This document discusses techniques for suppressing grating lobes in distributed subarray (DSA) antennas. It describes how grating lobes, which are unintended beams that limit system performance, are produced by the large spacing between subarrays in a DSA. The principle of pattern multiplication is introduced as a technique for reducing grating lobes by designing the transmit and receive array patterns such that nulls in one pattern coincide with grating lobes in the other pattern. Simulation results showing the grating lobe and null locations for sample transmit and receive arrays are presented, demonstrating that pattern multiplication can effectively suppress grating lobes in the combined two-way pattern.

1. SUPPRESSION OF GRATING LOBES IN DSA
USING PRINCIPLE OF PATTERN MULTIPLICATION
by
Kavindra krishna
Research Scholar
AMU
Department of Electronics Engineering , AMU
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2. Contents
 What is DSA.
 Problem with DSA.
 Grating Lobes.
 Techniques to reduce the grating lobes in DSA.
 Principle of pattern multiplication.
 Two Way pattern design with pattern multiplication.
 Condition for grating lobes & null to be occured.
 References.
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3. What is DSA
DSA – Distributed Sub Arrays.
 Distributed Sub Arrays (DSA)-is a network of spatially separated sub arrays ,
connected to a common source via a transport medium that provide wireless
service with in geographic area or structure.
Figure [1] :- schematic of cruise on which DSA is present.
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4. Problem with DSA
 Grating Lobes –
 Due to larger spacing between the sub arrays.
Larger spacing means more than 1λ.
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5. Grating Lobes
 Grating Lobes – just like side lobes that have same amplitude as main
beam and are unintended and creates interference
with main lobes, so it might limit our System
performance.[1,3]
Figure[3] :- Grating lobes produced by linear DSA (M=5, N=5, lx =7.5λ and dx=1.5λ.) element array.
.
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6. Techniques to reduces the grating lobes in DSA
 Implement sub arrays of un-equal size, with random
location of sub arrays with respect to center of array.
 Overlapping sub arrays architecture to push the grating
lobes away from main beam.
 Two-way pattern design.
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7. Principle of Pattern of Multiplication
 The total field pattern of an array-is the
multiplication of the individual source pattern and
pattern of an array[2].
 Symbolically-
……..(1)
Where- Ftotal – total field pattern of an array.
Fi(θ,Ф)—field pattern of individual source.
Fa(θ,Ф)--- field pattern of an array.
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Ftotal = Fi(θ,Ф) Χ Fa(θ,Ф)

8. Two Way Pattern design with
Pattern of Multiplication
1) Determine the radiation pattern of Tx DSA {Ft(θ,Ф)}
2) Determine the radiation pattern of Rx DSA. {Fr(θ,Ф)}
3) Multiply both Tx radiation pattern & Rx radiation pattern, in
such a way so that resultant two way pattern {F(2 way)} have
suppressed grating lobes.
F(2 way) = Ft(θ,Ф) Χ Fr(θ,Ф)………….(2)
Where :- F(2 way) – resultant two way pattern.
Ft(θ,Ф) – radiation pattern of Tx DSA.
Fr(θ,Ф) – radiation pattern of Rx DSA.
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9. Condition of Grating Lobes &
Null to be Occurred
 We know about Array Factor of 2D Array[5] :-
Figure [2] :- shows the placement of sub arrays in DSA network.
Figure [3] :- shows the internal view of sub-arrays placed along X & Y axis.
Where :- Nx—number of element present in sub-arrays along x-axis.
Ny—number of element present in sub-arrays along y-axis.
dx—spacing b/w the elements present in sub-array X.
dy--spacing b/w the elements present in sub-array Y.
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10. contd….
 The array factor can be expressed as[5] :-
AF=AFxAFy= 𝐴 𝑛 𝑒𝑗𝑛𝛽𝑙𝑥𝑆𝑖𝑛𝜃𝐶𝑜𝑠∅𝑀 𝑥
𝑛=1 𝐴 𝑚 𝑒𝑗𝑚𝛽𝑙𝑦𝑆𝑖𝑛𝜃𝐶𝑜𝑠∅𝑀 𝑦
𝑚=1 …..(4)
Where :- β - phase constant ; λ- wavelength.
 Furthermore,if phases are introduces due to scan of beam in the direction
(θs,Фs) then[5]-
AF= 𝐴 𝑛
𝑀 𝑥
𝑛=1 ejnβlx{SinθCosФ-SinθsCosФs} 𝐴 𝑚
𝑀 𝑦
𝑚=1 ejmβly{sinθCosФ-SinθsCosФs}
…………(5)
 Finally, if the array have the uniform excitation (An=Am=1),then Eq.(0) can
be expressed as a sum of geometric series as[5] :-
…………(6)
where :- ……….(7)
………(8)
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11. Contd……
 the grating lobes of this equation can be predicted because it
have uniform spacing[5] :-
 Grating lobes can occurs at the locations when ξx & ξy are the multiple of 2π .
……..(9a)
………(9b)
Where :- p , q = 0,1,2,3…….∞.
 The location of nulls of this equation can occurs at[5] :-
…….(10a)
…..(10b)
where :- p , q are integer values start from 0,1,2,3…..
λ - wavelength ; Nx &Ny are number of element in sub arrays along x & y axis.
dx & dy are the spacing bw the element in sub arrays ; lx & ly spacing bw the sub-arrays.
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12. Contd………
 if we observe Eq.(9) & Eq.(10) then we can get the
condition for which grating lobes & nulls can coincide to
each other when-
………………(11a)
… …………(11b)
Where :-Nx &Ny are number of element in sub arrays along x & y axis.
dx & dy are the spacing bw the element in sub arrays .
lx & ly spacing bw the sub-arrays.
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13. Contd…..
 The simulation result of Eq.(9) & Eq.(10) in MATLAB with the
condition of Eq.(11).
 Transmit Array Configuration :-
• Mx = My = 5
• Nx = Ny = 5
• dx = dy = 0.5λ
• lx = ly = 5λ
• Θs = Фs = 0 deg.
 The simulation result with this data is shown on next slide-
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14. Contd…..
Figure[4] :- shows the grating lobes & null location for transmit array at f = 100MHz.
(Mx=My=5;Nx=Ny=5;dx=dy=0.5λ;lx=ly=5λ)
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15. Contd…..
 Receive Array Configuration :-
• Mx = My = 5
• Nx = Ny = 10
• dx = dy = 0.5λ
• lx = ly = 5λ
• Θs = Фs = 0 deg.
 The simulation result with this data is shown on next slide-
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16. Contd…..
Figure[5] :- shows the grating lobes & null location for receive array at f = 100MHz.
(Mx=My=10;Nx=Ny=10;dx=dy=0.5λ;lx=ly=5λ)
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17. Contd…..
 Final , two way pattern with pattern of multiplication is-
F(2 way) = Ft(θ,Ф) Χ Fr(θ,Ф)
• .
Table [A] :- shows the configuration data of both transmit & receive distributed sub arrays.
 The simulation result with this data is shown on next slide-
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Transmit Array Configuration Receive Array Configuration
Mx = My = 5 Mx = My = 10
Nx = Ny = 5 Nx = Ny = 10
dx = dy = 0.5λ dx = dy = 0.5λ
lx = ly = 5λ lx = ly = 5λ
Θs = Фs = 0 deg. Θs = Фs = 0 deg

18. Contd…..
Figure[6] :- shows the overlap pattern of both transmit & receive array at f = 100MHz.
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19. Conclusion
 It is understood that undesired grating lobes produced by
widely-spaced sub arrays can be suppressed using the
principle of pattern multiplication by intentional placement
of nulls coincident to grating lobe locations.
 To visualize the placement of grating lobes and nulls for
transmit and receive array patterns, their locations are
plotted in direction cosine space using a simple program
developed in MATLAB.
 This forms the basis of two-way pattern synthesis in deciding
the optimum element spacing, sub array spacing, and
number of elements in each sub array, for the transmit and
receive arrays.
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20. [1] Mahafza R Basseam, Radar System Analysis and Design Using MATLAB, 3rd Edition, CHAPMAN & HALL/CRC New York
Washington, D.C.2000.
[2]Prasad .K.D, Introduction to Antenna and Wave Propagation,2nd Edition,pp.335-336,Satya Prakashan New Delhi India 2007
[3] Hovanessian A.S, Radar Systems Design and Analysis, 2nd Edition, pp. 271-290, ArTech House,INC, Norwood, MA, 1998.
[4] ]Ong.Chin.Siang,Jin Wang “ 2.4GHz Digital Phased Array Architectures For Distributed Sub Arrays" The Proceeding of the IEEE thirty
seventh South-eastern Symposium,march,20012.
[5] Jun Liu,zi-Jing Zhang ,Yun Yang “Implementation of Two way Pattern design in DSA”The IEEE Phased Array Radar LETTER,VOL 19
NO.10 August 2012.
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Automation, Robotics and Application, held at Wellington,6-8 December 2011.
[7] Dr. Probir K. Bondyopadhyay, “The First Application of Distributed Sub Arrays” 2000 The Proceedings of IEEE International
Conference on Phased Array Systems & Technology, Dr. Michael Thorburn, ed., pp. 29-33, IEEE Operations Center, New Jersey, 2005.
[8] David K. Barton, Radar System Analysis, pp.83-89, 327-331, Artech House, Dedham, MA, 1979.
[9] Filippo Neri, Introduction to Electronic Defense Systems, 2nd Edition, pp. 156- 170, Artech House, Norwood, MA, 2009.
[10] Merrill I. Skolnik, Introduction to Radar Systems, 3rd Edition, pp. 210-238, McGr aw-Hill, New York, NY, 2005.
THANK-YOU
References
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