Digital Signal Processing Reference
In-Depth Information
square (LMS) or other adaptive gradient algorithms [40, 41, 42]. The adaptive algorithms
can be applied in baseband or instantaneous frequency (IF), and if required, the weights
can even be adjusted using analog adaptive loops [43]. This approach was introduced in
[43] and was referred to as concurrent adaptive nulling and localization (CANAL). The
work in [43], however, is very sensitive to the noise power estimate, has not been applied
to GPS, and did not consider a receiver with dual-polarized antennas.
Interference nulling and DOA estimation for GPS receivers can be pursued using
dual-polarized antenna arrays. This improves the receiver capability for counteracting
different types of the jammers, such as vertically polarized, horizontally polarized, and
left-hand circularly polarized (LHCP) interferers. Further, the dual-polarized antenna
array has around twice the number of degrees of freedom as its single-polarized antenna
array counterpart.
14.3
GPS Receiver Model with Dual-Polarized
Antenna Array
A GPS antenna array with
N
dual-polarized antennas is depicted in Figure 14.1. The
dual-polarized antenna can be viewed as the linear combination of the vertical and hori-
zontal elements. At each antenna, two received signals corresponding to the vertical
and horizontal polarizations are collected. Each signal is assigned a separate weight. In
baseband processing, an adaptive beamformer with complex weights, operating on the
in-phase and quadrature signal components, is applied to linearly combine the dual-
polarized antenna outputs.
Assume an
N
uniform linear array (ULA) with interelement spacing
d
. Consider
D
GPS signals incident on the array from the directions
θ
1
,
θ
2
, …,
θ
D
, and
M
interferers
V
1
W
1H
X
1V
H
1
X
1H
W
1V
Input x(k)
Output y(k)
V
N
∑
W
NH
X
NV
H
N
X
NH
W
NV
FIgure 14.1
GPS receiver with dual-polarized antenna array.
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