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Hello,
I'm developing a radar project but I have a problem. The project consists
in the position (elevation and azimuth) and velocity estimation of a
target using a 2D array antenna. The DOA of the signal reflected by the
target has to be estimated using beamforming. I'm reading something about
DOA problem but any model is based on the assumption that the signal
trasmitted is a narrowband signal, a complex sinusoide and in my case I
have a chirp. What model do I have to use in this case? I have to
implement the beamformer in Matlab and I should obtain something like a 2D
FFT but I don't know how to go on. If you have any suggestion, material or
link please help me.
Thank you so much.
   

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If the signal bandwidth is less than 10% of the carrier, it is typically 
considered to be narrowband.  The advantage of modeling your signal as 
narrowband is simplicity since a lot of things that would require use of 
functions of frequency to describe can be considered to be constants..

Have you looked at matched filtering of the radar return signal?  Most systems 
I'm familiar with use the output of a matched filter and look at the energy in 
a range-azimuth-elevation bin compared to the noise power in that bin.

Fortunately for you, you have chosen a waveform that is (relatively) doppler 
insensitive so you don't have to build a bank of matched filters that are 
adjusted for different values of radial target velocity.

In article <u...@giganews.com>, "Fox" 
<a...@libero.it> wrote:
>Hello,
>I'm developing a radar project but I have a problem. The project consists
>in the position (elevation and azimuth) and velocity estimation of a
>target using a 2D array antenna. The DOA of the signal reflected by the
>target has to be estimated using beamforming. I'm reading something about
>DOA problem but any model is based on the assumption that the signal
>trasmitted is a narrowband signal, a complex sinusoide and in my case I
>have a chirp. What model do I have to use in this case? I have to
>implement the beamformer in Matlab and I should obtain something like a 2D
>FFT but I don't know how to go on. If you have any suggestion, material or
>link please help me.
>Thank you so much.
>   
>
>

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Thank you for your reply. Just like you suggested me I think I can
approximate my signal as narrowband and use standard method for DOA
estimation. The problem now is that I have a bidimensional array of
sensors let's say MxM. Every sensor gets N samples so we have a MxMxN
matrix of data.  For example in the classical (linear)beamformer I have to
estimate f(theta)=a(theta)'Ra(theta) where a(theta) is a Mx1 vector of
propagation and R is the matrix correlation of the received signal x. x is
a MxN vector of data and R=xx' is MxM. The DOA is the thetha that maximizes
f(theta). In the bidimensional case the problem should be maximize
f(theta,phi)=A(theta,phi)'RA(theta,phi) but I don't know how to compute R
because the acquired data is a MxNxM matrix. 
Thanks in advance.
 

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"Fox" <a...@libero.it> wrote in message 
news:b...@giganews.com...
> Thank you for your reply. Just like you suggested me I think I can
> approximate my signal as narrowband and use standard method for DOA
> estimation. The problem now is that I have a bidimensional array of
> sensors let's say MxM. Every sensor gets N samples so we have a MxMxN
> matrix of data.  For example in the classical (linear)beamformer I have to
> estimate f(theta)=a(theta)'Ra(theta) where a(theta) is a Mx1 vector of
> propagation and R is the matrix correlation of the received signal x. x is
> a MxN vector of data and R=xx' is MxM. The DOA is the thetha that 
> maximizes
> f(theta). In the bidimensional case the problem should be maximize
> f(theta,phi)=A(theta,phi)'RA(theta,phi) but I don't know how to compute R
> because the acquired data is a MxNxM matrix.
> Thanks in advance.
>
>

How many wavelengths in M?

One approach that may work would be to do something like this:

For azimuth:

1) Form a beam (Left channel) with only some of the elements in the array - 
with the center of the element group left of center.

2) Form a beam (Right channel) with only some of the elements in the array - 
with the center of the element group right of center.

Make the centers of the two array groups so they are separated by a fraction 
of a wavelength.  You can ponder just how much... 1/4 or 1/2  The two array 
groups can (perhaps must) overlap to do this.

Measure the signal angle difference between the Right and Left channels. 
You can clip, XOR and average - that's one way to measure the angle.
Perhaps detect the presence of the signal by looking at the variance of the 
angle measure.

Fred

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John Herman wrote:

> If the signal bandwidth is less than 10% of the carrier, it is typically 
> considered to be narrowband.  The advantage of modeling your signal as 
> narrowband is simplicity since a lot of things that would require use of 
> functions of frequency to describe can be considered to be constants..

Television is considered broadband, yet except for channel 2 the 
bandwidth (about 6MHz) is less than 10% of the carrier frequency
(about 55MHz for channel 2).

Maybe, though, it is that the bandwidth is more than 10% of the IF
frequency, which is where most of the filtering is done, anyway.

Even more cable modems, which are called broadband, might be 6MHz
out of 700MHz, less than 1%.

-- glen

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