We obtain an analytical formula of SNR with orthogonal chaotic spreading se
quence for synchronous CDMA(code division multiple access) communication sy
stems based on ergodic theory. We construct arbitrary dimensional chaotic s
preading sequences as complete product bases in the corresponding Hilbert s
pace. It is shown that mean SNR (signal to interference noise ratio) of syn
chronous CDMA systems with product-bases sequences does not depend on the d
imensionality of the corresponding chaotic dynamics and equals the mean SNR
of synchronous CDMA systems with one-dimensional sequences given in [8].