# Amplitude distribution of Rician faded complex signal

I have question regarding Rician fading simulation. I am trying to develop Rician fading channel simulator in LabVIEW, but I ran into some problems. I have complex sinusoid as my line-of-signs signal. Then I generated white gaussian noise samples for I and Q components which represent one scatered wave. I added this scattered wave to my LoS sinusoid. According to this I should get a faded signal with folowing amplitude distribution at different signal amplitudes:

## When I calculate amplitude and its distribution with histogram I get following result:

## I am using the same amplitude values and sigma value. There is significant difference in these results and my questions are:

1. What could be the problem here?
2. If I make multiple scatered waves, will it make difference?
3. Do I need to take into account Rician factor and somehow scale power of generated scatered waves?
• Are you sure your curves sum to 1? If they don't, then they are not PDFs. For example, the green curve looks much smaller in area than the pink one. Try scaling them all so they are all the same area / integral / summation. – Peter K. Mar 18 '15 at 11:53
• Ok, I will check your suggested solution and get back when I have something. – Rob Mar 18 '15 at 15:16
• Do I need to integrate these curves and then divide by sum of all elements? If so, I tried that and area under the curves is proportional the same. – Rob Mar 19 '15 at 8:26
• They should be precisely the same, if you want to compare them on the same graph. If you have the data in same-sized vectors, then Excel's or Matlab's sum should give the same value for each one, and the sum should be 1 for each of them. Otherwise the curves are not PDFs. Looking at the two plots, it's clear that the scales on your generated plot are not the same, so I don't think your data is scaled to sum to 1. Once you do that, let's see what the data looks like then. – Peter K. Mar 19 '15 at 11:30
• It works now! I tried different method for calculating histogram and now the data are scaled to sum to 1. Now all curves match. Thank you very much for help. – Rob Mar 19 '15 at 14:15