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