There are several tests like NIST test suite or testU01 which are proposed to investigate whether the sequences generated by a pseudorandom number generator can be considered random. In some applications like CDMA telecommunication systems, ideally PRNGs should have a delta-like auto-correlation and zero cross-correlation.
My question is: Is there any statistical tests developed to investigate the independence of the sequences generated by such PRNGs to ensure they have delta-like auto-correlation and zero cross-correlation (with a desired significance level)