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Home > Archive > Electrical Engineering > April 2006 > Is there a definition of "Direction of Arrival"?
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Is there a definition of "Direction of Arrival"?
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| Brenneman 2006-04-25, 5:21 pm |
| Hi,
This is a beamforming problem, but since the people who do this work
are typically EEs, I thought I'd give this ng a try.
I am a mathematician working on some interferometric problems, and I
find myself having trouble getting an actual definition of "direction
of arrival" (or DOA).
Some older analyses using linear antenna arrays seem to use the
inclination angle, theta, (i.e. the angle with the +z-axis or
"azimuthal angle") for the DOA, but for a source that is not coplanar
with the array, there is a factor of Cos(phi) in the phase portion of
the steering vector (where phi is the angle with the +x-axis or polar
angle).
Some analyses seem to define a generic phase angle from the inner
product of the source orientation with the array position vector. This
definition is consistent for a linear array, but it is not for a planar
array.
Is there a rigorous definition of what is meant for "direction of
arrival" (or angle of arrival) that holds for a general array and
source? You can respond directly to this post or via my e-mail address.
TIA,
Matt
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| Salmon Egg 2006-04-25, 10:21 pm |
| On 4/25/06 12:56 PM, in article
1145994988.527551.308610@i40g2000cwc.googlegroups.com, "Brenneman"
<brennemt@muohio.edu> wrote:
> Hi,
>
> This is a beamforming problem, but since the people who do this work
> are typically EEs, I thought I'd give this ng a try.
> I am a mathematician working on some interferometric problems, and I
> find myself having trouble getting an actual definition of "direction
> of arrival" (or DOA).
>
> Some older analyses using linear antenna arrays seem to use the
> inclination angle, theta, (i.e. the angle with the +z-axis or
> "azimuthal angle") for the DOA, but for a source that is not coplanar
> with the array, there is a factor of Cos(phi) in the phase portion of
> the steering vector (where phi is the angle with the +x-axis or polar
> angle).
>
> Some analyses seem to define a generic phase angle from the inner
> product of the source orientation with the array position vector. This
> definition is consistent for a linear array, but it is not for a planar
> array.
>
> Is there a rigorous definition of what is meant for "direction of
> arrival" (or angle of arrival) that holds for a general array and
> source? You can respond directly to this post or via my e-mail address.
>
> TIA,
>
> Matt
>
Although I have not worked on antennas for a long long time the term
"direction of arrival" seems virtually useless. Probably, the information of
interest is in what is called the "antenna pattern" or some term like that.
This pattern is expresed as a function of angle (phi and theta in spherical
coordinates) and indicates the relative strength of a signal received from a
point source at infinity in that direction. Because of reciprocity, it also
indicates the transmission pattern.
Bill
-- Ferme le Bush
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