  mmWave communication systems overcome high attenuation by using multiple
antennas at both the transmitter and the receiver to perform beamforming. Upon
entrance of a user equipment (UE) into a cell a scanning procedure must be
performed by the base station in order to find the UE, in what is known as
initial access (IA) procedure. In this paper we start from the observation that
UEs are more likely to enter from some directions than from others, as they
typically move along streets, while other movements are impossible due to the
presence of obstacles. Moreover, users are entering with a given time
statistics, for example described by inter-arrival times. In this context we
propose scanning strategies for IA that take into account the entrance
statistics. In particular, we propose two approaches: a memory-less random
illumination (MLRI) algorithm and a statistic and memory-based illumination
(SMBI) algorithm. The MLRI algorithm scans a random sector in each slot, based
on the statistics of sector entrance, without memory. The SMBI algorithm
instead scans sectors in a deterministic sequence selected according to the
statistics of sector entrance and time of entrance, and taking into account the
fact that the user has not yet been discovered (thus including memory). We
assess the performance of the proposed methods in terms of average discovery
time.
