  Millimeter wave (mmWave) communication with large array gains is a key
ingredient of next generation (5G) wireless networks. Effective communication
in mmWaves usually depends on the knowledge of the channel. We refer to the
problem of finding a narrow beam pair at the transmitter and at the receiver,
yielding high Signal to Noise Ratio (SNR) as Beam Alignment (BA). Prior BA
schemes typically considered deterministic channels, where the instantaneous
channel coefficients are assumed to stay constant for a long time. In this
paper, in contrast, we propose a time-domain BA scheme for wideband mmWave
systems, where the channel is characterized by multi-path components, different
delays, Angle-of-Arrivals/Angle-of-Departures (AoAs/AoDs), and Doppler shifts.
In our proposed scheme, the Base Station (BS) probes the channel in the
downlink by some sequences with good autocorrelation property (e.g.,
Pseudo-Noise (PN) sequences), letting each user estimate its best AoA-AoD that
connects the user to the BS with two-sided high beamforming gain. We leverage
the sparse nature of mmWaves in the AoA-AoD-time domain, and formulate the BA
problem as a Compressed Sensing (CS) of a non-negative sparse vector. We use
the recently developed Non-Negative Least Squares (NNLS) technique to
efficiently find the strongest path connecting the BS and each user. Simulation
results show that the proposed scheme outperforms its counterpart in terms of
the training overhead and robustness to fast channel variations.
