Why does DPSK constellation shrink when noise is added? I am generating a DQPSK waveform at complex base band with constellation points on the unit circle and when I add AWG noise the constellation shrinks.  The noisy constellation "blob" migrate inside the unit circle.  My question is why is this happening and is it supposed to happen or am I missing something?

My method of adding noise is:

Xnoise = X + sigma/2 * (randn(N) + 1j*randn(N))


where sigma is the overall standard deviation for the noise.  It's being divided by 2 since I'm using two separate randns for the real and imag parts and the two Gaussians added together give me the correct variance.
It looks like your circle got bigger. The constellation is fine.