  The recent trends of densification and centralized signal processing in radio
access networks suggest that future networks may comprise ubiquitous antennas
coordinated to form a network-wide gigantic array, referred to as the
ubiquitous array (UA). In this paper, the UA communication techniques are
designed and analyzed based on a geometric model. Specifically, the UA is
modeled as a continuous circular/spherical array enclosing target users and
free-space propagation is assumed. First, consider the estimation of multiuser
UA channels induced by user locations. Given single pilot symbols, a novel
channel estimation scheme is proposed that decomposes training signals into
Fourier/Laplace series and thereby translates multiuser channel estimation into
peak detection of a derive function of location. The process is shown to
suppress noise. Moreover, it is proved that estimation error due to
interference diminishes with the increasing minimum user-separation distance
following the power law, where the exponent is 1/3 and 1 for the circular and
spherical UA, respectively. If orthogonal pilot sequences are used, channel
estimation is found to be perfect. Next, consider channel-conjugate data
transmission that maximizes received signal power. The power of interference
between two users is shown to decay with the increasing user-separation
distance sub-linearly and super-linearly for the circular and spherical UA,
respectively. Furthermore, a novel multiuser precoding design is proposed by
exciting different phase modes of the UA and controlling the mode weight
factors to null interference. The number of available degrees of freedom for
interference nulling using the UA is proved to be proportional to the minimum
user-separation distance.
