Electromagnetic Dimensionality of Deterministic Multi-Polarization MIMO Systems
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Multiple-Input Multiple-Output (MIMO) systems are viewed as the last available supply for the ever-growing demand on higher data rates in modern wireless communication systems. Smart exploitation of the traditional wireless resources (time-slots or bandwidth under the same transmit power level) has reached its saturation point. By making better use of the free space between the radio links, based on the multipath radio wave propagation, MIMO systems have shown significant capacity improvement with the same traditional wireless resources. In this multi-disciplinary research, we are exploring the link between the electromagnetic propagation and the information theory. Unlike the majority of recent research work, we model the propagation channel matrix between the transmit/receive elements in a deterministic manner under the Maxwellian framework. Having included the environment properties and the characteristics of the radiating elements, the deterministic approach provides a realistic assessment of the MIMO system performance in specific scenarios. The problem addressed in this research is the evaluation of the multi-antenna systems degrees of freedom (DOF) by employing all the available electromagnetic diversity resources (spatial, pattern and polarization). Based on a developed well-defined power independent dimensionality (PID) metric, we start by investigating the information-bearing potential of the collocated multi-polarization MIMO system. We study the hexapole system (exploiting both electric and magnetic fields in conveying independent information) and compare it to the tripole systems (exploiting the vectorial polarization diversity of one field only). We present numerical results for 3 deterministic scenarios: a canonical free-space (near and far field exact solution), a canonical perfect electric conductor (PEC) corridor using rigorous modal analysis, and a lossy-wall corridor using image ray tracing (IRT). Next, we provide deterministic results for the more interesting sampling problem of the electromagnetic vector fields: given a specific MIMO array size, what is the optimum number of packed multi-polarization antennas (i.e. multi-polarization 1D, 2D or 3D sampling) that yields the largest PID for a given environment and what is the estimate of this PID? Using a canonical case of multi-polarized arrays inside a multipath-rich PEC corridor, we show that the spatial frequency spectrum of the electromagnetic field governs the optimum PID of the site-specific scenario. The problem is analogous to the DOF determination of an essentially time-limited-band-limited 1D scalar function using the framework of the prolate spheroidal wave functions. We also present simulation results for the same sampling problem in a lossy-wall indoor environment using IRT.