Antenna elements arranged in a multiple-input-multiple-output configuration can impact the capacity of a wireless-communications system and combat multipath effects. But one of the keys to improved performance is finding the optimum MIMO layout for a given system scenario, and when it makes sense to stop adding antenna elements and simply optimizing the existing antennas. Last month, this two-part article introduced basic MIMO concepts; this conclusion explains how to calculate the envelope correlation of a MIMO system for a given number of antenna elements.

Thaysen et al.²⁶ related the mutual orientations, the location, and the mutual coupling to the envelope correlation between two identical antennas on an infinite ground plane. They investigated symmetrical as well as asymmetrical coupling scenarios using two identical PIFAs located close to each other on the same ground plane, in order to determine the envelope correlation versus distance for fixed orientations, and the mutual coupling versus rotation of the antennas for fixed distance. The results (simulated using IE3D simulation software³⁷) illustrate how to orientate and locate the antennas in order to minimize the envelope correlation. Two different cases were investigated: one with parallel PIFAs and another with orthogonal orientation as shown in Fig. 3 (the horizontal distance, d, is defined such that d is positive in the case illustrated in Fig. 3(a). For the parallel case [Fig. 2(a)] with a 10-mm separation, it was found that the envelope correlation is ρ_e = 0.8 and simply by rotation of one the antennas 180 deg., the envelope correlation decreases to ρ_e = 0.4. Similar results were seen for the orthogonal antennas setup [Fig. 3(b)] where the envelope correlation decreases from ρ_e = 0.5 to ρ_e = 0.25. For the orthogonal setups, the highest envelope correlation is obtained when the open end and the feed line are vertically on line.

Those researchers found that the deviation in the center frequency (min. |S₁₁|) was most affected in the case of parallel antennas, each having the feed point in the same end, where a change of 12 percent was observed. In the other scenarios (the two orthogonal cases), the change was less than 2 percent compared to a single PIFA element. The maximum envelope correlation of ρ_e = 0.8 was obtained for the parallel setup, when the antennas are vertically overlapping each other, and highest value was obtained for the setup having the feed line in same ends.²⁶

Also, an almost exponential relation between the mutual coupling and the envelope correlation was found.²⁶ A mutual coupling limit of –10 dB was found in these studies. Below that limit, the envelope correlation was almost constant, being ρ_e = 0.15, and therefore any effort in decreasing the mutual coupling could be limited to this level.

Placing the antennas on a finite ground plane affects their performance.⁶ For the designs illustrated in Fig. 4, the antennas were optimized in terms of the input impedance and bandwidth of the planar inverted-F antenna (PIFA) (e.g., by changing the distance between the feed and the ground contact) dependent on the location of the PIFA on the ground plane. The best antenna configurations were chosen from some performance metrics (correlation and bandwidth). However, the proximity effects of a mobile telephone's cover, the artificial hand, and the head should be included in the analysis.⁸ Hence, the results concerning the optimal configurations might differ somewhat when such effects as the cover, hand, and head are taken into account.

For MIMO application, where low envelope correlation is essential, the location and orientation of the antennas should be optimized not only with respect to envelope correlation but also with respect to bandwidth. It has been found that for the two-antenna configuration, optimal locations and orientation with respect to the MIMO performance, i.e., bandwidth and envelope correlation between the antennas, are not necessarily the ones with the lowest envelope correlation.⁶ A certain bandwidth is required as well. Taking both the envelope correlation and bandwidth into account, it was found that configuration B4 yielded the best performance. Here, the bandwidth is 12.2 percent centered around 1.79 GHz; the envelope correlation is below 0.1, and the strongest mutual coupling is –7.7 dB.

From the 15 different two-antenna configurations investigated by Thaysen et al.,⁶ the relation between the envelope correlation and the mutual coupling indicated that low mutual coupling leads to low envelope correlation. However, low envelope correlation does not necessarily come from low mutual coupling. Also, it was observed that low mutual coupling results in low bandwidth, primarily caused by the poor impedance match (high reflection coefficient) of the antennas in these configurations. High bandwidth occurs in the configurations that also yield high mutual coupling. Thaysen et al.¹⁶ concluded that high mutual coupling reduces the freedom in choosing an optimal configuration.

Taking the increased complexity into account, it is possible that careful optimization of a given number of antenna elements is preferred compared to a scenario where an extra antenna element has been added.³⁸ In\ ref. 6, evaluation of the MIMO system was based solely on the antenna performance, such as the envelope correlation, mutual coupling, resonance frequency, bandwidth, and radiation efficiency of the antenna elements, especially with a focus on the envelope correlation and the bandwidth. However, the real advantage of a MIMO should be the improvement in capacity. Thus, the capacity should be evaluated. To determine the full advantage, capacity should be evaluated in a multipath environment.⁸

To calculate the capacity of a MIMO system, information is needed for both the propagation environment and the antenna configurations. Realistic evaluation of MIMO antenna structures requires multielement propagation measurements with MIMO antenna configurations. One way to obtain these multielement propagation measurements is to characterize an actual prototype in real scattering environment. This, however, is a very time-consuming process. Moreover, the entire measurement must be repeated for all MIMO antenna proposals.

Thaysen et al.⁸ presented measurement-based results for evaluating MIMO antenna performance. The results were produced by merging the complex radiation pattern of the antennas under test with a MIMO coupling matrix. The MIMO coupling matrix represents a small macrocell MIMO environment measured in downtown Helsinki (see for example, ref. 39 for maps). The MIMO coupling matrix was measured by Dr. Vainikainen's group at Helsinki University of Technology.^{39, 40}

These multielement propagation measurements enable a combination of measured propagation paths with the radiation pattern of the antenna elements.^{39, 41} However, this requires the extraction of the full double-directional propagation channel parameters. The measurement setups consisted of a channel sounder for measuring the spatial and temporal characteristics of the radio channel, a linear transmitting antenna array, and a spherical receiving antenna array, both employing dual-polarized patch antennas.^{42, 43}