International Core Journal of Engineering 2020-26 | Page 212

where
r i denotes the vector coordinate of the antenna i,
N randomly placed elements
Calculating initial array objective
function value: k 0
u ij and v ij denote the plane coordinate value of antennas
respectively, E(r 1 , r 2, r 3,… r N ) denotes the set of position
vectors of N antenna elements.
The problem of position selection of the antenna element
is converted to the problem that optimizes the vector set. The
relation between the r i and the angle position vector T i can
be expressed as:
r i
( x i , y i ) ( real ( R ˜ e j ˜ T i ), imag ( R ˜ e j ˜ T i ))
Setting annealing parameters:
Initial temperature, T
Rate of annealing, a
The low temperature, e
(2)
Perturb an element randomly
Calculating the objective
function value k of the new array
where R denotes the radius of the layout region of UCA .
Huge computational efforts are inevitable for the approach
since the problem size grows rapidly as the element number
increasing and the baseline distribution in the area are
intermittent. In order to improve the computing speed and
solve local discontinuity problems, a novel modified
objective function is proposed as:
1
Receive new array,
e ( k  k 0 )/ T ˚ x
<
max E ( r 1 , r 2 ,..., r N )
N
¦ min r  r
i
j
Receiving the new array and
updating k 0
(3)
i , j 1
The minimum distance of adjacent elements is taken as
objective function. According to the goal of baseline
uniformity, the objective function in (3) has advantages in
meeting the minimum element spacing constraint and
forming a uniform UV sampling coverage.
Reducing the temperature:
T = T / (1  T u a )
B. Improved Simulated Annealing Algorithm(SA)
In this paper, optimized simulated annealing algorithm
(SA) has been applied to get the novel objective functions.
The improved SA algorithm takes the modified objective
function E which has been defined in equation (3) as the
optimized output, and realizes it through the algorithm
against the disturbance of variable r i of the position of the
element. Since there is a contradiction between the optimal
solution and the solution time cost in SA algorithm.
Optimization of the SA algorithm mainly through these ways.
Improving the initial temperature THOT, which can avoid
falling into the situation of local optimal solution. Increasing
the temperature iteration scale M, which can effectively
obtain the optimal solution or approximate optimal solution.
Increasing annealing factor e, where nonlinear fast annealing
factor is used. Since the convergent of SA algorithm is in an
exponential form, the optimal solution of randomness has a
condition limitation compared with traditional deterministic
optimization methods. The expression of fast annealing is as
follows:
T ( i ) THOT /( 1  DTEMP ˜ M )
End annealing,
T ˘ e
<
Outputting k 0 and
element position
Fig. 1. Algorithm flowchart
C. Implementation of the Proposed method
The optimization simulation process of the proposed
method is given as follows.
1) Creating the initial population. In the layout
optimization design of UCA, it is necessary to ensure that the
constraint conditions of the optimization problem are
satisfied. Therefore, when the array element number is 21,
the initial population of all zero in 1 row and 21 columns
c=[0,0,…,0] is generated first. Here, candidate position
accuracy is 0.1°, and in all the circumference of a circle is
defined on the one candidate position initial population,
P [ 1 , 1 ,... 1 ] T . The candidate position number M is 180-(-
180)/0.1= 36000.
(4)
where THOT denotes the initial annealing temperature, M
denotes the iteration scale, DTEMP is the cooling ratio which
is used to improve the annealing process.
2) Calculating the objective function value under the
constraint condition, and take individual N from the
candidate population P i (i = 1,2, … , N) as the number of
optimized array elements.
Process of the proposed method has been shown in Fig. 1.
3) Setting the annealing scheme for annealing operation.
According to the definition, the larger the objective function
value is, the corresponding individual is the desired
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