1. Adaptive Beam Forming (ABF) Overlapping Beam Forming Networks (OBFN)
Author: Evan Wayton
Overview
The problem at hand is to compare the performance of a Uniformly Spaced Line Array (USLA)
implemented with non-overlapping sub array (NOSA), 2:1 overlapping sub array (2:1 OSA), and 3:1
overlappingsubarray(3:1 OSA) architectureswhenboth conventional beamforming(CBF) andadaptive
beam forming (ABF) are utilized. These three architectures are shown below in Figure 1.
Figure 1: NOSA, 2:1 OSA, and 3:1 OSA with M=24 elements
The use of sub arrays (shown as separate colors in Figure 1) reduces the number of digital receive
elements required of the array, by allowing digital receivers to be placed at the sub array level rather
than at the element level. The sub array architecture also has the benefit of being a “cookie cutter”
solution for modular arrays, which promotes an easily reproducible sub system. Other applications of
subarrays are time delaysteeringforwideband waveforms, and multiple simultaneous receive beams
[1]
Historically,overlappingsubarray architectures have helped allow beams to be scanned off broadside
withoutintroducingagratinglobe into the main lobe of the sub array pattern [2]. Though, overlapping
the sub arrays can increase the manufacturing complexity.
The overlapping sub array architecture is in no way limited to a single dimension, nor is it limited to
planarapplications. Forthe sake of time,we will introduce auniformly space linearray(USLA) underthe
three different architectures.

2. Key Results
Matlab code was generated in order to implement the non-overlapping, 2:1 and 3:1
overlapping sub array architectures. This code was then used in order to verify that as the
overlap is increased, grating lobes can be held outside of the main lobe of the sub array
pattern, even when steered off broadside.
Next, adaptive beam forming was performed on all three architectures in order to compare
performance, and relative suppression of grating lobes. It was found that for a fixed number of
elements per sub array, the number of grating lobes present, and the amplitude of the grating
lobes can be reduced by using the overlapping sub array architecture. The summary of these
results is shown in Figure 2 and Figure 3 below:
Figure 2
Figure 3
0 0.5 1 1.5 2 2.5 3
-30
-28
-26
-24
-22
-20
Peak Grating Lobe Level as a function of the Overlap Factor [0 2 3]
Overlap Factor
PeakGratingLobeLevel[dB]
20 dB
0 0.5 1 1.5 2 2.5 3
0
5
10
15
Number of Grating Lobes as a function of the Overlap Factor [0 2 3]
Overlap Factor
NumberofGratingLobes

3. Analysis and Simulation
For the NOSA, the phase progressions which control the beam patterns are (as shown on slides 129 of
the notes):
Stage 2: ∑ exp (−2𝜋𝑗
𝑑
𝜆
𝐾(𝑚 − 1)(cos(Ѳ) − cos(ɸ)))𝑀
𝑚=1
Stage 1: ∑ exp (−2𝜋𝑗
𝑑
𝜆
(𝑘 − 1)(cos(Ѳ)))𝐾
𝑘=1
For the 2:1 OSA, the phase progressions which control the beam patterns are found to be:
Stage 2: ∑ exp (−2𝜋𝑗
𝑑
𝜆
(
𝐾
2
) (𝑚 − 1)(cos(Ѳ) − cos(ɸ)))𝑀
𝑚=1
Stage 1: ∑ exp (−2𝜋𝑗
𝑑
𝜆
(𝑘 − 1)(cos(Ѳ)))𝐾
𝑘=1
For the 3:1 OSA, the phase progressions which control the beam patterns are found to be:
Stage 2: ∑ exp (−2𝜋𝑗
𝑑
𝜆
(
𝐾
3
) (𝑚 − 1)(cos(Ѳ) − cos(ɸ)))𝑀
𝑚=1
Stage 1: ∑ exp (−2𝜋𝑗
𝑑
𝜆
(𝑘 − 1)(cos(Ѳ)))𝐾
𝑘=1
Analysis and Simulation: CBF
First,the beampatterns (which in this case are identical to the bearing responses) were computed for
the non-overlapping, non-weightedarray (NOSA) architecture. These results are shown in Figure 3 and
Figure 4 below:

4. Figure 3: Stage 1, Stage 2, and Composite beam patterns for CNOBF at 90° and 98°
Figure 4: Stage 1, Stage 2, and Composite beam patterns for CNOBF with Taylor weights at 90° and 98°
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
CNOBF: No Weights, Phi = 90 [deg]
96 Elements, 4 Elements per Sub Array, 24 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
CNOBF: No Weights, Phi = 98 [deg]
96 Elements, 4 Elements per Sub Array, 24 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
CNOBF: Taylor Weights, Phi = 90 [deg]
96 Elements, 4 Elements per Sub Array, 24 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
CNOBF: Taylor Weights, Phi = 98 [deg]
96 Elements, 4 Elements per Sub Array, 24 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite

5. It is seen from Figure 3 that at broadside, the grating lobes are completely cancelled by the Stage 1
beampattern.As soon as Stage 2 is steered off broadside to 98°, the grating lobes no longer align with
the nulls of the Stage 1 beam pattern, and hence manifest in the composite pattern. The peak of the
grating lobes when steered to 98° is seen to be approximately 12 dB down from the main lobe.
Figure 4 showsthat the fixedTaylorweightsdonotaidinsuppressingthe grating lobes, though they do
lower the side lobe levels. It is interesting to note that the shading created by the weights on Stage 2
widened the gratinglobesseen at 0.5 and -0.5, and in doing so caused the the “splitting” of the grating
lobes as seen in the broadside plot of Figure 4.
Next, the phasingcorresponding to that of a 2:1 OBF with Taylor weights on both the Stage 1 Sub Array
and Stage 2 ArrayFactor wasimplementedin Matlab. Note that here that Taylor weights were used on
both stages, which has allowed suppression of the grating lobes when the sub array was steered to
broadside,butstill the gratinglobe appearonlyapproximately 25 dB down upon steering off broadside
to 98°. The 2:1 OBF has provided us with an improvement in peak grating lobe level from -12 dB for
NOSA, to -25 dB for 2:1 OBF, as seen in Figure 5.
Figure 5: Stage 1, Stage 2, and Composite beam patterns for 2:1 OBF with Taylor weights at 90° and 98°
The nextstepwas to investigate the impact of a 3:1 OBF architecture. It is shown in Figure 6 that when
the sub array is steered off broadside to 98°, the peak relative grating lobe level is further reduced to
that of the peak of the Taylor weighting, approximately -42 dB down (since the grating lobes have
successfully been pushed outside of the main beam).
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
2:1OBF- Taylor Weights, Phi = 90 [deg]
96 Elements, 8 Elements per Sub Array, 23 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
2:1 OBF- Taylor Weights, Phi = 98 [deg]
96 Elements, 8 Elements per Sub Array, 23 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite

6. Figure 6: Stage 1, Stage 2, and Composite beam patterns for 3:1 OBF with Taylor weights at 90° and 98°
Therefore, we have shown that the overlapping sub array architecture can be used in order to reduce
gratinglobe effects.Of course,asthe beamissteeredfurtheroff broadside,the gratinglobe will appear
whenitentersthe mainlobe of Stage 1. One methodof dealingwiththiswhichthe authorwouldlike to
investigate, is the combination of a 3:1 OBF with a “split” array, much like the homework problem of
week 6. Another method which could be used in conjunction with the 3:1 OBF architecture is the
addition of an extra element in order to cancel grating lobes.
Analysis and Simulation: ABF
Nextwe will investigate the impact of the above sub array architectures in using ABF. Note that in the
above examples we have maintained a constant number of elements, only changing the number of
elements per sub array.
As derived in the lecture notes the power from a non-overlapping ABF with a sub array architecture is
found to be:
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB] 3:1 OBF- Taylor Weights, Phi = 90 [deg]
96 Elements, 12 Elements per Sub Array, 22 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite
-1 -0.5 0 0.5 1
-60
-50
-40
-30
-20
-10
0
Cosine(look angle)
NormalizedPower[dB]
3:1 OBF- Taylor Weights, Phi = 98 [deg]
96 Elements, 12 Elements per Sub Array, 22 Sub Arrays
Stage 2: Array Factor
Stage 1: Sub Array
Composite

7. When the above overlapping architecture is used, it is seen that only the α(Ѳ,ɸ) term changes. In
particularthe K becomesaK/i,where i=2,and i=3 for2:1 and 3:1 overlappingarchitecturesrespectively.
This implies that for the above examples where K=4 for NOSA, K=8 for 2:1 OSA, and K=12 for 3:1 OSA,
the K/I ratios wouldbe the same forall three cases (4/1=8/2=12/3). Therefore, there is no difference in
bearingresponse forthe 3 casesabove.The bearingresponse isshownbelow, in Figure 7, for a SNR= 20
dB.
Figure 7: ABF bearing response for NOBF, 2:1 OBF, and 3:1 OBF with with K= 4, 8, and 12 respectively.
Contact moved from 90° to 98° from left to right plot.
-1 -0.5 0 0.5 1
18
20
22
24
26
28
30
32
34
36
38
Cosine(look angle)
NormalizedPower[dB]
ABF: Phi = 90 [deg]
96 Elements, 4 Elements per Sub Array, 24 Sub Arrays
SNR = 20 dB
-1 -0.5 0 0.5 1
18
20
22
24
26
28
30
32
34
36
38
Cosine(look angle)
NormalizedPower[dB]
ABF: Phi = 98 [deg]
96 Elements, 4 Elements per Sub Array, 24 Sub Arrays
SNR = 20 dB

8. Therefore,forthe interestof the projectwe willinvestigate the impactABF with overlapping sub arrays
for a fixed numberof elementsper sub array,K. For the plotsshowninFigure 8, the numberof elements
per sub array has been fixed to be K=12. The number of sub arrays, M does not impact the result,
thoughit wasvariedinorderto maintaina constantnumber of elements. The impact of Mwould more
readilybe seenif ABIwere utilizedwith the overlapping architecture, as the degrees of freedom could
be reduced by reducing the number of sub arrays.
It is seen that for a fixed number of elements per sub array, the increasing degree of overlapping sub
arrays helps in thinning the number of grating lobes present. Also, it is seen from Figure 8 that as the
SNR increases, the grating lobe effects become more pronounced.

9. Figure 8: Grating lobe “thinning” from utilization of overlapping sub array architecture
0 50 100 150
10
20
30
40
50
60
No Overlap ABF: Phi = 90 [deg]
96 Elements, 12 Elements per Sub Array, 8 Sub Arrays
Cosine(look angle)
NormalizedPower[dB]
0 dB
10 dB
20 dB
0 50 100 150
10
20
30
40
50
60
2:1 ABF: Phi = 90 [deg]
96 Elements, 12 Elements per Sub Array, 15 Sub Arrays
Cosine(look angle)
NormalizedPower[dB]
0 dB
10 dB
20 dB
0 50 100 150
10
20
30
40
50
60
3:1 ABF: Phi = 90 [deg]
96 Elements, 12 Elements per Sub Array, 22 Sub Arrays
Cosine(look angle)
NormalizedPower[dB]
0 dB
10 dB
20 dB

10. Conclusion:
Overlappingsubarray architecturesactas a methodto reduce the number of digital receivers required
on the array. Placingthe digital receiversatthe sub array level, rather than at the element level allows
for a reduction in the number of digital receivers required. This allows processing to be done at the
beam level, rather than at the element level. The overlapping architecture can add additional
complexities in manufacturing.
The degree to which adaptive processing techniques are used in any given field depends on many
factors. That being said, there are still modern radars being produced which do not, for one reason or
another, have the luxury of adaptive processing.
Overlapping sub arrays can be used in order to thin, or push out the effects of the grating lobes. The
utilizationof ABFwithan overlappingsub array architecture, along with either using extra elements or
splittingthe array(asin Homeworkassignment6) couldbe usedto furthersuppressthe presence of the
grating lobes.
This work can be extended from one dimension to any array shape, as overlapping sub arrays may be
realized in all sorts of arrays.

11. References
[1] GlennHopkins,“Subarrays”PowerPointPresentation.GeorgiaTech Research Institute. Sensors and
Electromagnetic Applications Laboratory.
[2] D.H. Sinnott,G.R.Haack, “The use of overlappedsubarraytechniquesin simultaneous receive beam
linear arrays”, AD-P003 501. Electronics Research Laboratory. Defence Science and Technology
Organisation Department of Defense.
[2] B. Mathews,J.Griesbach,A.Brown,“WIDEBANDRADAR ADAPTIVEBEAMFORMINGUSING
FREQUENCYDOMAIN DERIVATIVEBASEDUPDATING”,
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.184.8460
[4] Fante,R. L., “SystemsStudyof OverlappedSubarrayedScanningAntennas”,IEEETrans.Antennaand
PropagationAP-28:668-669.
[5] T. Barnard, “ELE791 AdaptProcessingNotesSpring2015.pdf”