This paper shows an optimal spreading sequence in the Weyl sequence class, which is similar to the set of the Oppermann sequences for asynchronous CDMA systems. Sequences in Weyl sequence class have the desired property that the order of cross-correlation is low. Therefore, sequences in the Weyl sequence class are expected to minimize the inter-symbol interference. We evaluate the upper bound of cross-correlation and odd cross-correlation of spreading sequences in the Weyl sequence class and construct the optimization problem: minimize the upper bound of the absolute values of cross-correlation and odd cross-correlation. Since our optimization problem is convex, we can derive the optimal spreading sequences as the global solution of the problem. We show their signal to interference plus noise ratio (SINR) in a special case. From this result, we propose how the initial elements are assigned, that is, how spreading sequences are assigned to each users. In an asynchronous CDMA system, we also numerically compare our spreading sequences with other ones, the Gold codes, the Oppermann sequences, the optimal Chebyshev spreading sequences and the SP sequences in Bit Error Rate. Our spreading sequence, which yields the global solution, has the highest performance among the other spreading sequences tested.

A great deal of effort has been spent to develop strategies for allocation of resources in DS-CDMA systems in order to mitigate effects of interference between users. Here, the choice of spreading sequences and appropriate power allocation play a crucial role. When developing such strategies, CDMA system designers need to ensure that each user meets its quality-of-service requirement expressed in terms of the signal-to-interference+noise ratio. We say that a set of users is admissible in a CDMA system if one can assign sequences to the users and control their power so that all users meet their quality-of-service requirements. In [1], the problem of admissibility in a synchronous CDMA channel was solved. However, since the simplistic setting of perfect symbol synchronism rarely holds in practice, there is a strong need for investigating asynchronous CDMA channels. In this paper, we consider a K-user asynchronous CDMA channel with processing gain N and identical performance requirements for all users assuming chip synchronism. We solve the problem of admissibility of the users in such a channel if N K, and identify optimal sequences. We also show that constant power allocation is optimal. Results obtained in this paper give valuable insights into the limits of asynchronous CDMA systems.