Dynamic Array Thinning for
Adaptive Interference Cancellation
Paolo Rocca* and Randy L. Haupt+
*
University of Trento, Dept. Information Engineering and Computer Science, Via Sommarive, 14, 38050, Trento, Italy
paolo.rocca@disi.unitn.it
+
The Pennsylvania State University, Applied Research Laboratory, PO Box 30, State College, PA, USA 16804
rlh45@psu.edu
Abstract— This paper describes an approach to adaptive nulling
that changes an array thinning configuration to move sidelobe
nulls. Dynamically thinning an array requires that each element
in the array can be made active by connecting it to the feed
network with a switch. If the number of active elements remains
constant, then the gain of the array remains constant. Our results
show that nulls can be placed in the array factor by changing the
thinning configuration.
This paper presents a preliminary investigation on the use
of dynamically thinned arrays for the suppression of undesired
signals in the sidelobes. The elements that are turned off are
varied in order to position nulls or lower sidelobes to
sufficiently suppress interference entering the sidelobes.
Initial computer results show that interference suppress is
indeed possible.
I. INTRODUCTION
II. FORMULATION
A diagram of the dynamically thinned array is shown in Fig.
1. Each element is equipped with a radio-frequency (RF)
switch that connects the element to either the feed network,
"on" state, or a matched load, "off" state. If all the switches
are on, then the array is a fully populated uniform array.
Statistically, the average sidelobe level is proportional to the
number of active elements in the array. An expression for the
rms sidelobe level of a thinned array is given by [12]
1
sll 2 =
(1)
N on
A thinned array is a uniform linear or planar array in
which some of the elements are connected to the feed network
while others are connected to matched loads. If the thinning
increases away from the center of the array, then the
amplitude density of the radiated field is tapered and results in
lower sidelobes and gain compared to an identical non-thinned
array. Array thinning has several advantages over amplitude
tapering, including a simple feed network, no amplitude
weights/attenuators, and reduced number of active elements
for the same beamwidth of a fully-populated uniform array.
For these reasons, thinned arrays have shown attractive
features for both satellite [1] and terrestrial [2] antenna
systems.
Different strategies have been proposed for the design of
thinned arrays. The first used statistical thinning [3] where the
density of the elements which remain “on” was chosen
proportionally to the amplitude of a reference distribution (e.g.,
Taylor). More recently, other approaches based on stochastic
optimization algorithms (e.g., genetic algorithms [4], particle
swarm optimizer [5], and ant colony optimizer [6]), as well as
hybrid techniques [7][8] have been presented. The use of suboptimal, but fast, deterministic strategies [9] exploiting the
autocorrelation properties of known binary sequences have
also enabled the synthesis of massively thinned very large
structures.
Although effective in the reduction of the peak sidelobe
level (PSL) as well as the average sidelobe level, the patterns
afforded by thinned arrays are static. Therefore, the presence
of interference signals or jammers, although impinging away
from the main lobe region, can drastically reduce the
performance of the antenna system. To avoid this drawback,
some adaptive techniques have been proposed in the literature
[10][11].
where sll 2 is the power level of the average sidelobe level
and N on is the number of elements turned on. An expression
for the peak sidelobe level is found by assuming all the
sidelobes are within three standard deviations of the rms
sidelobe level and has the form [12]
P ( all sidelobes < sll p2 )
(1 − e
− sll 2p / sll 2
)
N /2
(2)
for linear and planar arrays having half wavelength spacing.
Fig. 1 Sketch of the antenna layout
F (ϑ , I ) =
N
∑I
n
exp[ jk (n − 1)d cos(ϑ )]
20
Directivity (dB)
In the presence of interfering signals, the thinning
configuration is dynamically changed using the RF switches
until the undesired signals are placed in nulls of the radiation
pattern (Fig. 2). To increase the efficiency and the reliability
of the system in dealing with real-time scenarios, the
sequences of the elements that are turned on and off are apriori computed. In particular, the choice of the thinning
configurations is done in order to satisfy the following
requirements: (a) the various patterns should allow to suppress
interference signals coming from whatever direction of the
sidelobe region; (b) the number of thinning configurations
should be as small as possible to reduce the time needed to
find that one able to suppress the interfering signals; (c) the
shape of the main lobe should be kept constant to correctly
received the desired signal within the main lobe.
Due to its simplicity of implementation and efficiency, the
strategy proposed in [3] has been adopted to define the various
thinning configurations. Let us considered a linear array
composed by N isotropic sources with uniform inter-element
spacing d . The corresponding array factor is expressed as:
10
Interference
Initial thinning
Second thinning
0
-10
-20
0
45
θ (degrees)
90
Fig. 2 Power patterns generated by two different thinning configurations.
(3)
n =1
where the vector I = {I n , n = 1,..., N } corresponds to the
thinning configuration generated through the RF switches (Fig.
1) and I n = {0,1} is a binary quantity representing the element
excitation. Moreover, k = 2π λ is the free-space
wavenumber, λ being the wavelength, and ϑ is the angle
measured from the array axis.
The system is required to receive the interference signals
in a region of the secondary lobes where PSL is below a
predefined threshold, PSLth , in order to guarantee a
sufficiently high signal-to-interference ratio (SIR). Thus,
k
starting from an initial thinning configuration ( I )
determined as in [3], the region of the sidelobes where the
condition
k
F ϑ , I < PSLth , ϑ ∈ ϑ fn ; π2 ,
(4)
Fig. 3 Sidelobe region where
PSL < PSLth .
dynamically changed among the K different configurations
until a sufficient value of SIR is achieved.
III. RESULTS
As a representative example, let us consider a linear array
with 32 elements equally spaced of d = λ 2 . Moreover, let
us impose PSLth = −25dB as a threshold to guarantee the
reception of the desired signal with an adequate signal-tonoise ratio. To obtain the required thinning configurations, the
ϑ fn being the first null direction, is verified are stored in array is statistically thinned to model a -30 dB, n = 5 Taylor
k
the nulling vector, ϑ null [without loss of generality, in (4) amplitude taper. Accordingly, the statistically density-taper
approach of [3] has been used.
k
F ϑ , I is supposed to be symmetric]. As a representative
By applying the proposed synthesis approach, it has been
1
2
example, Figure 3 shows the null regions ϑ null ∪ ϑ null (i.e., found that the K = 5 thinning configurations reported in Fig.
the darker strips) for the thinning configurations affording the 4 have shown to guarantee a suppression of the interferences
patterns of Fig. 2 when imposing PSLth = −40dB . The below the required threshold in the whole sidelobe region. In
Fig. 4, the solid dots in the figures indicate elements that are
K
k
process is iterated until the vector ϑ null = ϑ null covers all turned on while the empty circles are the elements that are
switched off.
k =1
If an interfering signal is incident on this array at an angle
the secondary lobe region. The K different thinning
u
=
cos(ϑ ) = 0.6 when the thinning configuration k = 5 is
sequences are then stored.
In a noisy environment, when the performance (i.e., the SIR) used, the array is not able to provide a sufficient suppression
of the undesired signal (Fig. 5) since the level of the
of the antenna system reduces, the on-off sequence is
(
(
)
[
]
)
∪
0
k=1
Relative Power Pattern
-5
k=2
k=3
-10
-15
-20
-25
-30
-35
-40
k=4
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
u=cos(θ)
Fig. 5 Power pattern generated by the thinning configurations k=5.
k=5
0
-5
Relative Power Pattern
Fig. 4 Thinning configurations modelling a 30dB Taylor amplitude taper.
secondary lobes is −15.8 dB . Therefore, applying the
proposed dynamic thinning method and changing the thinning
configuration to that reported in Fig. 4 and k = 2 , the
corresponding pattern (Fig. 6) is characterized by a lower null
in the direction of the interfering signal. As a matter of fact,
the sidelobe decreases at the angle of the interference to
−33dB thus guaranteeing a reliable operating condition. The
directivity of the main beam only slightly changes since a
couple of more elements is turned on with respect to the
previous thinning configuration.
IV. CONCLUSIONS
In this work, an innovative strategy for the design of dynamic
thinned array able to adaptively control the on-off sequence to
cancel the incoming interference signals has been presented.
A set of RF switches has been used to change the status of the
array elements according to the various thinning
configurations computed by means of a statistical density
tapering technique. Preliminary results have shown the
potentiality of the proposed method.
[2]
[3]
[4]
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-15
-20
-25
-30
-35
-40
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
u=cos(θ)
Fig. 6 Power pattern generated by the thinning configurations k=2.
[5]
[6]
[7]
[8]
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