Communications: directive radio wave systems and devices (e.g. – Directive – Including antenna pattern plotting
Reexamination Certificate
2002-12-02
2004-08-31
Buczinski, Stephen C. (Department: 3662)
Communications: directive radio wave systems and devices (e.g.,
Directive
Including antenna pattern plotting
C342S368000, C342S372000
Reexamination Certificate
active
06784835
ABSTRACT:
DETAILED DESCRIPTION OF THE INVENTION
The present invention relates to an array antenna, particularly relates to an array antenna capable of forming a beampattern with an adjustable beamwidth and low sidelobes.
BACKGROUND ART
Conventional Dolph-Tchebysheff arrays were proposed by Dolph in 1946 [1] and are designed by mapping the Tchebysheff polynomial into the array's space factor. Dolph has proven that for a desired sidelobe level, the Tchebysheff polynomial of order L−1 can be mapped into the spatial factor of a uniform linear array (ULA)—an array of a plurality of antenna elements having a certain inter-element space—of L elements resulting in a pattern with the sidelobe level as desired and a mainlobe with the minimum possible width. Originally, the design of Dolph-Tchebysheff current distributions was restricted to linear arrays and was applicable to broadside steering only. In fact, little has changed since the classical Dolph-Tchebysheff method came about. For instance, some advances on how to compute the Dolph-Tchebysheff current distribution [1] itself were made by Stegen [3], Davidson [4] and Jazi [5]. More recently, Jazi proposed [6] to use a Tchebysheff polynomial elevated to the n-th so to elevate the order of nulls in the pattern and reduce the number of sidelobes, yielding patterns with the same prescribed sidelobe level, but with a higher directivity, at the expense of slightly broadening the mainlobe.
Finally, the application of Tchebysheff current distributions to a uniform circular array (UCA) was verified [2], making use of a technique that allows the transformation of a UCA into a virtual ULA, long ago presented in [7]. Consequently, a 360° spatial span can be scanned with a nearly perfectly invariant beampattern by electronically rotating of a Dolph-Tchebysheff beampattern.
Problem to be Solved by the Invention
The drawback of this approach is that the mainlobe's beamwidth of the UCA is larger than that of a ULA with the same number of elements and the same inter-element spacing, because the later has a larger aperture than the former. In fact, it is easy to verify from equations (1) and (2) below, which give respectively the broadside aperture of a ULA and the maximum aperture of a UCA with L elements and inter-element spacing &Dgr;e, that for large arrays the ratio, A
ULA
/A
ULC
=&pgr;, independently of &Dgr;e.
Equation 1
A
ULA
(
L,&Dgr;e
)=(
L−
1)&Dgr;e (1)
Equation
2
A
UCA
(
L
,
Δ
e
)
=
Δ
e
2
sin
(
π
L
)
(
1
-
cos
(
2
π
L
⌊
L
2
⌋
)
)
(
2
)
Therefore, in applications such as direction of arrival (DOA) estimation in an intelligent transportation system (ITS) where it is desired to perform a spatial scanning only over a limited angular span with a fixed beamwidth, rotation-invariant, equiripple low sidelobe pattern, a ULA would provides the narrowest beam for the same desired SideLobe Ratio (SLR) at broadside. On the other hand, in this case, the mainlobe's width gets larger as the array is steered to angles closer to end-fire, so that the rotation invariance is lost. Thus, the designer faces the dilemma of either sacrificing too much on the beamwidth by choosing a Dolph-Tchebysheff UCA beampattern or too much on the rotation invariance, by choosing a Dolph-Tchebysheff ULA beampattern.
Yet from another point of view, even when the spatial scanning is desired over the whole 360° spatial span, unlike radar applications where the beamwidth of the rotation-invariant array pattern must be as narrow as possible, in communications, there are many applications such as spatial equalization and beam space-time coding, where it is desirable that the beamwidth of the rotation-invariant pattern be adjustable. Therefore, although the contribution in [2] really adds to the flexibility of the design of low sidelobe arrays in terms of its rotation invariance, due to the use of the classical Dolph-Tchebysheff method, it does not deliver the necessary complete flexibility desired.
In order to strengthen the points made above, a brief review of the existing techniques mentioned will be made. We start with the Tchebysheff polynomial used in the classic Dolph design that can be written as below [8].
Equation
3
T
(
N
,
x
)
=
{
cos
(
N
arccos
(
x
)
)
if
&LeftBracketingBar;
x
&RightBracketingBar;
≤
1
cosh
(
N
arccos
h
(
x
)
)
if
&LeftBracketingBar;
x
&RightBracketingBar;
≥
1
(
3
)
Given a prescribed sidelobe ratio in dB (SLR
dB
), the voltage sidelobe ratio (SLR
V
) can be computed according to the following equation:
Equation
4
SLRv
=
10
-
SLR
dB
20
.
(
4
)
In order to design a sidelobe pattern with the given SLRv, first the value of x that makes the |T(N,x)| equal to SLRv is computed. Such a value is given by the following equation:
Equation
5
x
0
=
cos
(
arc
cos
h
(
SLRv
)
N
)
(
5
)
Note that N=L−1, where L is the element number. Since the Tchebysheff polynomial has only real coefficients and all of its roots lie in the interval x E[−l, l], |T(N,x)| is monotonically increasing for |x|>l. Therefore:
Equation 6
|
T
(
N,y
)|>|
T
(
N,z
)|>1
∀y>z>
1 (6)
Within the interval x E[−l, l], however, the polynomial has its amplitude limited to 1, as can be seen in FIG.
1
. Dolph visualized that, if a ULA with L elements and inter-element spacing &Dgr;e is used, the excitation of the n-th antenna element is calculated by:
Equation
7
A
n
=
∑
m
=
1
L
T
(
L
-
1
,
x
0
cos
(
π
m
L
)
)
ⅇ
-
j
(
2
n
-
L
-
1
)
π
m
L
(
7
)
where n=1, 2, . . . , L. If the phases of the signals at all elements are driven so to steer the mainlobe's peak towards an angle &thgr;
S
, the resulting beampattern will exhibit a space factor exactly given by the equation below (FIG.
2
).
Equation 8
|
T
(
L−
1
,x
0
cos(&pgr;&Dgr;
e
(cos(&thgr;)−cos(&thgr;
s
))))| (8)
While the amplitude limitation of the Tchebysheff polynomial is responsible for the equiripple sidelobes, the monotonic behavior for |x|>1 is responsible for its mainlobe's width inflexibility.
The beamwidth of a pattern steered to &thgr;
S
, can be computed once the criterion that defines the limits of the mainlobe is chosen. In the case of equiripple low sidelobe patterns, a reasonable choice is the point where the mainlobe crosses the sidelobe upper bound, i.e., the sidelobe level beamwidth (&Dgr;&thgr;
SL
) is defined in terms of the distances between the steering angle (&thgr;
S
) and the angles to the right (&thgr;
R
) and to the left (&thgr;
L
) of the mainlobe's peak where the gain equals the sidelobe level. If a ULA is used, steering towards any direction rather than broadside causes the mainlobe to enlarge, especially at angles close to the end-fire. Therefore there is a limiting angle after which the beamwidth will enlarge enough to have part of it falling outside the visible region. Making use of the symmetry of the array, this limit can be defined in terms of a minimum steering angle, for which &thgr;
L
vanishes. Thus:
Equation
9
θ
s
min
′
=
arccos
(
1
-
1
π
Δ
e
arccos
(
1
x
peak
)
)
.
(
9
)
Equation 10
&thgr;′
s
=arcsin
(sin(&thgr;
s
)) (10)
In the case of the Dolph-Tchebysheff, in the equation above, as well as in those to follow, x
peak
, ass
Giuseppe Abreu
Kohno Ryuji
Buczinski Stephen C.
Frommer William S.
Frommer & Lawrence & Haug LLP
Smid Dennis M.
Sony Corporation
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