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### looking for simple DF (AOA) algorithm

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```Hi,

Can anyone describe or point me to a simple,yet efficient DF (direction
finding) algorithm for a 4 antenna element array (1 pair North-South, 1 pair
East-West). The algo doesn't need to be particularly robust or resistant to
multi-path, just easy to implement in a DSP, and efficient...

Here's how i'm starting...

The different arrival times at the E-W attennae will result in a phase
difference between the 2 antenna signals. The following expression converts
the phase difference into an angular difference.

Theta = ArcSin [(Delta-Phi/f)*(c/2*pi*d)]

I must convert from rectangular (I,Q) to polar (A, Phi) to get Delta-Phi. If
possible, I'd want to minimize rectangular-polar conversion, since its
computationally intensive.

By using the expression above, I'll get two vectors which represent the fact
that the angle of incidence could have occured on either side of the E-W
antenna pair. To resolve the linear ambiguity, i'd have to calculate the
resultant vectors from the N-S pair. If i could convert easily from polar to
rectangular , i could just add the vectors, and the phantom vectors would

Can i find the resultant vector without doing and polar-rectangular
conversion? I'd rather just do one Arcsin at the end to calculate theta
(using a lookup table).

JC

jcsy@shaw.ca

```
 0

```"jcs" <cyrussy@hotmail.com> wrote in message news:<pnNdb.41396\$TM4.1636@pd7tw2no>...
> Hi,
>
> Can anyone describe or point me to a simple,yet efficient DF (direction
> finding) algorithm for a 4 antenna element array (1 pair North-South, 1 pair
> East-West). The algo doesn't need to be particularly robust or resistant to
> multi-path, just easy to implement in a DSP, and efficient...
>
> Here's how i'm starting...
>
> The different arrival times at the E-W attennae will result in a phase
> difference between the 2 antenna signals. The following expression converts
> the phase difference into an angular difference.
>
> Theta = ArcSin [(Delta-Phi/f)*(c/2*pi*d)]
>
> I must convert from rectangular (I,Q) to polar (A, Phi) to get Delta-Phi. If
> possible, I'd want to minimize rectangular-polar conversion, since its
> computationally intensive.
>
> By using the expression above, I'll get two vectors which represent the fact
> that the angle of incidence could have occured on either side of the E-W
> antenna pair. To resolve the linear ambiguity, i'd have to calculate the
> resultant vectors from the N-S pair. If i could convert easily from polar to
> rectangular , i could just add the vectors, and the phantom vectors would
>
> Can i find the resultant vector without doing and polar-rectangular
> conversion? I'd rather just do one Arcsin at the end to calculate theta
> (using a lookup table).

I'm a bit curious about your approach. If I understand correctly, you
use two linear arrays and try to resolve the left-right ambiguities
by combining the two beampatterns? I can see that such an approach
could work for a wave coming from NE (or at 45 degrees from any
axis), but does this work for general angles?

Rune
```
 0

```Look at "Adaptive Antennas" by R. T. Compton, Jr.  It should have what you seek.

Maurice Givens

"jcs" <cyrussy@hotmail.com> wrote in message news:<pnNdb.41396\$TM4.1636@pd7tw2no>...
> Hi,
>
> Can anyone describe or point me to a simple,yet efficient DF (direction
> finding) algorithm for a 4 antenna element array (1 pair North-South, 1 pair
> East-West). The algo doesn't need to be particularly robust or resistant to
> multi-path, just easy to implement in a DSP, and efficient...
>
> Here's how i'm starting...
>
> The different arrival times at the E-W attennae will result in a phase
> difference between the 2 antenna signals. The following expression converts
> the phase difference into an angular difference.
>
> Theta = ArcSin [(Delta-Phi/f)*(c/2*pi*d)]
>
> I must convert from rectangular (I,Q) to polar (A, Phi) to get Delta-Phi. If
> possible, I'd want to minimize rectangular-polar conversion, since its
> computationally intensive.
>
> By using the expression above, I'll get two vectors which represent the fact
> that the angle of incidence could have occured on either side of the E-W
> antenna pair. To resolve the linear ambiguity, i'd have to calculate the
> resultant vectors from the N-S pair. If i could convert easily from polar to
> rectangular , i could just add the vectors, and the phantom vectors would
>
> Can i find the resultant vector without doing and polar-rectangular
> conversion? I'd rather just do one Arcsin at the end to calculate theta
> (using a lookup table).
>
> JC
>
> jcsy@shaw.ca
```
 0

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7/24/2012 12:18:35 AM