the Presence of Beam Squint

In this article, channel estimation for millimeter-wave massive multiple-input-multiple-output (MIMO) systems with hybrid beamforming is considered. With a large number of antenna elements, a progressive time delay across antenna elements incurs a change in the beam direction as a function of subcarriers in an orthogonal frequency-division multiplexing system. Considering the difference in delay across the entire array, a new channel estimation framework is proposed by using a maximum likelihood criterion as a function of the analog training beam and pilot subcarrier assignment. The resulting design achieves asymptotic orthogonality among the channel paths and minimizes the mean squared error. An extension of the proposed design to a uniform planar array is discussed. The Cramér-Rao lower bound for joint channel estimation with hybrid beamforming is derived to verify the effectiveness of the proposed design.