A worst-case estimate of an envelope correlation coefficient (ECC) is obtained for small multiple-input multiple-output (MIMO) mobile antennas operating below 1 GHz. The worst-case estimate is numerically derived in this paper using spherical and exponential wave functions. The derived result confirms that the worst-case ECC can be easily obtained from the rotation angle between the radiation patterns of two MIMO elements, which are attained directly from the amplitude of 2D electric field patterns without any additional phase and polarization information. As a practical example, MIMO mobile antennas with different antenna element arrangements are compared to verify the validity of the proposed worst-case estimate. Moreover, based on these analyses, we also suggest an effective approach to reduce the ECC of a small MIMO mobile antenna operating below 1 GHz by properly locating the antenna elements to make the radiation patterns perpendicular to each other. This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/ by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. ⓒ Copyright The Korean Institute of Electromagnetic Engineering and Science. All Rights Reserved.
ZHAO et al.: WORST-CASE ESTIMATE OF ENVELOPE CORRELATION COEFFICIENT FOR SMALL MIMO MOBILE ANTENNAS BELOW 1 GHz
45worst-case estimate of the ECC through a direct derivation using the spherical and exponential wave functions. Then, the correctness of this worst-case estimate is verified by comparing MIMO mobile antennas that operate at 0.8 GHz and under different arrangements of the antenna elements. Moreover, by investigating the different factors (rotation angle, translation of phase centers, and occasional pattern variance) related to the ECC, we prove the rotation angle, which is chosen to estimate the worst-case ECC, is also an effective applicable factor to reduce the ECC for a MIMO mobile antenna below 1 GHz. A low ECC can be attained when the rotation angle of a MIMO mobile antenna approaches 90° by locating two antenna elements on the perpendicular edges of the ground plane.
II. WORST-CASE ESTIMATE OF ECCIn this paper, we assume the antennas are operating in an isotopic/uniform multi-path condition (XPR = 1 and P θ = P φ = 1/4π) [13,14].Based on the above assumption, the ECC ( e ) is inversely proportional to the diversity of the radiation patterns and can be expressed in the spherical coordinate Ω = ( θ , ϕ ) using thewhere, and E θ n and E ϕ n are the θ -and ϕ -polarized complex electric field intensities of the antenna element n. Meanwhile, we note the diversity and corresponding ECC are mainly determined by three factors (rotation angle, translation of phase centers, and occasional pattern variance) in MI-MO antennas. Thus, our investigation of the worst-case ECC will start by exploring and comparing these three factors.In addition, we analyz...