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Joint Unitary Triangularization for Gaussian Multi-User MIMO Networks
The problem of transmitting a common message to multiple users over the
Gaussian multiple-input multiple-output broadcast channel is considered, where
each user is equipped with an arbitrary number of antennas. A closed-loop
scenario is assumed, for which a practical capacity-approaching scheme is
developed. By applying judiciously chosen unitary operations at the transmit
and receive nodes, the channel matrices are triangularized so that the
resulting matrices have equal diagonals, up to a possible multiplicative scalar
factor. This, along with the utilization of successive interference
cancellation, reduces the coding and decoding tasks to those of coding and
decoding over the single-antenna additive white Gaussian noise channel. Over
the resulting effective channel, any off-the-shelf code may be used. For the
two-user case, it was recently shown that such joint unitary triangularization
is always possible. In this paper, it is shown that for more than two users, it
is necessary to carry out the unitary linear processing jointly over multiple
channel uses, i.e., space-time processing is employed. It is further shown that
exact triangularization, where all resulting diagonals are equal, is still not
always possible, and appropriate conditions for the existence of such are
established for certain cases. When exact triangularization is not possible, an
asymptotic construction is proposed, that achieves the desired property of
equal diagonals up to edge effects that can be made arbitrarily small, at the
price of processing a sufficiently large number of channel uses together.Comment: Extended version of published paper in IEEE Transactions on
Information Theory, vol. 61, no. 5, pp. 2662-2692, May 201
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