Single-Bit Millimeter Wave Beam Alignment Using Error Control Sounding Strategies

Hybrid Beam Alignment for Multi-Path Channels: A Group Testing Viewpoint

“…In our setup, we consider that the BS performs hybrid BA during which it simultaneously uses N RF scanning beams at each time slot, where N RF is the number of RF chains at the BS. Given a fixed beamwidth, ω, the BS's goal is to find the angular intervals of angular width ω that include AoAs using the fewest number of BA time slots [17], [18].…”

“…We consider an interactive BA scenario in which the BS determines the next N RF scanning beams at each time slot based on the past scanning beams used and their resulting measurements. We assume that the BS can determine if a past scanning beam includes a path or not before the next BA time slot [17], [18]. If a scanning beam includes at least a path, we denote this by an acknowledgment (ACK), otherwise, it is denoted by a negative ACK (NACK).…”

“…Next, we investigate the impact of the channel noise on the performance of the proposed analog and hybrid BA methods. At each time slot of the BA, motivated by prior works such as [9], [17], [18], we consider that the BS performs hypothesis testing in which the energy of the received signal at each RF chain is compared with a threshold, T , to determine whether or not any paths are present in the used scanning beams. Our hypothesis testing consists of these two hypotheses:…”

“…Optimization of the hypothesis testing threshold can be done in several ways (for example see [9], [17], [18]) which would result in different values of Pr[FA] and Pr[MD]. This optimization is out of the scope of this paper and left for future publication.…”

“…Noh et al [13] develop a BA method for the case of noisy hybrid interactive BA when the channel has single-path and Song et al [14] provide a BA method for the case of noisy hybrid non-interactive BA when the channel has multi-paths. The connection between BA and group testing (GT) was investigated in [18], where the authors consider the problem of analog non-interactive BA method for multipath channel and propose a GT-based BA procedure based on combinatorial GT literature [19]. Unlike the analog BA setting which is well investigated in the literature, less is known about the hybrid BA and the relation between the number of RF chains and BA duration is not yet investigated.…”