Abstract:
An important open problem in multiple antenna communications theory
is to compute the capacity of a wireless link subject to flat Rayleigh
block-fading, with no channel-state information available either to
the transmitter or to the receiver. The isotropically-random (i.r.) unitary
matrix--having orthonormal columns, and a probability density that is
invariant to pre-multiplication by an independent unitary
matrix--plays a central role in the calculation of capacity and in
some special cases happens to be capacity-achieving. In this paper we take
an important step towards computing this capacity by obtaining, in
closed-form, the probability density of the received signal when
transmitting i.r. unitary matrices. The technique is based on
analytically computing the expectation of an exponential quadratic
function of an i.r. unitary matrix and makes use of a Fourier
integral representation of the constituent Dirac delta functions
in the underlying density. Our formula for the received signal density
enables us to evaluate the mutual information for any case of
interest, something that could previously only be done for single
transmit and receive antennas. Numerical results show that at high SNR the
mutual information is maximized for M = min(N,T/2) transmit
antennas, where N is the number of receive antennas and T is the
length of the coherence interval, whereas at low SNR the mutual
information is maximized by allocating all transmit power to a single
antenna.
Status:
Submitted to IEEE Trans. Info. Theory, March 2001.
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