A complex correlator is better than a simple correlator because the two channels are independent. Let Z represent the complex sum of visibility and noise,
The RMS noise in both real and imaginary parts of Z is
References
D'Addario, L. R. "Cross Correlators." Ch. 4 in Synthesis Imaging in Radio Astronomy: Third NRAO Summer School, 1988 (Ed. R. A. Perley, F. R. Schwab, and A. H. Bridle). San Francisco, CA: Astronomical Society of the Pacific, 1989.
