  Hybrid precoding is a cost-effective approach to support directional
transmissions for millimeter-wave (mm-wave) communications, but its precoder
design is highly complicated. In this paper, we propose a new hybrid precoder
implementation, namely the double phase shifter (DPS) implementation, which
enables highly tractable hybrid precoder design. Efficient algorithms are then
developed for two popular hybrid precoder structures, i.e., the fully- and
partially-connected structures. For the fully-connected one, the RF-only
precoding and hybrid precoding problems are formulated as a least absolute
shrinkage and selection operator (LASSO) problem and a low-rank matrix
approximation problem, respectively. In this way, computationally efficient
algorithms are provided to approach the performance of the fully digital one
with a small number of radio frequency (RF) chains. On the other hand, the
hybrid precoder design in the partially-connected structure is identified as an
eigenvalue problem. To enhance the performance of this cost-effective
structure, dynamic mapping from RF chains to antennas is further proposed, for
which a greedy algorithm and a modified K-means algorithm are developed.
Simulation results demonstrate the performance gains of the proposed hybrid
precoding algorithms over existing ones. It shows that, with the proposed DPS
implementation, the fully-connected structure enjoys both satisfactory
performance and low design complexity while the partially-connected one serves
as an economic solution with low hardware complexity.
