Optimization of half wave dipole array for
generation of ultra-low side lobes
V N Lakshmana kumar
ECE Department, M.V.G.R College of Engineering, Vizianagaram, A.P, India [email protected]
Dr.M.Satyanarayana
ECE Department, M.V.G.R College of Engineering, Vizianagaram, A.P, India [email protected]
Dr.S.P.Singh
ECE Department, MGIT, Hyderabad, Telangana, India [email protected]
Abstract: Generation of low side lobe patterns is a challenging task in design of antenna arrays. Conventional techniques like chebyshev and Taylor methods have succeed in giving low side lobe levels but have some limitations. In this paper Particle swarm optimized amplitude distribution for N element half wave dipole linear array is presented. Ultra low side lobe patterns with SLL beyond -46dB and narrow beam widths are obtained. The performance of half wave dipole linear array is compared with isotropic linear array. Also the PSO based radiation patterns are compared with radiation patterns obtained using Genetic algorithm (GA) and simulated annealing (SA) techniques.
Keywords: SLL (side lobe level), PSO, GA, SA, half wave dipole. 1. Introduction
The Limitations of most of the single antennas are low gain and wide beam width. These are deciphered by array antennas which promise large gain and narrow beam width [1]. Antenna arrays provide us the flexibility to control the radiation pattern in a desired fashion by changing the amplitude distribution, spacing between the elements and phase excitation of each element [1,2].It is very important to reduce the side lobe levels in array antennas in order to avoid electromagnetic interference problems and reduce wastage of power in during transmission. Isotropic uniform linear array provides maximum side lobe level of -13.46dB [1]. Dolph chebyshev and Taylor methods are most popularly used techniques to control the side lobe level. Chebyshev method is not effective when the inter element spacing is greater than half the wave length. The limitations of Chebyshev are overcome by technique proposed by Taylor [3-5]. Even though they provide low side lobe levels, they give mutual coupling effects in practical implementation and also the beam widths are not fully controlled. To overcome these limitations and to generate radiation patterns with SLL beyond -40dB, different optimization techniques like genetic algorithm (GA), particle swarm optimization technique (PSO), simulated annealing (SA) etc. can be used. These techniques give narrow beam width for large number of elements in the array [6]. Wire antennas find many applications in VHF and UHF bands. GSM is using 900MHZ and 1800 MHZ bands for mobile communications. Different LTE bands are being used for 3G and 4G communications. The LTE band-3 uses 1710-1785MHZ as uplink frequency and 1805-1880MHZ as down link frequency [7]. The LTE band-5 uses 824-849MHZ as uplink frequency and 869-894MHZ as down link frequency. Even LTE band-7 is using 2600MHZ.Monopole, half wave dipole and loop antennas are being used extensively since several decades. In telecommunications and radars, reflective array antennas are used. Reflective antenna array uses half wave dipole antennas as driven elements in front of flat reflective surface. The dipole array should provide narrow beam width and very low side lobes for point to point communication.
In this paper, first N element isotropic linear array is optimized using particle swarm optimization technique to get ultra-low side lobe patterns. The obtained amplitude coefficients are then given as amplitude distribution for half wave dipole array. The performance of this non uniform amplitude half wave dipole array is compared with uniform half wave dipole array and also with arrays optimized using genetic algorithm (GA), simulated annealing (SA). The next sections discuss the particle swarm optimization technique, mathematical analysis and results.
2. Particle swarm optimization (PSO)
position according to its previous experience and that of its neighbors [9, 10]. The following are the steps of PSO algorithm [11].
1) State the solution space. An array of population of particles with random positions and velocities are initialized.
2) The fitness value for each particle is calculated. The fitness function and solution space are taken according to the problem.
3) The particle’s fitness value is compared with pbest (personal best). If present fitness value is better than the pbest, then pbest will be updated with fitness value.
4) Also current fitness value is compared with gbest (global best solution).If current fitness value is better than the gbest, then update gbest with current fitness value.
5) For each iteration the velocity and position will change based on the following equations.
))
(
(
*
))
(
(
*
)
(
*
)
(
new
w
V
old
C
1r
1pbest
X
old
C
2r
2gbest
X
old
V
n=
n+
n−
n+
n−
n (1))
(
)
(
)
(
new
X
old
V
new
X
n=
n+
n(2) Where w is called inertia weight, C1 and C2 are acceleration constants and r1 and r2 are the random
numbers distributed over (0, 1).
6) The process of iteration continues till desired solution is obtained. 3. Formulations
The basic element pattern of half wave dipole is given by
θ
θ
π
θ
sin
]
cos
5
.
0
[
)
(
Cos
F
=
(3) If N element linear array is considered, then using pattern multiplication theorem the total resultant field is obtained as product of basic element pattern and array factor [1]. It is given by
= +=
N n X X j n n ne
X
A
F
E
1 ) ( cos 2)
(
)
,
(
)
,
(
φ θ λ πφ
θ
φ
θ
(4)Where A(Xn) is the excitation level of nth element. Xn is the normalized spacing position and
φ
(
X
n)
is thephase excitation of nth element. The first term in this equation (4) is the basic element pattern and the second expression (summation term) represents the array factor. A(Xn) is obtained by optimization of amplitude
coefficients by particle swarm optimization (PSO), genetic algorithm (GA) and Simulated annealing (SA) techniques. The fitness function is given by
)]
,
(
log(
20
max[
AF
θ
φ
sll
f
=
=
(5)Where
AF
(
θ
,
φ
)
is the array factor of isotropic N element linear array. The element locations in the array is found using Ishimaru spacing [12] and given by
−
−
=
N
N
n
X
n1
2
(6) 4. ResultsUsing particle swarm optimization technique, the amplitude excitation coefficients are generated for isotropic N element array which gives the ultra-side lobe patterns. Figures 1to 4 shows the amplitude distribution for N=8, 16, 32 and 64 arrays. Using pattern multiplication theorem, the radiation patterns for half wave dipole arrays are obtained for N=8, 16, 32, 64 and 128 elements. Figures 5 to 9 shows the comparison of radiation patterns for uniform half wave dipole array, optimized non uniform half wave dipole array and isotropic linear array. The maximum side lobe level obtained in case of uniform dipole array is -13.66dB.Whereas using particle swarm optimization (PSO) technique it has reduced to -48.05dB. Just as PSO technique, using genetic algorithm (GA) and simulated annealing (SA) techniques, the half wave dipole array can be optimized to give ultra-low side lobes. Figures10 and 11 shows the comparison of radiation patterns of half wave dipole arrays for N=16 and 32 elements by these three techniques. From figures 10, 11 and table 2 it is observed that PSO technique is giving the lowest side lobe levels compared to GA and SA techniques.
Fig.1 Amplitude excitation distribution obtained by PSO for N=8
Fig.2 Amplitude excitation distribution obtained by PSO for N=16
Fig.4Amplitude excitation distribution obtained by PSO for N=64
Table1 Amplitude excitation coefficients obtained by PSO for N=16
S.NO Spacing(Xn) Amplitude Coefficients A(Xn)
1 -0.9375 0.0759
2 -0.8125 0.1499
3 -0.6875 0.2763
4 -0.5625 0.4365
5 -0.4375 0.6130
6 -0.3125 0.7813
7 -0.1875 0.9146
8 -0.0625 0.9902
9 0.0625 0.9940
10 0.1875 0.9240
11 0.3125 0.7918
12 0.4375 0.6216
13 0.5625 0.4438
14 0.6875 0.2832
15 0.8125 0.1525
16 0.9375 0.0710
Fig.5Radiation pattern of half wave dipole array for N=8
Fig.6Radiation pattern of half wave dipole array for N=16
Fig.7Radiation pattern of half wave dipole array for N=32
Fig.9 Radiation pattern of half wave dipole array for N=128
Fig.10Comparison of radiation patterns by GA, PSO and SA techniques for 16 element dipole array
Fig.11Comparison of radiation patterns by GA, PSO and SA techniques for 32 element dipole array
Table2 Comparison table for side lobe level by PSO, GA and SA techniques
No. Of Elements Maximum Side lobe level (in dB)
N GA PSO SA
8 -45.7321 -48.0598 -48.0116
16 -43.5560 -46.5631 -43.6830
32 -42.1910 -46.1907 -42.2314
Table3 First null beam widths for different N values obtained by PSO technique
No. Of Elements N First null beam width in degrees
8 60.75 16 29.47 32 14.65 64 7.42 128 3.88
Table 3 shows that FNBW (first null beam width) decreases as the number of elements in the array are increased 5. Conclusion
The optimized radiation patterns for half wave dipole array are generated using particle swarm optimization (PSO) technique for reduced side lobe levels. In uniform half wave dipole array, the maximum side lobe level obtained is -13.66dB. Drastic improvement in side lobe level is obtained using PSO. Around -46 to -48 dB of SLL is obtained. Using genetic algorithm (GA) around 41 to 45 dB of SLL is obtained. And it is from 41 to -48 dB in case of simulated annealing (SA). As the number of elements in the array is increased from 8 to 128, very narrow pencil beams with beam widths less than 10o are observed. These narrow beam and ultra-low side lobe patterns are useful for high resolution radar communication and point to point communications in the UHF range.
References
[1] Balanis Constantine A., “Antenna Theory Analysis and design”, John Wiley &Sons, 3rd Edition, 2005, chapter6. [2] Kraus, J.D. and R.J. Marhefka 2003, Antennas for all applications, Tata McGraw Hill Edition 2003, chapter 5.
[3] C.L.Dolph, “A current distribution for broad side arrays which optimizes the relation between beam width and side lobe level”, Proc. IRE 34, 1946, pp.335-348.
[4] T.T.taylor, “Design of line source antennas for narrow beam width and low side lobes”, IRE Transactions A.P-7, pp-16-28, 1955.
[5] Fung Tseng, “Design of array and line-source antennas for Taylor patterns with a null”, IEEE transactions on Antenna and Propagation, Vol. 27, Jul 1979.
[6] K.-K. Yan and Y. Lu, “Side lobe reduction in array-pattern synthesis using genetic algorithm”, IEEE Transactions on Antennas and Propagation, Vol. 45, July 1997, pp.1117 -1122.
[7] Valentina plaazzi, Jimmy hester, Jo Bito, “A Novel Ultra-Lightweight Multiband Rectenna on Paper for RF Energy Harvesting in the Next Generation LTE Bands”, IEEE Transactions on Microwave theory and Techniques,( Volume: PP, Issue:99 ),pp.1-14,2017. [8] J.Kennedy and R.C.Eberhart, “Particle Swarm Optimization”, Proceedings of the IEEE International conference on Neural Networks,
Vol.4, pp.1942-1948, December 1995.
[9] M.M.Khodier, C.G.Christodoulou, “Linear array geometry synthesis with minimum side lobe level and null control using Particle swarm optimization,” IEEE Transactions on Antennas and Propagation, Vol. 53, August 2005, pp.2674 -2678.
[10] J.Nanbo and Y.Rahmat Samii, “Advances in particle swarm optimization for antenna designs: Real-number, binary, single-objective and multi-objective implementations,” IEEE Transactions on Antennas and Propagation, Vol. 55, March 2007, pp.556 -567.
[11] M. Rattan,” Design of a linear array of half wave parallel dipoles using particle swarm optimization”, Progress In Electromagnetics Research, Vol. 2, 131–139, 2008.
[12] Akira Ishimaru , Unequally Spaced Arrays Based on the Poisson Sum Formula , IEEE Transactions on Antennas and Propagation ,Vol. 62, April 2014.
Authors Information
Mr. V.N.lakshmana kumar has received his bachelor’s degree in 2005 from JNTU Hyderabad in Electronics and communication engineering. He has done his post-graduation in systems and signal processing from JNTU Hyderabad. Currently he is pursuing Ph.D. in the field of Antennas from JNTU Hyderabad. He is a member of IEEE, IETE and IE. His areas of interest are signal processing and microwave antennas.
Dr.M.satyanarayana is working as Associate professor in ECE department of MVGR College of engineering. He has received his doctorate degree from Andhra University in the area of microwave antennas. Currently he is guiding scholars in the field of antennas and VLSI. He is a member of R&D section of MVGR College of engineering (Autonomous). He is a member of IEEE, IETE and IE.
