2 research outputs found
Joint Unitary Triangularization for MIMO Networks
This work considers communication networks where individual links can be
described as MIMO channels. Unlike orthogonal modulation methods (such as the
singular-value decomposition), we allow interference between sub-channels,
which can be removed by the receivers via successive cancellation. The degrees
of freedom earned by this relaxation are used for obtaining a basis which is
simultaneously good for more than one link. Specifically, we derive necessary
and sufficient conditions for shaping the ratio vector of sub-channel gains of
two broadcast-channel receivers. We then apply this to two scenarios: First, in
digital multicasting we present a practical capacity-achieving scheme which
only uses scalar codes and linear processing. Then, we consider the joint
source-channel problem of transmitting a Gaussian source over a two-user MIMO
channel, where we show the existence of non-trivial cases, where the optimal
distortion pair (which for high signal-to-noise ratios equals the optimal
point-to-point distortions of the individual users) may be achieved by
employing a hybrid digital-analog scheme over the induced equivalent channel.
These scenarios demonstrate the advantage of choosing a modulation basis based
upon multiple links in the network, thus we coin the approach "network
modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio
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