4.4 Optimum transmitter with global measure of performance.(4 Nonlinear Decision Feedback MIMO Transceivers)

Foundations and Trends in Communications and Information Theory, December, 2006 by Jiang, Yi; Palomar, Daniel P.

This section deals with the design of the optimum transmitter P according to problem (4.13). While the linear MIMO transceiver design in Chapter 3 relies on the additive majorization theory, the nonlinear DF transceiver design relies on the concept of multiplicative majorization (see Definition 2.6) and the recent matrix decomposition called the generalized triangular decomposition (GTD).To facilitate our discussion, we reproduce the main idea here. The GTD is detailed in Appendix B.1.

Theorem 4.2. (GTD Theorem) Let H [member of] [C.sup.mxn] be a matrix with rank K and singular values [[sigma].sub.H,1] [greater than or equal to] [[sigma].sub.H,2] [greater than or equal to] ... [greater than or equal to] [[sigma].sub.H,K] > 0. (7) There exists an upper...