  In a two-user broadcast channel where one user has full CSIR and the other
has none, a recent result showed that TDMA is strictly suboptimal and a product
superposition requiring non-coherent signaling achieves DoF gains under many
antenna configurations. This work introduces product superposition in the
domain of coherent signaling with pilots, demonstrates the advantages of
product superposition in low-SNR as well as high-SNR, and establishes DoF gains
in a wider set of receiver antenna configurations. Two classes of decoders,
with and without interference cancellation, are studied. Achievable rates are
established by analysis and illustrated by simulations.
