# 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.