# What determines the maximum/minimum values in I/Q constellation diagram?

I need to do some data analysis on I/Q samples and was trying to know what are the parameters that determine the maximum/minimum values of these samples. In other words, what determines the maximum/minimum values set on the constellation diagram axes?

Does the type of the modulation scheme play a role? i.e., 64-QAM is expected to have constellation axes larger than that in 4-QAM ?

Does the energy in the symbols that these I/Q samples are mapping also play a role? i.e., a stream of symbols that have bits of voltage levels +5/-5 are expected to generate I/Q samples larger in value that a stream of symbols with bits of voltage levels +1/-1 ?

Does the power level that the transmitter is going to send the modulated signal with also play a role?

All the internet sources that I looked at always discuss how I/Q QAM modulation works and none of it provides quantitative explanations that could help me. The only image that I found having numbers on the axes is shown below:

It shows that for 64-QAM the max value of I/Q is 7 and for 4-QAM is 1. Is this just an illustration or how it actually works? Could I infer that for n-QAM, the max I/Q value is log2(n)+1 ?

In addition, I looked at some data-sets of I/Q samples and found that all samples lie in the range of -1 to +1 despite the fact that different modulation schemes were used. Is there a kind of normalization that's generally used that I am not aware of? If so, is there a method to convert them to their original values?

Also, are there related equations that could show how the max/min I/Q samples values are set?

• These numbers are completely arbitrary. It is the level of noise at any given point in your system, and then the SNR that you desire to have at that point that sets the magnitude. The lower the SNR the higher the error rate but the actual quantified values depend on so many other items in your overall system design. As a quick view, consider the background noise as a round cloud around each of those dots; then consider what happens as you scale the diagrams shown while keeping the clouds the same size. Notice how you need a much bigger scaling for 64 QAM vs 4 QAM to keep them separated! – Dan Boschen May 11 at 18:59