  Asymptotic spectral distribution (ASD) of the crosscorrelation matrix is
investigated for a random spreading short/long-code asynchronous direct
sequence-code division multiple access (DS-CDMA) system. The discrete-time
decision statistics are obtained as the output samples of a bank of symbol
matched filters of all users. The crosscorrelation matrix is studied when the
number of symbols transmitted by each user tends to infinity. Two levels of
asynchronism are considered. One is symbol-asynchronous but chip-synchronous,
and the other is chip-asynchronous. The existence of a nonrandom ASD is proved
by moment convergence theorem, where the focus is on the derivation of
asymptotic eigenvalue moments (AEM) of the crosscorrelation matrix. A
combinatorics approach based on noncrossing partition of set partition theory
is adopted for AEM computation. The spectral efficiency and the minimum
mean-square-error (MMSE) achievable by a linear receiver of asynchronous CDMA
are plotted by AEM using a numerical method.
