Uniform Decomposition of Mutual Information using MMSE Decision Feedback Detection

We consider efficient techniques for the design of a transceiver for a matrix channel with minimum mean square error (MMSE) decision-feedback (DF) detection when perfect channel information is available at both the transmitter and receiver. By combining the canonical property of the MMSE-DF detector and our recently developed equal-diagonal QRS decomposition of a matrix we obtain a uniform decomposition of mutual information in which each of the synthesized scalar subchannels has the same mutual information (under the assumption of error-free feedback). To assist our analysis of this uniform decomposition, we provide a new QR interpretation of the MMSE-DF receiver. This enables us to show that the natural detection order is optimal (in an SINR sense), and that for the proposed transmitter, the MMSE-DF detector is asymptotically equivalent to the maximum likelihood detector when the SNR is high. We also derive a low-complexity quadratic recursive algorithm for the characterization of all eligible S-factors in the QRS decomposition. When coupled with our QR interpretation of the MMSE-DF detector, this enables us to efficiently design the optimal transmitter and to efficiently implement the MMSE-DF receiver.