separate the fast fading and the shadowing

I have V2V narrowband measurments at 5.9GHz registred in a matrix of 190x5000. the figure represents a trace from the measurments. I have used a FIR filter to separate the shadowing component and fast fading . In order to ensure that the separation is done well, the histogram of the shadowing component should fit to Normal distribution while the fast fading histogram should have an asymetrical distribution. Well, The result I get is diffrent (the shadowing PDF is asymetric and the fast fading is normal distributed), what could be wrong ?I have tried to change the size of the filter but it didn't work

Answer 1

[possibility]

Regardless of your figure, let me clarify the following:

- Shadowing in power unit is commonly modeled as a lognormal distribution,

- Shadowing in dB is modeled as NORMAL distribution.

I am not sure about what you mean by "fast fading distribution". If you're looking for small-scale fading effects, that is modeled as Rician or Rayleigh distributions depending on the existence of line-of-sight (LOS) between transmitter and receiver.

A low pass FIR filter would give an output of the signal which includes only large-scale effects, i.e. shadow fading. That'd be theoretically log-normally distributed. When you take 10log10() of that output, you'd get a normally distributed signal.

Hope this helps.

[yusra Ch]

Yes, that's what I mean. I have used a filter to obain the large scale fading (dB). when I represents it's histogram as you said it should be modeled as normal distribution, but I get an asymetrical histogram! later on I substract the large scale fading from the recieved power in order to get the small scale fading. So, In the perfect separation of the large and small scale fadings, the large one should be modeled with Noraml distribution and the small one should have an asymetrical distribution (Rician, rayleigh, etc...).

Answer 2

[possibility]

Try converting your data into power units first

data_in_power=10.^(yourdata./10);

And then apply FIR filter onto that data.

X=yourFIRfilter(data_in_power)

If your FIR filter is a low-pass filter, X should be log-normally distributed. Then you can safely convert it back to dB to see the normal distribution.

I believe the problem is that you weighting the data most likely by multiplying it. Signal processing operations (such as filters, mixers, etc.) are implemented in power domain. More precisely,

10log10(powerinWatt*filtercoefficients) is not equal to (filtercoefficients)*10log10(powerinWatt)

[yusra Ch]

As I have mentioned before, I have the power in dBm units and I represent the histogram in dBm units too. do you refer that I should represent the histogram in lineal units?

[yusra Ch]

One question, How can I verify that my recieved power, large scale and small scale fadings are not noise.