I want to calculate the Cross-Correlation of two statistically independent (uncorrelated) functions $$ X_{1}(t)=X(t) + V_{1}(t) $$ $$ X_{2}(t)=X(t-T_{L}) + V_{2}(t) $$ where $$ E[V_{1}(t).V_{2}(t)]=E[V_{1}(t)].E[V_{2}(t)] $$ and $$ E[V_{1}(t).V_{2}(t).X(t)]=E[V_{1}(t)].E[V_{2}(t)].E[X(t)] $$
The question is, if the sum in $X_{1}(t)$ and $X_{2}(t)$ returns a uncorrelated function. Thanks in advance!