New expression of SNR formula for CDMA system

CDMA is communication systems in mobile radio networks. To improve CDMA systems, new spreading sequences have been proposed. To design spreading sequences, it is necessary to increase the SNR. In classical approaches, the denominator of the SNR is not differentiable. We transform the SNR formula with the two types of orthogonal basis vectors. The denominator of this expression is differentiable. We can derive the new spreading sequence which is optimal for the SNR by a numerically approach.