I sent out a complex vector $x_i \in \{x_1,...x_n \}$ and receive a vector $y$.
I use correlation $y^Hx_i$ to detect which $i$ was sent.
If $y$ is corrupted by AWGN channel, the optimum rule should be $$\hat{i} = \text{argmin}_i |y-x_i|^2 = \text{argmax}_i \text{Re}\{y^H x_i\}$$ we compare the real part of correlation results.
But many applications and texts use the absolute value of correlation results, for example Primary Synchronization Signal Detection Algorithm in LTE-A and Cross_Correlation_between_different_PSS.
Why should we use absolute value? Maybe because of fading that rotates the receive vector?
Could you give me some resources that explain this convention in detail?