  We propose an efficient method for designing broad beams with spatially flat
array factor and efficient power utilization for cell-specific coverage in
communication systems equipped with large antenna arrays. To ensure full power
efficiency, the method is restricted to phase-only weight manipulations. Our
framework is based on the discovered connection between dual-polarized
beamforming and polyphase Golay sequences. Exploiting this connection, we
propose several methods for array expansion from smaller to larger sizes, while
preserving the radiation pattern. In addition, to fill the gaps in the feasible
array sizes, we introduce the concept of $\epsilon$-complementarity that
relaxes the requirement on zero side lobes of the sum aperiodic autocorrelation
function of a sequence pair. Furthermore, we develop a modified Great Deluge
algorithm (MGDA) that finds $\epsilon$-complementary pairs of arbitrary length,
and hence enables broad beamforming for arbitrarily-sized uniform linear
arrays. We also discuss the extension of this approach to two-dimensional
uniform rectangular arrays. Our numerical results demonstrate the superiority
of the proposed approach with respect to existing beam-broadening methods.
