  Initial access (IA) is a fundamental physical layer procedure in cellular
systems where user equipment (UE) detects nearby base station (BS) as well as
acquire synchronization. Due to the necessity of using antenna array in
millimeter-wave (mmW) IA, the channel spatial information can also be inferred.
The state-of-the-art directional IA (DIA) uses sector sounding beams with
limited angular resolution, and thus requires additional dedicated radio
resources, access latency and overhead for refined beam training. To remedy the
problem of access latency and overhead in DIA, this work proposes to use a
quasi-omni pseudorandom sounding beam for IA, and develops a novel algorithm
for joint initial access and fine resolution initial beam training without
requiring extra radio resources. We provide the analysis of the proposed
algorithm miss detection rate under synchronization error, and further derive
Cram\'er-Rao lower bound of angular estimation under frequency offset. Using
QuaDRiGa simulator with mmMAGIC model at 28 GHz, the numerical results show
that the proposed approach is advantageous to DIA with hierarchical beam
training. The proposed algorithm offers up to two order of magnitude access
latency saving compared to DIA, when the same discovery, post training SNR, and
overhead performance are targeted. This conclusion holds true in various
propagation environments and 3D locations of a mmW pico-cell with up to 140m
radius.
