In this paper, a free deterministic equivalent is proposed for the capacity
analysis of the multi-input multi-output (MIMO) multiple access channel (MAC)
with a more general channel model compared to previous works. Specifically, a
MIMO MAC with one base station (BS) equipped with several distributed antenna
sets is considered. Each link between a user and a BS antenna set forms a
jointly correlated Rician fading channel. The analysis is based on
operator-valued free probability theory, which broadens the range of
applicability of free probability techniques tremendously. By replacing
independent Gaussian random matrices with operator-valued random variables
satisfying certain operator-valued freeness relations, the free deterministic
equivalent of the considered channel Gram matrix is obtained. The Shannon
transform of the free deterministic equivalent is derived, which provides an
approximate expression for the ergodic input-output mutual information of the
channel. The sum-rate capacity achieving input covariance matrices are also
derived based on the approximate ergodic input-output mutual information. The
free deterministic equivalent results are easy to compute, and simulation
results show that these approximations are numerically accurate and
computationally efficient.Comment: 26 pages, 7 figures, Accepted by IEEE Transactions on Information
Theor
