Reflection Coefficients from FMCW Radar Homodyned Signal

Hello, All--

I have an FMCW radar dataset that consists of reflections from a layered 
ice medium.  Let s[t] be the original frequency-swept signal that has 
been sent out from the receiving antenna, and s'[t] be the signal that 
has been received.  Signals s[t] and s'[t] are homodyned by 
multiplication in the time domain.  Let s_h[t] be the homodyned signal 
in the time domain.  I then use the Zoom-FFT (Chirp-Z Transform) to take 
the homodyned signal into the frequency domain, thereby obtaining s_h
[f].  I believe that each of the "peaks" in the homodyned frequency-
domain signal s_h[f] corresponds to a layer (reflector) in the ice.  The 
beat frequency is related to the distance to each of the reflectors.

Is there a way to determine the reflection coefficients of each of the 
layers from the homodyned signal s_h[f]?  I am thinking of using a 
layer-stripping approach, but I am uncertain how to scale the amplitudes 
of the peaks in the homodyned signal s_h[f].  Here is a Matlab snippet 
of my code:

%calculate the chirp-z transform
z = czt(multiply,m,w,a);
N = length(z);
%note that we are calculating the power here
%I suspect that the power is related to the
%reflection coefficients
Pyy = z.* conj(z)/N;

Can anyone shed some light on how to calculate the reflection 
coefficients of a layered medium from the homodyned signal s_h[f]?

Nicholas  
 

On 26 Apr, 07:20, Nicholas Kinar <n.ki...@usask.ca> wrote:
> Hello, All--
>
> I have an FMCW radar dataset that consists of reflections from a layered
> ice medium.  Let s[t] be the original frequency-swept signal that has
> been sent out from the receiving antenna, and s'[t] be the signal that
> has been received.  Signals s[t] and s'[t] are homodyned by
> multiplication in the time domain.  Let s_h[t] be the homodyned signal
> in the time domain.  I then use the Zoom-FFT (Chirp-Z Transform) to take
> the homodyned signal into the frequency domain, thereby obtaining s_h
> [f].  I believe that each of the "peaks" in the homodyned frequency-
> domain signal s_h[f] corresponds to a layer (reflector) in the ice.  The
> beat frequency is related to the distance to each of the reflectors.

The application is well-known from seismology. The signalling scheme
is not one I am familiar with. Pulsed signals are more common in
seismics applications.

As for the recieved signals, be aware of internal reflections in
layers.

> Is there a way to determine the reflection coefficients of each of the
> layers from the homodyned signal s_h[f]?  I am thinking of using a
> layer-stripping approach, but I am uncertain how to scale the amplitudes
> of the peaks in the homodyned signal s_h[f].

It depends on how precise you want to know the reflection
coefficients.
If you want very precise numbers, you need to separate true
reflections
from multiples, transmission losses, scattering, and a various number
of other effects. Not very easy in practice.

Rune  

> It depends on how precise you want to know the reflection
> coefficients.
> If you want very precise numbers, you need to separate true
> reflections
> from multiples, transmission losses, scattering, and a various number
> of other effects. Not very easy in practice.
> 
> Rune  
> 


Thanks, Rune.  I will have to look into the literature for this.  The 
FMCW radar signalling scheme is more widely used in hydrogeophysics, 
where the interest is in resolving thin layers.  FMCW radar seems to 
excel in this because the minimum distance that can be resolved between 
successive reflectors is strongly related to the bandwidth of the 
frequency sweep.

Nicholas