  In this paper, we consider precoder designs for multiuser
multiple-input-single-output (MISO) broadcasting channels. Instead of using a
traditional linear zero-forcing (ZF) precoder, we propose a generalized ZF
(GZF) precoder in conjunction with successive dirty-paper coding (DPC) for
data-transmissions, namely, the GZF-DP precoder, where the suffix \lq{}DP\rq{}
stands for \lq{}dirty-paper\rq{}. The GZF-DP precoder is designed to generate a
band-shaped and lower-triangular effective channel $\vec{F}$ such that only the
entries along the main diagonal and the $\nu$ first lower-diagonals can take
non-zero values. Utilizing the successive DPC, the known non-causal inter-user
interferences from the other (up to) $\nu$ users are canceled through
successive encoding. We analyze optimal GZF-DP precoder designs both for
sum-rate and minimum user-rate maximizations. Utilizing Lagrange multipliers,
the optimal precoders for both cases are solved in closed-forms in relation to
optimal power allocations. For the sum-rate maximization, the optimal power
allocation can be found through water-filling, but with modified water-levels
depending on the parameter $\nu$. While for the minimum user-rate maximization
that measures the quality of the service (QoS), the optimal power allocation is
directly solved in closed-form which also depends on $\nu$. Moreover, we
propose two low-complexity user-ordering algorithms for the GZF-DP precoder
designs for both maximizations, respectively. We show through numerical results
that, the proposed GZF-DP precoder with a small $\nu$ ($\leq\!3$) renders
significant rate increments compared to the previous precoder designs such as
the linear ZF and user-grouping based DPC (UG-DP) precoders.
