Eigenvalue Distribution of Correlation Matrix in Asynchronous CDMA with Infinite Observation Window Width

Asymptotic spectral distribution (ASD) of the cross-correlation matrix is derived for a large-system asynchronous direct sequence-code division multiple access (DS-CDMA) with random spreading sequences. The crosscorrelation matrix is formed by an infinite input symbol length. Two levels of asynchronism are considered. One is symbol-asynchronous but chip-synchronous, and the other is chip-asynchronous. The results are applicable to arbitrary chip waveforms. The existence of a nonrandom ASD is proved by moment convergence theorem, where the focus is on the existence of asymptotic eigenvalue moments (AEM) of all orders. A combinatorics approach based on noncrossing partition of set partition theory is adopted for AEM computation.