Page 127 - Antennas for Base Stations in Wireless Communications

100 Chapter Three

calculation are varied within a preset range and the element spacing
is assumed to be equal to 0.8l o . After the boundaries for the current
amplitudes and phases are determined, we need to find the boundaries
for the element spacings. By considering the physical sizes of the ele-
ments and neglecting the mutual coupling effect between the elements,
we assume that the lower and upper boundaries for the element spacing
are 0.75l o and 0.85l o , respectively. Next we need to define the objective
functions in the genetic algorithm.
Objective Functions There are several criteria for the radiation pattern
to be synthesized. The main lobe has to be synthesized with the absolute
maximum value along a specified direction. Also, the power levels of the
2
nulls have to be specified to form a nearly Cosec q pattern. Moreover,
the peak gain of the main beam has to be maximized. Other than the
radiation pattern, a requirement is also placed on the input return loss
of each array element. The objective functions of the genetic algorithm
are listed here:
■ Minimum gain > 15 dBi (from 1.71 to 2.17 GHz)
■ Upper sidelobes < −25 dB (from 1.71 to 2.17 GHz)
■ S < −10 dB, where ii = 11, 22…88 (from 1.71 to 2.17 GHz)
ii
■ Peak angle of main lobe = 0° (from 1.71 to 2.17 GHz)
2
■ Cosec q pattern (from 1.71 to 2.17 GHz)
1. Lower first null and lower first lobe ∼ −10 dB
2. Lower second null and lower second lobe ∼ −15 dB
3. Lower third null and lower third lobe ∼ −20 dB
4. Lower fourth null and lower fourth lobe ∼ −25 dB
■ The ripples between a null and the nearest lobe are limited to 1 dB
difference

Practically realizing a cosecant radiation pattern is a difficult task.
By using GA, eight objective functions are set to synthesize the cosecant
patterns for the eight-element array case. The power levels of the lower
first null, lower first lobe, lower second null, lower second lobe, lower
third null, lower third lobe, lower fourth null, and lower fourth lobe are
included and located in specified angles to form the cosecant pattern.
Boundaries of the Variables Different geometric parameters of the array
elements, including the heights of the patches (h p ), heights of the
L-probes (h lp ), lengths of the L-probes (L p ), element spacings of the patches
(E 1 , E 2, E 3, E 4, E 5, E 6, E 7 ), relative excitation phases of the L-probes (a° n ),
and relative excitation amplitudes of the L-probes (|a n |) are adjusted
in the optimization process, where n = 1, 2, …, 8. Impedance matching