Optimal sequences for asynchronous CDMA channels with different SIR requirements

We address the problem of admissibility in an asynchronous CDMA (A-CDMA) channel equipped with a bank of single-user matched filters. We say that a set of users is admissible in a CDMA channel if one can assign sequences to the users and control their power so that each user meets its signal-to-interference-plus-noise ratio (SINR) requirement. We identify a power allocation that solves a closely related problem. This problem is equivalent to the problem of admissibility if all users have the same SINR requirements. We show when both problems are equivalent in a general case. We provide criteria for optimizing correlation properties of sequences and prove a necessary condition for admissibility of the users.