An approach to aualyze the performance of the code division multiple access (CDMA) scheme, which is a core technology used in modern wireless communication systems, is provided. The approach characterizes the objective system by the eigenvalue spectrum of a cross-correlation matrix composed of signature sequences used in CDMA communication, which enable us to handle a wider class of CDMA systems beyond the basic model reported by Tanaka in Europhys. Left., 54 (2001) 540. The utility of the scheme is shown by analyzing a system in which the generation of signature sequences is designed for enhancing the orthogonality.