Optimizing the Sidelobe Level of a Two-Way

Antenna Array Pattern by Thinning the Receive

Aperture

Randy L. Haupt
Electrical Engineering
Colorado School of Mines
Golden, CO, USA
rhaupt@mines.edu

Abstract— The maximum sidelobe level of a two-way antenna pattern synthesis is to synthesize the transmit and receive
array pattern of a radar is usually considered to be the product patterns separately, then multiply them to get the two-way
of the maximum sidelobe level of the transmit array time the pattern. The approach in [9] synthesized a two-way pattern
maximum sidelobe level of the receive array. This paper shows using a gradient-based optimization to find a phase taper for
that a thinned receive array can be synthesized in order to place the uniform transmit array and an amplitude and phase taper
nulls of the receive pattern in the directions of the peak sidelobes for the receive array. One report provided three approaches to
of the transmit pattern to get even lower two-way maximum generate low sidelobes in the two-way pattern when the
sidelobe levels. The two-way pattern is synthesized using a transmit pattern is uniform and the receive pattern has low
genetic algorithm to find a thinned receive aperture that
sidelobes [10]:
minimizes the maximum two-way sidelobe level with a uniform
transmit array. 1. Make the transmit aperture smaller than the receive
aperture, so that the first null of the transmit and receive
Keywords— antenna array; phased array; radar; genetic patterns are at the same angle.
algorithm; optimization; low sidelobes; two-way pattern
2. Split the uniform transmit aperture into two then steer both
I. INTRODUCTION subapertures until their peak sidelobes are at the first nulls
of the receive pattern.
Radar designers suppress sidelobes in the radiation pattern
of a phased array antenna in order to avoid picking up 3. Place a quadratic phase taper on the uniform transmit
objectionable amounts of ground clutter and other spurious pattern.
signals [1]. Sidelobe suppression is usually in the form of an The first approach produced the best results, while the last
amplitude taper applied to the elements in the array. The approach did not work well at all. It is possible to improve on
amplitude taper can be in the form of a thinned array in which the first approach by using a genetic algorithm to optimize the
the amplitude taper is quantized to one bit. Elements towards receive amplitude taper in order to get the lowest possible two-
the center of the array are active while passive elements are way peak sidelobe levels.
inserted in the array lattice at increasing frequency towards the
array edges. Thinning can be optimized to yield the lowest This paper presents the synthesis of low sidelobe two-way
possible sidelobe levels using a global optimization method, patterns radar planar arrays with a uniform transmit array and
such as a genetic algorithm [2][3][4]. thinned receive array. T/R modules are located at all the active
elements, while inactive receive elements only have transmit
A low sidelobe taper on the transmit aperture reduces modules. Section II introduces the antenna array model.
efficiency because not all the T/R modules transmit at full Section III demonstrates the traditional approach to
power. Using attenuators to produce the amplitude taper synthesizing a two-way pattern. Section IV explains the logic
produces power dissipation problems. Changing the bias in the behind this new two-way pattern synthesis approach. Section V
transmit amplifier causes mismatch problems. Making the introduces a new approach to two-way array pattern synthesis.
transmit aperture uniform provides the maximum EIRP while The results show that the two-way pattern maximum sidelobe
eliminating amplitude taper implementation problems on the level can be lowered approximately 6.5 dB by optimizing the
transmit array. Using a uniform transmit array means that the two-way pattern rather than the transmit pattern and the receive
two-way pattern peak sidelobes are primarily determined by pattern separately at the expense of reduced gain.
the receive pattern sidelobes [5].
Sidelobe levels of the two-way antenna pattern are II. ARRAY MODEL
important in many applications, such as SAR [6][7] and Assume that the radar has an N-element planar array lying
meteorological radar [8]. In general, the approach to two-way in the x-y plane with a square lattice as shown in Fig. 1. The
transmit array factor when all the elements are uniformly
weighted is given by

Ny Nx
 jk  n 1 d x sin  cos    m 1 d y sin  sin  
AFtx   e (1)
m 1 n 1

where
N x  number of elements in x-direction
N y  number of elements in y-direction

k  2 
  wavelength
d x  element spacing in x-direction
d y  element spacing in y-direction
  angle measured from z-axis (elevation)
Fig. 2. Transmit uniform array factor.
  angle measured from x-direction (azimuth)
The thinned receive array factor is written as III. TRADITIONAL APPROACH TO SYNTHESIZING A TWO-
WAY ANTENNA PATTERN
Ny Nx
jk  n 1 d x sin  cos    m 1 d y sin  sin   The traditional approach to synthesizing a two-way pattern
AFrx   w m, n e (2) would thin the receive array aperture in order to minimize the
m 1 n 1
maximum sidelobe level of the receive array factor. In this
case, a genetic algorithm minimizes the cost function given by
where
1 element turned on cost  sllrxpeak (4)
wm, n  
0 element turned off
The two-way antenna pattern is just the product of (1) and (2) where sllrxpeak is the peak sidelobe level of (2). The genetic
algorithm used for this problem is found in [9]. The
corresponding receive pattern is then substituted into (3) to
AF2  AFtx  AFrx (3) yield the two-way pattern.

Fig. 1. Planar array model.

In this paper, we assume the array has 32 by 32 elements

that are spaced  / 2 apart in the x- and y-directions for a total
of N = 1024 elements. The transmit array is assumed to be
uniform, so its array factor is shown in Fig. 2. It has a
directivity of 35.1 dB and a peak sidelobe level that is 13.3 dB Fig. 3. The two-way pattern resulting from a uniform transmit and a uniform
receive pattern for an 8 element linear array.
below the main beam.
 34.3 dB below the main beam. Note that this two-way peak
sidelobe level approximately equals the sum (in dB) of the
peak sidelobe levels of the transmit and receive array factors.

IV. SYNTHESIZED TWO-WAY PATTERN: SMALL LINEAR

ARRAY EXAMPLE
In this section we present an illustrative example of
optimizing a two-way sidelobe pattern through a small linear
array. The linear array has 8 elements spaced  2 apart. The
object is to place nulls of one pattern at the location of sidelobe
peaks of the other pattern. Turning off two end elements is the
optimum solution (Fig. 6) -- no genetic algorithm needed here.
The 6 element receive pattern is superimposed on the uniform
transmit patter in Fig. 7. Note that when one pattern has a null
the other one has a peak. Forcing the receive pattern to have
nulls at the same locations as the sidelobes of the transmit
antenna results in a lower peak sidelobe level than the product
of the transmit antenna pattern and a low sidelobe receive
Fig. 4. Optimized thinned receive array factor. pattern. Fig. 8 is a plot of the optimized two-way pattern. Its
two-way directivity is 16.8 dB with a peak sidelobe level that is
The genetic algorithm found the receive array thinning 29.2 dB below the peak of the main beam. The two-way
shown in Fig. 3. This aperture has a directivity of 32.6 dB with pattern of a uniform 8 element transmit and receive array has a
a taper efficiency of directivity of 18.1 dB and peak relative sidelobe level of 26.4
dB. In this case, both the transmit and receive patterns have a
maximum sidelobe level of 13.2 dB but a two-way pattern
Non
  0.56 (5) maximum sidelobe level greater than the combined 26.4 dB.
N

where N on is the number of active elements. Fig. 4 shows the

resulting array factor that has a peak sidelobe level that is 21.1
dB below the main beam.
Fig. 6. The optimized receive and transmit arrays.

Fig. 7. The uniform transmit and optimized receive pattern for an 8 element
linear array.

Fig. 5. The two-way pattern resulting from a uniform transmit and an

optimized thinned receive array.

The two-way pattern is found by multiplying the

synthesized thinned array factor by the uniform array factor.
The resulting two-way array factor shown in Fig. 5 has a
directivity of 67.6 dB with a maximum sidelobe level that is
Fig. 8. Optimized two-way pattern for an 8 element linear array.
 V. SYNTHESIZED TWO-WAY PATTERN: PLANAR ARRAY sidelobe level of the receive pattern. The approach advocated
EXAMPLE in this paper finds a thinning for the receive array that
minimizes the peak sidelobe level of the two-way pattern.
Rather than minimizing the maximum sidelobe level of the
Although the receive pattern in this approach has a 1.9 dB
receive array factor, the genetic algorithm can minimize the
higher peak sidelobe level than the traditional approach, the
peak sidelobe level of the two-way pattern using the cost
two-way pattern has a peak sidelobe level that is 6.5 dB less
function
than the traditional approach at a cost of losing 0.2 dB in the
maximum directivity. Other optimization methods will yield
cost  sll2 peak (6) similar results. There is not a unique solution.

where sll2 peak is the peak sidelobe level of (3).

The genetic algorithm found the receive array thinning

shown in Fig. 9. This aperture has a directivity of 32.3 dB with
a taper efficiency of   0.53 . Fig. 10 shows the resulting
receive array factor that has a peak sidelobe level that is 19.2
dB below the main beam.
The two-way pattern is found by multiplying the
synthesized thinned receive array factor by the uniform
transmit array factor. The resulting two-way array factor
shown in Fig. 11 has a directivity of 67.4 dB with a maximum
sidelobe level that is 40.8 dB below the main beam. This two-
way peak sidelobe level is 8.3 dB less than the sum (in dB) of
the peaks sidelobe levels of the transmit and receive array
factors and 6.5 dB less than that obtained by optimizing only
the receive pattern.

Fig. 10. Receive array factor corresponding to Fig. 9.

Fig. 9. Thinned receive array optimized for a minimum maximum 2-way

sidelobe level.
Fig. 11. The optimized 2-way array factor.

VI. CONCLUSIONS
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