Normalizing Path Loss Model to Test Data

Looking for advice on methods of normalizing data. I have collected network level data and calculated the signal loss ('LOSS' in code below, measured in dB). I would like to compare this data to the free space path loss propagation model, as calculated in the code. To do this, I have tried to normalise the data between 0 and 1, however I am not getting the results I expected when I do this.

% Distance and path loss from test data
DIST = data.DIST;
LOSS = data.LOSS;

% distance vector
d = DIST;
% frequency
f = 1800e6;

% Calculate free space path loss model
FreeSpaceLoss = 20*log10(((4*pi*d*f)/3e8).^2);

% Normalise model
freeSpaceNorm = abs(FreeSpaceLoss)./max(abs(FreeSpaceLoss));

% Normalise test data
dataNorm = abs(LOSS)./max(abs(LOSS));

% Plotting data over normalised models 
figure, hold on
plot(DIST, freeSpaceNorm, 'LineWidth',1.5)
plot(DIST, dataNorm, '.', 'MarkerSize', 7)
xlabel('Distance (m)')
ylabel('Loss (dB)')
title('PL Models vs Data')
legend('fspl', 'test data')
hold off;

I get the resulting plot, but the path loss model does not start at zero. I may be missing something small, or misunderstanding why this is happening - just looking for any suggestions on the best way to compare the two datasets.

Thanks in Advance.

[Mathieu NOE]

hello

first remark - I wonder that a dB attenuation plot is scaled between 0 and 1 - I would think this is more a linear than a dB scaling. ?

with the equation you provide , I don't understand how you can get a dB loss of 1 dB at distance = 2000 (m ?) for f = 1800e6

% distance vector
d = 2000;
% frequency
f = 1800e6;
% Calculate free space path loss model
FreeSpaceLoss = 20*log10(((4*pi*d*f)/3e8).^2);

% gives : 
FreeSpaceLoss = 207.1356

second , if your distance data start with / contains zero , then the log of that will be -Inf and matlab will plot a blank at this value.

[Robyn Seery]

Okay I see that now, thank you.

So would you recommend I plot bothe data sets in mWs to compare their values? I need them to have the same starting points to conduct corellation analysis, hence my attempt at normalizing them!

Open to all best approaches to achieve a good method of comparison.

[Mathieu NOE]

hello

whatever the units or the scaling , it has to be coherent between measurements and theory...

now remember to remove zero valued data if you intend to use log scaling