Empirical Geometrical Bounds on MIMO Antenna Arrays for Optimum Diversity Gain Performance: An Electromagnetic Design Approach

We propose a general design methodology for synthesizing surface or volume multi-input-multi-output (MIMO) antenna arrays with optimum cross-correlation diversity gain performance through engineering the array's geometrical shape. The design algorithm is based on approximating arbitrary antenna geometrical configurations by the arrays of infinitesimal (electrically small) dipoles and then using the recently introduced cross-correlation Green's function in order to compute far-field cross correlations without the need to explicitly measure or compute far-zone fields. After directly expressing far-field cross correlation in terms of the geometrical details of the antenna array (position and orientation), the method applies a global optimization strategy (the genetic algorithm) to find optimum positions and orientations of the MIMO antennas' elements within a given geometrical shape, resulting in the statistically best system performance. We provide extensive numerical results, including various array topologies (both fixed and conformal), with investigations of the impact of the array density, positions, and the relative orientations of the composing antenna elements on the attainable diversity gain. This paper also outlines an expansion of the proposed design methodology in order to deal with the important special case when a ground plane is present in the MIMO environment. It is found using the proposed methods that small MIMO receiver terminals can be made to fit any geometrical shape by properly controlling the position and the orientation of each element. All the resulting arrays have dimensions that are smaller than 0.35λ × 0.35λ with the diversity gain of 80% or greater. It was also found that for each antenna topology, a critical number of antennas per unit area/volume exist, such that no further improvement of the diversity gain is possible. This upper bound is geometrical in nature, but it is obtained through an electromagnetic analysis, clearly demonstrating the impact of relative antenna positioning and orientations. Various 2-D and 3-D antenna array configurations, including disk, ring, spheres, and spherical layers, were investigated and their critical array densities are tabulated. Also, a practical example of conformal arrays mounted on an avionic nose was provided. It was also found that relative orientations alone can be exploited to substantially improve the performance of MIMO arrays by considering different scenarios comparing position-alone, orientation-alone, and position-and-orientation optimization processes with random arrays in terms of diversity gain performance. The method developed in this paper can be expanded to include more complex antenna types, but it is also suitable for scalable computing analysis of continuous large radiating and receiving antenna surfaces and massive MIMO. In particular, for mmWave applications, we expect that the need to optimize large arrays of tiny antennas will increase the demand for accurate and general design algorithms, such as the one proposed in this paper.