Unique Factorization Theory of Signals for Energy-Efficient MIMO and Cooperative Communications

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With the arrival of the Information Age, the explosive demand for information and knowledge exchange in our society has created two significant challenges: (a) the ever increasing demand in transmission capacity, and (b) the demand of high quality transmission. Recent developments are the multi-input multi-output (MIMO) wireless link and cooperative relay networks which, due to their potential in meeting these challenges caused by fading channels together with power and bandwidth limitations, have become two very important areas of research. Underlying the solution to these challenging problems are the techniques of space-time modulation (space-time block coding (STBC) or matrix signal design) which have been well developed for coherent MIMO and relay systems. However, efficiently attaining perfect channel state information at the receiver that is necessary for coherent detection is, in practice, a significantly challenging issue due to the rapid variation of fading coefficients. In addition, the noise in noncoherent relay systems is no longer Gaussian. Therefore, noncoherent STBC and distributed STBC are way behind coherent STBC and distributed STBC. Thus far, the systematic designs of noncoherent STBC and distributed STBC with high rate and full diversity using energy-efficient constellations are still open and challenging problems. More importantly, no progress has been made on determining the coding structure that enables the noncoherent diversity-multiplexing tradeoff to be attained. The goal of the present proposal is to establish a totally-novel mathematical tool: unique factorization theory of matrix signals, and apply it to the systematic design of energy-efficient STBC for coherent and noncoherent MIMO and cooperative communications. Specifically, the applications will be primarily concentrated on the following three areas: (1) To systematically design high rate full diversity noncoherent STBC and distributed STBC. (2) To systematically design a family of unitary STBCs that enable the noncoherent diversity-multiplexing tradeoff. (3) To systematically design high-rate full diversity collaborative nonlinear STBC with large coding gain.