Adaptive Interference Nulling and Direction of Arrival Estimation in GPS Dual-Polarized Antenna Receiver - Adaptive Signal Processing in Wireless Communications - page 433

eliminated. In practice, however, the adaptive weights, at convergence, are perturbed,
especially for low-power jammers and under fast convergence. The SVD of the nulling
weight matrix can be expressed as

Wu V
a

=Σ , (14 . 52)

aaa

where u a is a 2 N -by-2 N unitary matrix, V a is an L -by- L unitary matrix, and Σ a is a
2 N -by- L singular value matrix. The matrix u an of the first L - M singular vectors cor-
responding to the nonzero singular values in Σ a is orthogonal to the jammers' subspace,
and the spectrum can be expressed as

1

P () θ = . (14 . 53)

LM −

∑

2

H

a () θ u

an i _

i = 1

In the following examples, four RHCP GPS signals arrive at -20, 0, 15, and 45 degrees
with SNR of -20 dB. The eight look directions considered are the four GPS directions
and additional directions of -74, -55, 60, and 85 degrees. The number of snapshots
is set to 4,000. The nulling weight matrix is adaptively obtained by the constraint LMS
algorithm with the step size of 0.000005. In Figure 14.16, the spectrum with one RHCP
jammer is examined. The jammer signal is incident on the array with -40 degrees of

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

-100 -80 -60 -40 -20 0

Angle of arrival (degrees)

20 40 60 80 100

FIgure 14.16 Spectrum based on the nulling weight matrix obtained by the LMS algorithm
with eight dual-polarized antenna arrays, when one RHCP interferer arrives at -40 degrees.