Adaptive Interference Nulling and Direction of Arrival Estimation in GPS Dual-Polarized Antenna Receiver - Adaptive Signal Processing in Wireless Communications - page 429

10

5

0

-5

-10

-15

-20

-25

Jammer GPSGPS GPS PS

-30

-100 -80 -60 -40 -20 0

Angles of arrival (degrees)

20 40 60 80 100

FIgure 14.11 CANAL spectrum by LMS algorithm with eight dual-polarized antenna arrays,
when one RHCP interferer arrives at -40 degrees.

In the following examples, the interference localization performance based on adap-
tive cancellation weight vector using the constraint LMS algorithm is examined. We
consider eight dual-polarized ULAs with interelement spacing of a half wavelength. The
four RHCP GPS signals arrive from -20, 0, 15, and 45 degrees with SNRs of -20 dB.
Eight look directions include the four GPS directions and the additional directions of
-74, -55, 60, and 85 degrees. The number of snapshots is set to 4,000, and the step size is
0.000005. In Figure 14.11, the CANAL spectrum is presented when one RHCP interferer
arrives from -40 degrees with 20 dB JNR. It is evident that the directions of both the
interferer and the GPS signals are presented by clear peaks, when applying the con-
straint LMS algorithm. This is the result of equation (14.35) and the mismatching of the
true noise power value and the one offered implicitly by the converged weights. With
this mismatch, the subtraction gives rise to the GPS signal subspace, which can no lon-
ger be ignored in the equation.
Figure 14.12 shows the output powers at the GPS receiver for each iteration with step
sizes of 0.00005 and 0.000005. The output power is calculated by w 1 H ( k ) rw 1 ( k ), where
w 1 ( k ) represents the nulling weights of the first beamformer at the k t h iteration. The
dashed line represents the output power with step size of 0.00005, whereas the solid
line represents the output power with step size of 0.000005. It is obvious that the LMS
converges faster when increasing the step size. In Figure 14.13 , the first weight at the
first beamformer is presented. The dashed line represents the optimum weight value
obtained by the covariance matrix, whereas the solid line represents the adaptive weight.
It is clear that the adaptive weight converges to the optimum value.