=Paper=
{{Paper
|id=Vol-3058/paper24
|storemode=property
|title=A Linear 32x1 Elements Antenna Array Failure Correction Using Brain Storm Optimization Algorithm
|pdfUrl=https://ceur-ws.org/Vol-3058/Paper-044.pdf
|volume=Vol-3058
|authors=Narwant Singh Grewal
}}
==A Linear 32x1 Elements Antenna Array Failure Correction Using Brain Storm Optimization Algorithm==
<pdf width="1500px">https://ceur-ws.org/Vol-3058/Paper-044.pdf</pdf>
<pre>
A LINEAR 32x1 ELEMENTS ANTENNA ARRAY FAILURE
CORRECTION USING BRAIN STORM OPTIMIZATION ALGORITHM
Narwant S. Grewal1
1
 Department of Electronics & Communication Engineering, Guru Nanak Dev Engineering College, Ludhiana,
Punjab India


                 Abstract
                 The radiation characteristics of antenna array may be disturbed by the faults related to its
                 elements. The presented paper exploits the problem solving ability of brain storm
                 optimization (BSO) which indicates the collective human behavior replica to resolve
                 antenna-element failure problem of linear 32x1 elements antenna array. The amplitude
                 excitations of healthy antenna elements of the array have been re-assigned with the help of
                 the proposed method to obtain the pre-failure characteristics of considered case. The result
                 of numerical example shows the ability of BSO to solve faulty element problem of antenna
                 system in very effective manners.

                 Keywords 1
                 Antenna Array, Linear 32x1 elements Array, SLL, Element malfunctioning, Optimization,
                 brain storm optimization.

1. Introduction
The antenna array plays a crucial role in efficient designing of terrestrial communication link. An
antenna-array subsystem finds numerous roles in system viz. wireless sensor networks, Internet of
things, radar etc. as acquisition system for signal. Generally, antenna system contains huge elements
and there is chance of malfunctioning of antenna element. The failure conditions occur in the antenna
system causes disturbance in the space distribution of the elements in antenna subsystem. It causes
distortion of the original characteristics (side lobe level etc.) of antenna system. Sometimes there is
low possibility to repair the dead element with the fresh element under critical conditions. Luckily,
the recovering of original characteristics of antenna system with minimal error may be achieved
without replacing the faulty elements by controlling the amplitude or phase or both excitation of non-
disturbing units (element) of the antenna subsystem. The numerous traditional procedures are adopted
in the open literature to solve the array failure and correction problems. Some of the techniques
include conjugate gradient algorithm based on redistribution of complex excitation of healthy
elements [1]; a numerical technique to recover original characteristics under single element failure
condition [2]; a digital beamforming array method [3]; and applying an orthogonal process [4].
The numerical methods find it difficult to regain the desired beam shape of the antenna array with
disturbed conditions due to randomization of the layout of geometric of healthy antenna array
elements. Under such situations, the optimization techniques may play an important role in solving
antenna array failure issues because of their capability to identify more than one solution instantly
without any prior information. Several optimization methods employed in mitigating the failure
problem at antenna element level. Some of these listed as genetic algorithm (GA) [5-7], firefly
algorithm [10-12], and bat algorithm [13].


International Conference on Emerging Technologies: AI, IoT, and CPS for Science & Technology Applications, September 06–07, 2021,
NITTTR Chandigarh, India
EMAIL: narwant@gndec.ac.in
ORCID: 0000-0002-8295-7118
            © 2021 Copyright for this paper by its authors.
            Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
            CEUR Workshop Proceedings (CEUR-WS.org)
    In the presented work, a flexible approach based on brain storm optimization (BSO) [14] has been
used to re-optimize a linear 32x1 elements antenna array design under element failure condition. The
proposed technique has been already successfully applied in different engineering fields [15-16]. The
proposed technique is effectively applied to above mentioned sub-system with the help of modified
assignment of the element excitation to healthy elements for recovery of antenna’s original
characteristics.

2. Problem formulation
  The array factor of the linear array of 32 identical elements shown in Figure 1, having uniform half
wavelength spacing d between two elements is generally given as

                             AF = W K S (ϕ ,ϕ c )                                                    (1)

   where,

                                     {                      }T
                             W K = w1 , w2 , w3 .......w 32 , w z ∈ C N , z = 1,2,...32              (2)

    The equations (1) and (2) contains various parameters including the weighting vector WK, the
steering vector S , the direction variable and direction of main beam φ, φC . The real number
set/subset CN is used as weight factors of 32 elements linear antenna array.




Figure 1: A 32 elements based antenna array

   The steering vector represents by symbol S in (1) is given as

                                       j2πd  32 − 1                                              (3)
                              S = exp       z −     .(cos ϕ − cos ϕ c )   z = 1,2,...32
                                       λ        2                      

    The failed conditions have been introduced in the antenna array by replacing the weights of the
particular element or elements with 0. Then the distorted pattern is corrected with revised distribution
of the excitation weights in the array using BSO method. A template is constructed and taken as ideal
pattern of the array. The template with pre-failure pattern of array system is demonstrated in Figure 2.


3. Brain Storm Optimization algorithm
    Shi (Y. Shi, 2011) proposed the imitation of an innovative thinking methodology through which
the effective ideas have been facilitated among small group of people and named it BSO algorithm.
Every person in the group belongs to different culture, presents an idea or solution. The algorithm
starts by generating K number of ideas from K individuals. These ideas or solutions have been
separated in M number of groups based on resemblance in their opinion. The best solution belongs to
each group are selected to judge the global best solution. At last, new K numbers of ideas are
generated taking consideration of four Osborns rules namely No Bad Idea, Anything Accepted,
Combination of Ideas and Go for Quantity. The pseodocode of the algorithm has been presented in
         Figure 3. The combined idea is generated with the help of weighted sum of two ideas and it is given
         as

                                        xselected = T * xsel _ 1 + [1 − T ] * xsel _ 2                                   (4)

             A refined idea is generated with the help of the following expressions,

                                        xrefined = xselected + ζ * ρ (0,1)                                               (5)
                                                                                  Initialize the population of K ideas
                                                                               x n (0) ← {x1 (0), x 2 (0)...x K (0)}
                                                                                 Define parameters Prep, Pgen, P1 and P2
                                                                                                gn ← 0
                                                                      Choose clustering algorithm and divide the ideas (K) into
                                                                             groups (N) based on their similarity level
                                                                     while the terminating conditions at unsatisfactory level, do:
                                                                        Compute the ideas within groups using fitness function
                                                                     Rank the ideas and select the best idea as group head in each
                                                                                                group
                                                                                            If (rand <Prep):
                                                                         A new idea is generated and replaces the cluster head
                                                                                                  end if
                                                                                            If (rand <Pgen):
                                                                           Select one-cluster idea generation for the solution
                                                                                   If (rand <P1): Select cluster head
                                                                            else Select random idea from the same cluster
                                                                                                  end if
                                                                      else Select two-cluster idea generation for the solution and
                                                                                   choose two clusters randomly
                                                                                             If (rand <P2):
                                                                        Select cluster heads of chosen clusters and combine by
                                                                                           weighted sum
                                                                       else Pick ideas at random from the selected clusters and
                                                                                  combine them by weighted sum
                                                                                                  end if
                                                                                                  end if
Figure. 2:    (a) Template as ideal characteristics                            Generate refined idea using equation (5)
              (b) Original pattern (SLL=− 30 dB )                    Compare the solution with the global best and keep the best
                                                                                                  x*
                                                                                              gn ← gn+1
                                                                                                end while


                                                                  Figure 3: Pseudo code of the brain storm optimization


            The Gaussian random value is represented by ρ (0,1) and the contribution of this factor is decided
         by the factor ζ which depends upon maximum iteration G and the current generation g and it is given
         by

                                                                                                 
                                       ζ (t ) =     * ( x mx − x mn ) * rdm ( ) * exp
                                                  1                                          G                           (6)
                                                                                      1−         
                                                  4                                      G − g +1
                                                                                                  
4. Simulation results and discussion
   The brain storm optimization technique has been realized in MatLab and then the same has been
applied to the complicated problem of 32 element linear antenna array failure problem. The various
parameters of BSO have been set as per Table 1 during simulation of the algorithm.

Table 1
Control Parameters for BSO
 Parameter       Value      Parameter           Value       Parameter       Value      Parameter      Value
   No. of           300    Population            100          No. of           5            µ            0
 Generation                   size                           clusters
      Prep          0.2      P1, P2              0.4,            Pgen          0.8            σ            1
                                                 0.5

 In the presented work, the Dolph-Chebyshev 32 elements symmetric linear antenna array has been
taken. The elements of the array are uniformly placed at half wavelength distance from each other.
There are six-element failures conditions have been introduced in the array at 1st, 2nd, 3rd, 5th, 6th, 27th,
28th, 30th, 31st and 32nd locations.




 Figure 3: The modified antenna characteristic patterns of symmetric Dolph-Chebyshev under test linear




 Figure 4: Fitness curve
Table 2
Normalized Excitation amplitude value for ideal, Damaged and modified Radiation characteristics
with 1st, 2nd, 3rd, 5th, 6th, 27th, 28th, 30th, 31st and 32nd element malfunctioned condition(SLL= −
30 dB)
 Element            1              2            3         4         5       6         7         8
  Original        0.4439        0.2433       0.3035 0.3684 0.4367 0.5072 0.5785 0.6490
 Corrected          0              0            0      0.0184       0       0      0.0691 0.0765
 Element             9            10           11        12        13      14        15        16
  Original        0.7170        0.7809       0.8392 0.8904 0.9330 0.9660 0.9886 1.0000
 Corrected        0.1054        0.1279       0.1487 0.1825 0.1975 0.2242 0.2341 0.2434
 Element             17           18           19        20        21      22        23        24
  Original       1.0000         0.9886       0.9660 0.9330 0.8904 0.8392 0.7809 0.7170
 Corrected       0.2434         0.2341       0.2242 0.1975 0.1825 0.1487 0.1279 0.1054
 Element             25           26           27        28        29      30        31        32
  Original       0.6490         0.5785       0.5072 0.4367 0.3684 0.3035 0.2433 0.4439
 Corrected       0.0765         0.0691            0         0    0.0184       0         0         0

   The maximum side lobe level (SLL) of the considered array with malfunctioned conditions has
been distorted and reached up to −20.86 dB level at 81° and 99° from original level of −30 dB. The
proposed BSO has been applied in order to obtain the ideal characteristics of the antenna array and it
has been observed that SLL restored its value up to −29.74 dB level at 34° after corrected measures as
shown in Figure 3. It is further noticed that the first null beamwidth (17°) of the corrected array
pattern is larger than of the original pattern (10°) because there are large number of failed elements
present (31.25%) in the considered case. The first null beamwidth value of the corrected pattern is
expected to resemblance with the ideal characteristics pattern if the number of failed elements is small
<15%).
Figure 4 presents the fitness curve of 32 element antenna array with the 10 elements failed
conditions which pointed that the BSO algorithm converges in 220 generations approximately to
achieve the required objective. The normalized excitation coefficients of 32 elements antenna array
has been noted in Table 2. The malfunctioned conditions of elements of the antenna array have
been introduced by setting the value of 0 at failed location as shown in Table 2.


5. Conclusion
   The radiation characteristics of the antenna array faced serious distortion when certain elements of
antenna array undergo the failed conditions. In this work, an advanced and flexible approach based on
BSO has been suggested to obtain the result of the complex problem of 32 elements uniform antenna
array under 10 failed elements conditions. The proposed method has effectively improved the antenna
array characteristics by re-arrangement of weights of good elements of antenna array. The work can
be further expanded by applying the BSO algorithm to other antenna structures

6. References
[1]     T.J. Peters. “A conjugate gradient based algorithm to minimize the side lobe level of planar arrays with
        element failure.” IEEE Transactions on Antenna and Propagation, 39.10 (1991): 1497-1504.
[2]     M.H. ER and S.K. Hui. “Beamforming in presence of element failure.” Electronics Letters, 27. 3
        (1991): 273-275.
[3]     R.J. Mailloux. “Array failure correction with a digitally beamformed array.” IEEE Transactions on
        Antenna and Propagation, 44.12 (1996): 1542–1550.
[4]    S.H. Zainud-Deen, M.S. Ibrahem,, H.A. Sharshar and S.M.M. Ibrahem. (2004). “Array failure
       correction with orthogonal method.” Proceedings of the Twenty-First National Radio Science
       Conference, Cairo, Egypt, 2004, pp. B7-1-9.
[5]    B.K. Yeo and Y. Lu. “Array failure correction with a genetic algorithm.” IEEE Transactions on
       Antenna and Propagation, 47.5(1999): 823–828.
[6]    J.A. Rodriquez, F. Ares, and E. Moreno. “Genetic algorithm procedure for linear array failure
       correction.” Electronic Letters, 36.3 (2000): 196-198.
[7]    K. Brezinski, M. Guevarra and K. Ferens. “ population based equilibrium in hybrid sa/pso for
       combinatorial optimization: hybrid sa/pso for combinatorial optimization.” International Journal of
       Software Science and Computational Intelligence (IJSSCI), 12.2(2020): 1-13.
[8]    M.V. Lozano and J.A. Rodriquez. “Recalculating linear array antennas to compensate for failed
       elements while maintaining fixed nulls.” IEEE International Symposium on Antenna and Propagation,
       Orlando, FL, USA, 1999, 3, pp. 2048-2051.
[9]    J. Redvik. “Simulated annealing optimization applied to antenna arrays with failed elements.” IEEE
       International Symposium on Antenna and Propagation, Orlando, FL, USA, 1999, 1, pp. 458-461.
[10]   N.S. Grewal, M. Rattan and M.S. Patterh. “A Linear antenna array failure correction using firefly
       algorithm.” Progress In Electromagnetics Research M[Online], 27 (2012):241-254
       http://www.jpier.org/PIERM/pier.php?volume=27
[11]   N.S. Grewal, M. Rattan and M.S. Patterh.“A Linear Antenna Array Failure Correction with Null
       Steering using Firefly Algorithm.” Defence Science Journal, 64.2 (2014): 136-142.
[12]   N.S. Grewal, M. Rattan and M.S. Patterh. “A Linear Antenna Array Failure Correction Using
       Improved Bat Algorithm.” International Journal of RF and Microwave Computer-aided Engineering
       (Wiley) 2017;00:e21119. 27.7(2017).
[13]   N.S. Grewal, M. Rattan and M.S. Patterh. “A Non-Uniform Circular Antenna Array Failure Correction
       Using Firefly Algorithm.” Wireless Personal Communications (springer), 97.1(2017): 845–858
[14]   Y. Shi.(2011), “Brain storm optimization algorithm,” in Advances in Swarm Intelligence.” Lecture
       Notes in Computer Science, Springer, Berlin, Heidelberg, 6728(2011): 303–309
[15]   H. Duan, S. Li, and Y. Shi. “Predator-prey brain storm optimization for dc brushless motor.” IEEE
       Transactions on Magnetics, 49.10(2013): 5336–5340.
[16]   C. Sun, H. Duan and Y. Shi. “Optimal satellite formation reconfiguration based on closed-loop brain
       storm optimization.” IEEE Computational Intelligence Magazine, 8.4(2013): 39–51.

</pre>