On Achieving Optimal Rate of Digital Precoder by RF-Baseband Codesign for MIMO Systems

For many communications systems, such as the one for millimeter-wave communications, the design of the precoder that multiplexes independent data streams in space is subject to the unconventional constraint that the numbers of the available frequency converters and digital-to-analog (D/A) converters are only a fraction of the number of equipped antennas. In this paper, we study the joint design of both radio-frequency (RF) and baseband signal processing, where the RF signal processing is implemented by phase shifters with variable phase shifts. We propose two hybrid precoder designs that provide the same achievable rate as the optimal fully-digital precoder. The first design is the generalization of the optimal single-stream scheme developed by Zhang, Molisch, and Kung. The second design is obtained by simplifying the first design with simplification process that involves a new decomposition of the optimal unconstrained precoding matrix and the rearrangement of the separation of the baseband and RF circuits. The comparison of system complexity in terms of the numbers of required D/A converters, frequency converters, and phase shifters is provided and the performance of the proposed designs is verified by simulations.