Randomly selected spreading sequences for coded CDMA

We consider the effect of using randomly selected sequence multisets for the uplink of a code-division multiple-access channel. In particular, we calculate a tight lower bound on the expected value of the sum capacity, over the ensemble of randomly selected sequence multisets. We show that for large systems, the sum rate penalty for using randomly selected multisets is at most 1 nat, and vanishes, as the number of users becomes large, compared to the sequence length.