Following the description of these packages, validation results are presented. The
distribution terms of these packages are stated at the end of the document.
2. Spatial correlation – Directory Correlation_Multiple_Cluster
The main script is geometry2correlation.m. Through a dialogue with the user, this script
first collects all the information requested to fully characterise the scenario, namely the
number of antenna elements of the ULAs at the User Equipment (UE) and at the Node
B, their spacings, the PAS types of the impinging waves, their Azimuth Spreads (AS),
and their Angle of Departure (AoD)/Angle of Arrival (AoA).
In a second phase, the spatial correlation properties are derived by the script
correlation.m.
The first step of this phase is to normalise the PAS such that it can be regarded as a
probability distribution, which means that
()
ò
=
−
π
π
ϕϕ
1dPAS
(1)
On the other hand, this normalisation step, performed in normalisation_*.m scripts,
serves to derive the standard deviation of this pdf, based on the AS defined by the user,
as there is not necessarily an identity between them.
Being normalised, the PAS is then integrated over its definition domain according to the
relations established in [1] to derive the spatial correlation coefficients. The coefficients
of the homogeneous products between real (imaginary) parts are derived in Rxx_*.m
scripts, while the mixed products between real and imaginary parts are handled by
Rxy_*.m scripts. Their outcome is combined to produce either complex field spatial
correlation coefficients or real power ones, depending on the value of a calling variable
of the correlation.m script.
Finally, the correlation coefficients fill two matrices defined at the UE and at the Node B,
respectively
UE
R and
BNode
R . These spatial correlation matrices are combined through
a Kronecker product as proposed in [3, 4]. The structure of the Kronecker product
depends whether one wants to simulate a downlink transmission
UEBNode
RRR ⊗=
(2)
or an uplink one
BNodeUE
RRR ⊗=
(3)
where
⊗represents the operator of the Kronecker product.
As a matter of illustration, Figure 2 shows 2-cluster PASs, where both clusters are
constrained within [-60°, 60°] around their AOAs {-90°, 90°} and exhibit an AS of 30°.
Note that the second cluster has half the power of the first one. The envelope correlation
coefficient of two distant antennas impinged by these PASs is shown in Figure 3 as a
