  In this paper, we focus on the phenomenon of beam misalignment in
Millimeter-wave (mmWave) multi-receiver communication systems, and propose
robust hybrid precoding designs that alleviate the performance loss caused by
this effect. We consider two distinct design methodologies: I) the synthesis of
a `flat mainlobe' beam model which maximizes the minimum effective array gain
over the beam misalignment range, and II) the inclusion of the `error
statistics' into the design, where the array response incorporating the
distribution of the misalignment error is derived. For both design
methodologies, we propose a hybrid precoding design that approximates the
robust fully-digital precoder, which is obtained via alternating optimization
based on the gradient projection (GP) method. We also propose a low-complexity
alternative to the GP algorithm based on the least square projection (LSP), and
we further deploy a second-stage digital precoder to mitigate any residual
inter-receiver interference after the hybrid analog-digital precoding.
Numerical results show that the robust hybrid precoding designs can effectively
alleviate the performance degradation incurred by beam misalignment.
