suppression of grating lobes

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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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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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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Problem with DSA

Grating Lobes –

Due to larger spacing between the sub arrays.

Larger spacing means more than 1λ.

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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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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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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)

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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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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contd…. The array factor can be expressed as[5] :-

AF=AFxAFy= 𝐴𝑛𝑒𝑗𝑛𝛽𝑙𝑥𝑆𝑖𝑛𝜃𝐶𝑜𝑠∅𝑀

𝑥𝑛=1 𝐴𝑚𝑒

𝑗𝑚𝛽𝑙𝑦𝑆𝑖𝑛𝜃𝐶𝑜𝑠∅𝑀𝑦

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= 𝐴𝑛𝑀𝑥𝑛=1 ejnβlx{SinθCosФ-SinθsCosФs} 𝐴𝑚

𝑀𝑦

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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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 b\w the element in sub arrays ; lx & ly spacing b\w the sub-arrays.

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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 b\w the element in sub arrays .

lx & ly spacing b\w the sub-arrays.

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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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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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Contd…..

Receive Array Configuration :- • Mx = My = 5

• Nx = Ny = 10

• dx = dy = 0.5λ

• lx = ly = 5λ

• Θs = Фs = 0 deg.


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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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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.


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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

Contd…..

Figure[6] :- shows the overlap pattern of both transmit & receive array at f = 100MHz.

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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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[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. [6] Jay Hyuk Choi “Distributed Sub Array Antennas for Multi Function Phased Array Radar”The IEEE International Conference on 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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