I have to fix the amplitude of measured IQ receiver data. According to my information about the data, I can estimate that one signal needs to be corrected to the other in amplitude. The phase offset/imbalance can be ignored in this case. I would like to implement this in MATLAB. At the moment my I/Q signal looks like this:
I would like to correct it, that is shows a circle (would be the ideal result). But until now, I found no direct way to do that. I have no possibility to train or measure the amplitude imbalance from the I/Q receiver direclty. I have only the data. What have I to do, to normalize the Q component that the chart shows a circle?
I have already tried to calculate the amplitude offset: o=sqrt(Q^2/(1-I^2))
, but this doesn't work. Both signals have a small DC offset (really small, about $10^{-4}$ in relation to values between $0$ and $1$), but this is not relevant.