7
recently, the authors in [72] have established a similar full
3D channel model to support the performance evaluation of
AAA-based wireless communication systems. The vertical
radiation pattern of an antenna port has been expressed as
a function of the individual element radiation pattern and the
array factor of the column of elements constituting the port.
The authors used the developed 3D SCM to study the effect of
mechanical downtilt, electrical downtilt and the combination
of two downtilts on the coverage and capacity performance
of different AAA configurations and showed that downtilt
optimization can introduce significant gains in coverage and
capacity, when antenna ports have narrower vertical HPBWs.
There is still ongoing work in both industry and academia on
improving the 3D channel model and the estimates of different
elevation domain parameters [73]–[76]. An analysis of the
elevation domain parameters in the urban microcell scenario
with channel measurements at 2.3 GHz center frequency
can be found in [73]. A smaller ESD was observed for
higher Tx antenna height. Also, a significant difference in
the ESDs between the line-of-sight (LOS) and the non-line-
of-sight (NLOS) propagation conditions was reported, with
the ESD following a negative exponential model with respect
to the distance for the former and a linear model for the
latter. The authors in [74] identified the limitations of the
existing 3D channel models in describing the cross-correlation
coefficients of channel large-scale parameters, the distance
dependent properties of elevation domain parameters and the
inter-dependence between azimuth and elevation angles. They
used an outfield measurement campaign to propose a reliable
3D stochastic channel model that addressed these limitations.
A log-normal distribution was proposed to fit the probability
density function (PDF) of ESD, with a mean which decreased
with distance. A mixture of Von-Mises Fisher distributions
with a log-normally distributed concentration parameter was
used to model the interdependency between azimuth and eleva-
tion angles. A summary of the 3D channel model development
in the 3GPP can be found in [61].
Both the antenna port and the antenna element based ray-
tracing channel modeling approaches are outlined and com-
pared in section IV.
C. 3D Correlated SCMs
The compact structure of 2D AAAs deployed in FD-MIMO
systems to meet the form factor requirements often results
in small inter-element spacing between the antenna elements.
This increases the spatial correlation in the array. Recently,
measurement campaigns have also confirmed the small values
of elevation angular spreads in realistic propagation environ-
ments, resulting in the elements to be highly correlated in
the vertical domain [71]. This dramatic increase in spatial
correlation makes it imperative to characterize it and take it
into account while evaluating the performance gains realizable
through elevation beamforming techniques.
Spatial correlation has been popularly known to deteriorate
the system performance. While this is always true for point-
to-point MIMO communications [77], [78], spatial correlation
can actually be beneficial in multi-user massive MIMO set-
tings, where each user can experience high spatial correlation
within its channel vector, but the correlation matrices are
generally almost orthogonal for different users, resulting in
each user getting the full array gain proportional to the number
of antennas as shown in [79]. More discussion on this can be
found in section V-A.
The high correlation in FD-MIMO arrays can also reduce
the CSI feedback overhead incurred in the implementation of
elevation beamforming techniques. This is possible through
the design of elevation beamforming schemes using correlated
3D channel models that depend on the quasi-static spatial
channel covariance matrices of the users. A popular such
channel model for point-to-point MIMO system is the Kro-
necker model [80] and for MU-MISO system is the Rayleigh
correlated model [81]. The covariance matrices used to form
these models can be estimated using knowledge of the slowly-
varying large scale channel parameters instead of the small-
scale channel parameters that vary instantaneously. Note that
the 3D SCM discussed in the last subsection is a ray-tracing
model, which is one way to generate correlated FD-MIMO
channels. However, the explicit dependence of this channel
model on the number of propagation paths and associated
small-scale parameters like angles, powers and delays makes
the theoretical analysis of 3D beamforming generally in-
tractable. This has further motivated the characterization of
3D spatial correlation functions (SCF)s for FD-MIMO systems
that can be used to form these so-called correlated channel
models that depend only on the channel covariance matrices
and facilitate the design of 3D beamforming methods using
tools from RMT in the massive MIMO regime.
The initial SCFs proposed in literature were developed for
2D channels that ignore the elevation parameters in describing
the antenna patterns and propagation paths [82]–[88]. In [85],
approximate closed-form expressions for the spatial correla-
tion matrices were derived for clustered 2D MIMO channel
models, assuming a Laplacian azimuth angle of arrival (AoA)
distribution. The Kronecker channel model was shown to
provide a good fit to the ray-tracing channel model. This is
encouraging for researchers interested in the use of the former
for the design of massive MIMO techniques.
The notion of spatial correlation in 3D propagation envi-
ronments has been addressed in some research works. An im-
portant contribution in this area appeared in [66]. The authors
developed closed-form expressions for the spatial correlation
and large system ergodic mutual information (MI) for a 3D
cross-polarized channel model, assuming the angles to be
distributed according to Von Mises distribution. The authors in
[89], showed that elevation plays a crucial role in determining
the SCF. The derivation was based on the spherical harmonic
expansion (SHE) of plane waves and assumed the distribution
of AoAs to be 3D Von Mises-Fisher.
In [65], closed-form expressions for the SCFs of several
omnidirectional antenna arrays utilizing a 3D MIMO channel
model were derived. These SCFs then formed the covariance
matrices that were used for the evaluation of channel capacity.
The derived results were expressed as a function of angular and
array parameters and used to study the impact of azimuth and
elevation angular spreads on the capacity. However, this work
assumed the angular distributions to be uniform. The uniform