Millimeter-wave MIMO systems have gained increasing traction towards the goalof meeting the high data-rate requirements in next-generation wireless systems.The focus of this work is on low-complexity beamforming approaches for initialUE discovery in such systems. Towards this goal, we first note the structure ofthe optimal beamformer with per-antenna gain and phase control and thestructure of good beamformers with per-antenna phase-only control. Learningthese beamforming structures in mmW systems is fraught with considerablecomplexities such as the need for a non-broadcast system design, thesensitivity of the beamformer approximants to small path length changes, etc.To overcome these issues, we establish a physical interpretation between thesebeamformer structures and the angles of departure/arrival of the dominantpath(s). This physical interpretation provides a theoretical underpinning tothe emerging interest on directional beamforming approaches that are lesssensitive to small path length changes. While classical approaches fordirection learning such as MUSIC have been well-understood, they suffer frommany practical difficulties in a mmW context such as a non-broadcast systemdesign and high computational complexity. A simpler broadcast solution for mmWsystems is the adaptation of directional codebooks for beamforming at the twoends. We establish fundamental limits for the best beam broadening codebooksand propose a construction motivated by a virtual subarray architecture that iswithin a couple of dB of the best tradeoff curve at all useful beam broadeningfactors. We finally provide the received SNR loss-UE discovery latency tradeoffwith the proposed constructions. Our results show that users with a reasonablelink margin can be quickly discovered by the proposed design with a smoothroll-off in performance as the link margin deteriorates.
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