MATLAB: Real-valued signal constellation has hidden imaginary part

mxiscomplexsignal constellation

Hi guys!

I found something which isn't so nice in Matlab. When you create a demodulator object with

h = modem.pammod('M',2,'InputType', 'Bit','SymbolOrder','Gray');

the signal constellation should be real-valued. If you look at h.constellation you see no imaginary part, but isreal(h.constellation) gives back a zero, which means the constellation points do have a imaginary part. For me it was a little bit annoying, because I cannot use mxIsComplex to determine whether a signal constellation is complex or real-valued. Do you have any clever suggestions for a workaround.

best regards, Bernhard

Best Answer

Wow, thanks, Walter! Why does this work?

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MATLAB: How to optimize real-valued functions of complex variables within the Optimization Toolbox

A function of a complex variable "z" is simply a function of two variables; the real part "Re(z)" and imaginary part "Im(z)". Therefore, a function of a complex variable "z" should be a function of two variables "x1" and "x2" (i.e., "z = x1 + i*x2"). The input argument to the objective function will be the vector:

 X =   [x1]
       [x2]

Consider the example:

 f(z) = |z - (1+i)|^2 + |z - (2-3i)|^2

First, we create the following function:

function f = objfun(X)
z = X(1, :) + i*X(2, :); % Create complex value from real and imaginary parts
f = abs(z - (1 + i)).^2 + abs(z - (2 - 3i)).^2; % Evaluate complex function

Then, using the initial guess "z = 1 + 2i", the function can be optimized via the following command:

[X f] = fminunc(@objfun, [1; 2]); % Optimize function
z = X(1) + i*X(2) % Create optimal complex value

which produces the optimal value:

 z =
   -0.5000 + 2.0000i

Note that a warning message will be returned that FMINUNC is switching from the default algorithm.

Best Answer

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