System Level Performance Analysis of Advanced Antenna ... - Centers

Adaptive antennas in UMTS
In order to illustrate the spatial filtering gain from CBF, which is an allowed AA
technique for all the UL channels in UMTS, the radiation patterns that are created for the
different UEs depending on their DoA are analysed in the following. The amplitude antenna
gain of the AA at φ2 when a beam is pointed at φ1 can be expressed by
( ; ) ( ) ( φ ) φ φ
H
φ w c
G = , (2.5)
1
2
where [] H denotes Hermitian transposition, w(φ) is defined in (2.3), and c(φ) represents the
array steering vector, which yields
with
( ) [ ( ) ( ) ( ) ] T
φ = c φ c φ ,..., c φ
1
, 2
1
M
2
c , (2.6)
( φ ) = f ( φ ) exp[ − j(
m −1)
π sin(
φ ) ]
cm , (2.7)
where f(φ) is the complex radiation pattern of the antenna elements. The effective power
radiation pattern of the directional beam is influenced by the radio channel’s azimuth
dispersion seen at the Node-B, so the effective power antenna gain at φ2 when a directional
beam is pointed at φ1 equals [35]
2
( φ ; φ ) G(
φ ; ϕ)
p ( ϕ −φ
) dϕ
W 1 2
1 A 2
= ∫ , (2.8)
where pA(φ) is the power azimuth spectrum (PAS) of the radio channel at the Node-B. Field
measurements have shown that the PAS can be approximated with a Laplacian function for
typical urban environments, with a local average AS of 5°−10° [44]. Alternative models for
the PAS are discussed in [45] and [46], among others. However, the actual shape of the PAS
does not have a strong influence on the effective power antenna gain in (2.8), provided that
the AS at the Node-B is smaller than the beamwidth of the directional beams. For this study,
the radiation pattern of the antenna elements is given by
( φ ) for φ ∈[
− 90°
, 90 ]
⎧
⎪
β cos °
f ( φ ) = ⎨ β
⎪⎩
otherwise
R
4 . 1
, (2.9)
where β is the broadside antenna gain, and R is the front-to-back ratio. In this case, β = 18 dBi
and R = -33.8 dB. This radiation pattern is selected in order to provide a coverage area
corresponding to a hexagonal cell [47].
Figure 2.4 shows the effective radiation pattern of a set of directional beams that have
been generated with a uniform linear AA of four antenna elements. This plot has been
obtained for an AS of 5° and six beams pointing at φ = [-50°, -25°, -8°, 8°, 25°, 50°]. For
comparison, a sector beam covering the whole cell is also depicted. The radiation pattern for
the sector beam is assumed to equal that of the antenna elements of the AA, although it is also
generated by the AA. As in the case of the directional beams, the effective power radiation
pattern of the sector beam is affected by the PAS of the radio channel and equals
2
( φ ) f ( ϕ)
p ( ϕ φ ) dϕ
S = ∫
A −
(2.10)
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