Joint Unitary Triangularization for MIMO Networks

This paper considers communication networks where individual links can be described as those based on multiple-input multiple-output channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between subchannels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis, and corresponding decomposition, which are simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of subchannel gains of two broadcast-channel receivers. We then apply this decomposition to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which uses only scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user multiple-input multiple-output channel, where we show the existence of nontrivial cases, where the optimal distortion pair (which for high signal-to-noise ratios (SNRs) 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”.