How to calculate distance between 2 complex points?

Hi,

After modulating random data with QPSK, I obtained a matrix of complex numbers:

Signal_1 = 1.00 - 1.00i, -1.00 - 1.00i, -1.00 + 1.00i, -1.00 + 1.00i, -1.00 - 1.00i, 1.00 + 1.00i

After adding some noise to this complex matrix, it changed to something like this:

Signal_2 = 0.960 - 0.92i, -0.90 - 1.05i, -1.15 + 1.06i, -0.91 + 1.07i, -1.08 - 1.01i, 1.03 + 0.98i

By using scatterplot we can clearly see that each of the original points from Signal_1 was displaced, resulting in Signal_2.

Is there a way to implement a FOR loop to calculate the distance between the points of the 2 matrices?

I.e. distance(i) = distance between points Signal_1(i) and Signal_2(i), for i=1:length(Signal_1)

The purpose of calculating the distance is to know by how much the points moved due to the noise insertion.

It would be ideal to obtain a new matrix containing the distance of all the points of Signal_2 with respect to the points of Signal_1.

Bear in mind that each of the values of the 2 signals are complex numbers.

Thanks.

[Walter Roberson]

An important question here would be whether "movement" should be measured in Euclidean distance. My instinct is that ideally it should not be -- but it could be that Euclidean is a "good enough" approximation for your purposes.

[Jean-luc]

“The Error Vector Magnitude is a measure of the difference between the reference waveform and the measured waveform. This difference is called the error vector.”

In this scenario my reference waveform is Signal_1 and my measured waveform is Signal_2. I need to measure the Error Vector which is the distance between the points on the scatterplots. Any idea?

I tried the following:

dis_pts(i) = pdist2(Signal_1(i),Signal_2(i),'euclidean')

And I got a return error:

Error using pdist2 (line 224) PDIST2 does not accept complex data for built-in distances.

Answer 1

[Roger Stafford]

The reference to "phase" in your diagram would seem to imply that the 'Q' and 'I' quantities refer to the real and imaginary parts of your signals. If so, the function you need is 'abs' of the vector difference between the signals at each point. This would be the length Of "error vector" in your diagram.

[Jean-luc]

How to calculate the vector difference? coding wise.

[Roger Stafford]

Just ordinary subtraction in matlab:

 Signal_1-Signal_2

I am assuming that Signal_1 and Signal_2 play the roles of "MEASURED SIGNAL" and "IDEAL SIGNAL" in your diagram and that you are trying to find the length of the "Error Vector", and that Q and I are the real and imaginary parts thereof.

Answer 2

[Youssef Khmou]

Jean luc, you can perform the task without using the pdist function, here is version :

 S1=[1.00 - 1.00i, -1.00 - 1.00i,  -1.00 + 1.00i,  -1.00 + 1.00i,  -1.00 - 1.00i,  1.00 + 1.00i];
 S2=[0.960 - 0.92i, -0.90 - 1.05i,  -1.15 + 1.06i,  -0.91 + 1.07i,  -1.08 - 1.01i,  1.03 + 0.98i];
 figure, compass(S1), hold on, compass(S2,'r'),  legend(' original','noisy');

 %  Computing the distance 
 N=length(S1);
 D=0;
 for n=1:N
   D(n)=norm(S2(n))-norm(S1(n));
 end

 %  PHASE  converted to degrees
 Phase=(phase(S2)-phase(S1))*180/pi;