A Scalable and Statistically Robust Beam Alignment Technique for Millimeter-Wave Systems

Millimeter-wave (mm-wave) frequency bands provide an opportunity for much wider channel bandwidth compared with the traditional sub-6-CHz band. Communication at mm-waves is, however, quite challenging due to the severe propagation pathloss incurred by conventional isotropic antennas. To cope with this problem, directional beamforming both at the base station (BS) side and at the user equipment (UE) side is necessary in order to establish a strong path conveying enough signal power. Finding such beamforming directions is referred to as beam alignment (BA). This paper presents a new scheme for efficient BA. Our scheme finds a strong propagation path identified by an angle-of-arrival (AoA) and angle-of-departure (AoD) pair, by exploring the AoA-AoD domain through pseudorandom multi-finger beam patterns and constructing an estimate of the resulting second-order statistics (namely, the average received power for each pseudo-random beam configuration). The resulting under-determined system of equations is efficiently solved using non-negative constrained least-squares, yielding naturally a sparse non-negative vector solution whose maximum component identifies the optimal path. As a result, our scheme is highly robust to variations of the channel time dynamics compared with alternative concurrent approaches based on the estimation of the instantaneous channel coefficients, rather than of their second-order statistics. In the proposed scheme, the BS probes the channel in the downlink and trains simultaneously an arbitrarily large number of UEs. Thus, "beam refinement," with multiple interactive rounds of downlink/uplink transmissions, is not needed. This results in a scalable BA protocol, where the protocol overhead is virtually independent of the number of UEs, since all the UEs run the BA procedure at the same time. Extensive simulation results illustrate that our approach is superior to the state-of-the-art BA schemes proposed in the literature in terms of training overhead in multi-user scenarios and robustness to variations in the channel dynamics.