The Trade-off between Scanning Beam Penetration and Transmission Beam Gain in mmWave Beam Alignment

Beam search algorithms have been proposed to align the beams from an access point to a user equipment. The process relies on sending beams from a set of scanning beams (SB) and tailoring a transmission beam (TB) using the received feedback. In this paper, we discuss a fundamental trade-off between the gain of SBs and TBs. The higher the gain of an SB, the better the penetration of the SB and the higher the gain of the TB the better the communication link performance. However, TB depends on the set of SBs and by increasing the coverage of each SB and in turn reducing its penetration, there is more opportunity to find a sharper TB to increase its beamforming gain. We define a quantitative measure for such trade-off in terms of a trade-off curve. We introduce SB set design namely Tulip design and formally prove it achieves this fundamental trade-off curve for channels with a single dominant path. We also find closed-form solutions for the trade-off curve for special cases and provide an algorithm with its performance evaluation results to find the trade-off curve revealing the need for further optimization on the SB sets in the state-of-the-art beam search algorithms.