Fast 3D Beam Training With True-Time-Delay Arrays in Wideband Millimeter-Wave Systems

True-time-delay (TTD) arrays can implement frequency-dependent rainbow beams and enable fast beam alignment in wideband millimeter-wave (mmWave) systems. In this paper, we consider 3D rainbow beam training with planar TTD arrays. We first design a planar TTD-array-based codebook that can realize a partial or complete scan of the entire 3D sphere using a single Orthogonal Frequency Division Multiplexing (OFDM) symbol. We demonstrate that a rainbow-beam codebook with a proper configuration of delays and phase shifts, and a sufficient number of subcarriers, can simultaneously probe all angular directions in the desired coverage sector with the required beamforming gain. Leveraging this full coverage codebook, we propose two frequency-domain power-based 3D beam training algorithms for fast estimation of the azimuth and elevation angles corresponding to the dominant propagation direction. The proposed algorithms take into account practical hardware-imposed delay range constraints. We numerically evaluate the performance of the proposed algorithms in mmWave channels as a function of the TTD codebook and system parameters. We show that the proposed 3D beam training offers considerable overhead reduction relative to the state-of-the-art methods with planar phased antenna arrays (PAA).