Realizing Fully Digital Precoders in Hybrid A/D Architecture With Minimum Number of RF Chains

In this letter, the minimum number of required radio frequency (RF) chains for realizing any MIMO fully digital precoder (FDP) with the hybrid analog/digital precoder (HADP) architecture is investigated from a new perspective. First, in order to take full advantage of the digital domain, an extended system formulation of the hybrid structure is presented in which the digital precoder is taken from an abstract transformation space. Then, a constrained optimization problem is formulated, where the aim is to minimize the number of RF chains subject to an equality constraint on the multi-stream FDP and HADP outputs. We show that non-unique optimum solutions exist for only two RF chains. Based on these results, we further develop a single RF chain design. The implementation of the latter does not require extra hardware or computational complexity. We compare the proposed HADP design with recent works that require larger number of RF chains and demonstrate that significant improvement in performance can be achieved over direct HADP design.