On physically-based normalization of MIMO channel matrices

Various normalizations of the MIMO channel matrix are discussed from a physical perspective. It is demonstrated that the physics of antenna arrays and propagation channel should be taken into account when normalization is chosen, so that SNR has proper physical meaning, the conclusions are physical and correspond to realistic systems. The antenna array geometry and the transmission strategy (coherent/non-coherent) limits the choice of normalization and determines how the capacity and other performance metrics scale with the number of antennas, which is more pronounced for densely-populated antenna arrays. This is especially important for an asymptotic analysis, when the number of antennas increases to infinity. Limitations of such analysis from the physical perspective are pointed out.