  We consider a multiple-input multiple-output (MIMO) multiple access channel
(MAC), where the channel between each transmitter and the receiver is modeled
by the doubly-scattering channel model. Based on novel techniques from random
matrix theory, we derive deterministic approximations of the mutual
information, the signal-to-noise-plus-interference-ratio (SINR) at the output
of the minimum-mean-square-error (MMSE) detector and the sum-rate with MMSE
detection which are almost surely tight in the large system limit. Moreover, we
derive the asymptotically optimal transmit covariance matrices. Our simulation
results show that the asymptotic analysis provides very close approximations
for realistic system dimensions.
