Background:
What Is a Smart Antenna System?
In truth, antennas are not smart—antenna systems are smart. Generally co-located with a base station, a smart antenna system combines an antenna array with a digital signal-processing capability to transmit and receive in an adaptive, spatially sensitive manner. In other words, such a system can automatically change the directionality of its radiation patterns in response to its signal environment.
This can dramatically increase the performance characteristics (such as capacity) of a wireless system.
Array definitions.
An array of antenna elements is a
spatially extended collection of N similar radiators or elements, where N is a
countable number bigger than 1, and the term "similar radiators"
means that all the elements have the same polar radiation patterns, orientated
in the same direction in 3-d space. The elements don't have to be spaced on a
regular grid, neither do they have to have the same terminal voltages, but it
is assumed that they are all fed with the same frequency and that one can
define a fixed amplitude and phase angle for the drive voltage of each element.
Element pattern, Array pattern.
The polar radiation pattern of a
single element is called the "element pattern". It is possible for
the array to be built recursively
The array pattern is the polar
radiation pattern which would result if the elements were replaced by isotropic
radiators, having the same amplitude and phase of excitation as the actual
elements, and spaced at points on a grid corresponding to the far field phase centers of the elements.
How to
control radiation pattern (directivity)
If we can find a formula for radiation pattern we can change its
parameters to satisfy desired form.
Calculation of array patterns
The radiated field strength at a
certain point in space, assumed to be in the far field, is calculated by adding
the contributions of each element to the total radiated fields. The field
strengths fall off as 1/r where r is the distance from the isotrope to the
field point. We must take into account any phase angle of the isotrope
excitation, and also the phase delay which is due to the time it takes the
signal to get from the source to the field point. This phase delay is expressed
as 2 Pi radians times (r/lambda) where lambda is the free space wavelength of
the radiation. Contours of equal field strength may be interpreted as an
amplitude polar radiation pattern. Contours of the squared modulus of the field
strength may be interpreted as a power polar radiation pattern.
Here is an example of a power polar radiation pattern for two isotropes
spaced 1/4 wavelength apart along the x axis (horizontally on your screen or
paper) and fed with equal amplitudes and phases
TWO ISOTROPES 1/4 WAVELENGTH APART FED IN PHASE
If we increase the spacing to 1/2 wavelength, but still keep the excitation in phase and equal amplitudes, we see deep nulls developing
Antenna
parameters
Phase (α)
Current amplitude (I)
Angle with major lobe (Φ)
Angle with the normal (Θ)
Wavelength
(ƛ)
Antennas
with a given radiation pattern may be arranged in a pattern
(line, circle, plane, etc.) to
yield a different radiation pattern
Circular array - antenna
elements arranged around a circular
ring.our
application is based on Circular array of antennas
Array Design
Variables
1. General array shape (linear,
circular, planar, etc.).
2. Element spacing.
3. Element excitation amplitude.
4. Element excitation phase.
5.
Patterns of array elements
Pattern multiplication theorem
Array.
Array
Pattern = Array element Pattern * Array Factor (AF)
the
array factor for the circular array is as follows
Using
CFO.
CFO
is used to calculate values that would make the radiation pattern like this
Max(AF) = AF(ɸ1)+Af(ɸ2)+AF(ɸ3)
–AF(ɸ4) – AF(ɸ5) –AF(ɸ6)
ɸ1
, ɸ2 , ɸ3 .. are angels where major lobe occurs (Desired angel).
ɸ4
, ɸ5 , ɸ6 ...are angels where minor lobe is occurs
(Undesired
angel).
In
CFO we can say that
Max
fitness = Af(desired1) + AF(desired2) –AF(Undesired1)
And
that the objective function is
Using
suitable number of probes and time steps. values of Current ( I ) and phase
shift ( alpha ) for each antenna on the array can be calculated that would
satisfy the desired radiation pattern.
Applying CFO:
CFO
Algorithm analysis:
1-to make
initial positions for all probes it will take (by any way) à O (P)
2-to
calculate the mass of any it will take O (M)
3-you have
to calculate the acceleration for all probes like that
So to
compute the acceleration for any for you have to loop for all probes à O (P D)
And to
compute all acceleration for all probes it will take à O (P² D)
4-to compute
the new position for all probes it will take à O (P D)
5-so in
every time step you will take à O (M) + O (P²) + O (P) = O (M+ D P²)
6-then the
total order of the algorithm is à O (T (M+ D P²))
As D is the
number of diminution
Implementing
CFO:
We have to
put the probes in the decision space and let every probe converge to all probes
that have a greater mass than our probe. So we have to put initial
probes on the outer surface of the decision space. So when it converge together
it will defiantly converge to the optimum solution, but if all probes in the
middle of the D.Space and the optimum solution at the top surface then
all probes will not rich this optimum.
How to make
all probes initially at the outer surface of the D.Space:
If we have 2-D
problem we can put them as
And this
will not be a big problem we just make two loops to set those probes.
If we have 3-D
problem:
Then use
three loops ……………..
But what if
we have n-D problem
We attain to
a function that takes the probe number and number of probes and it generate the
whole position of the probe.
private double[]
get_initial(int p, int
Np, victor min, victor
max)
{
double[] v = new double[min.Vars.Length];
int temp;
for (int i = 0; i
< v.Length; i++)
{
temp = (int)(p / Math.Pow(Np, i)) % Np;
v[i] = min.Vars[i] + temp * (max.Vars[i] - min.Vars[i]) / (Np - 1);
}
return v;
}
-in the last two graphs (2-D & 3-D) and that is the maximum number
of the diminutions we can imagine and drawn we found that the number of probes
will be Np = X ^ Nd
Np à number of probes
Nd à number of diminutions
X à is a positive integer has minimum value (2)
In our
problem the diminution will be as 2N as
N is the
number of antennas
Let’s take
the minimum value of X à 2
Then the
number of probes will be (2 ^ 2N) = (4 ^ N)
And the
order of calculating mass is O (N)
Then the
total order will be O (T (M+P²)) à O (T (N+4^2N)) à O (T (8^N))
It’s
unaccepted order
We have to
find another algorithm to get the initial probes
Let’s say we
will put them randomly, and to be more accurate we will put X probes at
every diminution as:
2 probes per
diminution à min, max
3 probes per
diminution à min, mid, max
……
……
And all other
diminutions for those 2, or 3 probes we will put them as a random number
between min and max.
The number
of probes using the new algorithm:
Np = X *
Nd
As Np à number of probes
Nd à number of diminutions
X à positive integer number has a min
value (1)
Then the
order of CFO is:
O (T (M+P²))
à O (T (N + X² * 4N²)) à O (T * X² * N²)
I think it’s
a reasonable order I can live with it.
Next problem
faced us:
-Can the
probes rich the optimum solution if it’s on any corner?
When we put
the probes randomly by default the most of it will be in the middle of the
D.Space. So when they converge together it will not converge to the optimum
solution.
How can we
make them converge to the corners?
If they
converge to the corners then they will diverge from each other, but how?
-we can
reverse the motion of any probe if we multiply it by (-1)
So we can make
(G) be (-G) ; )
So we solve
a problem be making another one, What if the optimum solution in the middle of
the D.Space? à The probes will not converge to the optimum solution in that
case.
So we can use those two ways of motion at the same time, on
the same initial probes, with same number of time steps, and the algorithm will
take the same Time à(order)
There are
3-free variables in the CFO algorithm à G, Alfa, Beta
As so many
test cases on solving the antenna array problem by using many different values
to G, Alfa, Beta we found it make the most converge at those values:
G = 14
Alfa = 6
Beta = 4
Current
rounding up
After many
test cases of current values that satisfies the most accurate values of fitness
was mostly found close to 1 as minimum or 3 as maximum.
Also values of current found to get so
close to 1 or 3.
So rounding up/down values of current
found to be useful when seeking for the best fitness
References:
CFO algorithm :
1 - Progress In Electromagnetics Research, PIER 77, 425–491, 2007
CENTRAL FORCE OPTIMIZATION: A NEW
METAHEURISTIC WITH APPLICATIONS IN APPLIED
ELECTROMAGNETICS - R. A. Formato
kinematic relativity :
1 - http://www.kinematicrelativity.com/
2 - http://en.wikipedia.org/wiki/Kinematics
Array and array antenna :
1 - Antenna Arrays - Hon Tat Hui
2 - http://www.electronics-tutorials.com/antennas/antenna-basics.htm
3 - http://personal.ee.surrey.ac.uk/Personal/D.Jefferies/antarray.html
4 - http://www.radio-electronics.com/info/antennas/dipole/dipole.php
5 - http://en.wikipedia.org/wiki/Phased_array
6 - http://www.analyzemath.com/antenna_tutorials/antenna_arrays.html
7 - Array and Phased Array - Antenna Basics - Hubregt J. Visser
Smart antenna :
1 - http://en.wikipedia.org/wiki/Smart_antenna
Antenna gain and Directivity:
1 - http://www.about-wireless.com/terms/antenna-gain.htm
2 - http://en.wikipedia.org/wiki/Directive_gain
3 - http://en.wikipedia.org/wiki/Directivity
Isotropic radiator and Radiant intensity:
1 - http://en.wikipedia.org/wiki/Isotropic_radiator
2 - http://en.wikipedia.org/wiki/Radiant_intensity
Project Team:
-Ahmed Hassan Khalaf
-Ali Ahmed Ali
-Shrief Hassan
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