  Analog beamforming with phased arrays is a promising technique for 5G
wireless communication in millimeter wave bands. A beam focuses on a small
range of angles of arrival or departure and corresponds to a set of fixed phase
shifts across frequency due to practical hardware constraints. In switched
beamforming, a discrete codebook consisting of multiple beams is used to cover
a larger angle range. However, for sufficiently large bandwidth, the gain
provided by the phased array is frequency dependent even if the radiation
pattern of the antenna elements is frequency independent, an effect called beam
squint. This paper shows that the beam squint reduces channel capacity of a
uniform linear array (ULA). The beamforming codebook is designed to compensate
for the beam squint by imposing a channel capacity constraint. For example, our
codebook design algorithm can improve the channel capacity by 17.8% for a ULA
with 64 antennas operating at bandwidth of 2.5 GHz and carrier frequency of 73
GHz. Analysis and numerical examples suggest that a denser codebook is required
to compensate for the beam squint compared to the case without beam squint.
Furthermore, the effect of beam squint is shown to increase as bandwidth
increases, and the beam squint limits the bandwidth given the number of
antennas in the array.
