# Wheeler Method for Evaluation of Antennas Submerged in Lossy Media
## 1 Introduction  
Antenna radiation efficiency is an important parameter for calculating the wireless link budget and optimizing antenna structures. This can be controlled and improved by modifying the antenna topology in the case of the constant antenna volume [1, 2, 3, 4]. Currently, various methods such as pattern integration method, the Wheeler method [5, 6, 7, 8], radiometric method [9], and the Q-factor method [10] have been reported for measuring radiation efficiency in free-space.  
For some applications, such as in underwater, underground, and in-body scenarios, wireless signals propagate through lossy media [11, 12, 13, 14, 15]. These usually have short-range communication systems due to the high attenuation of electromagnetic (EM) waves in the lossy medium. Meanwhile, the antenna characteristics are significantly different from those in free space. In this respect, antennas submerged in lossy media has been analytically and numerically studied using ideal dipole antennas. These studies include modified parameters such as radiation efficiency, directivity, gain and effective area [16, 17], and the effects of the insulation layer of submerged antennas and the equivalent circuit model of uninsulated antenna [18, 19].  
Since the conventional radiation efficiency [20] is only useful for lossless media, studies of radiation efficiency in lossy media have been in demand. The radiation characteristics of submerged antennas in lossy media have been mostly measured using the gain comparison method which employs standard gain reference antennas [21, 22, 23, 24]. The recently reported measurement technology using a reverberation chamber was conducted to measure the radiation efficiency in consideration of the spurious radiation effect of the feed cable [25]. However, the attenuation area is different depending on the conditions of the lossy medium, such as shape, size, and antenna location [21]. In addition, it is difficult to apply this approach for applications such as establishing a wireless link between implanted devices. To resolve these drawbacks, a modified radiation efficiency is introduced based on thetotal power of the radiated field through the spherical surface with a radius of propagation distance [16; 17; 26; 27]. However, the modified radiation efficiency method still exhibits an inverse proportion between measurement data accuracy and testing time to obtain total radiated power in all spherical surfaces.  
This paper introduces and demonstrates an efficient evaluation method for the radiation efficiency of submerged antennas in lossy media by using the Wheeler method. Without the required measurement facilities or essential accessories to obtain electric field intensity or power density, the presented Wheeler cap method has been devised featuring a short testing time and high accuracy using only the Wheeler metallic cavity. This paper is organized as follows: Section 2 introduces the antenna radiation efficiency for lossy media; in Section 3, the evaluation method of radiation efficiency in media with various dielectric constant and loss tangent has been demonstrated by using the Wheeler method, and the measured efficiency of a wire antenna within the artificial lossy material [28] at the UHF band (0.3 to 3 GHz) is concluded to be in good agreement with the measured efficiencies; Section 4 concludes the paper.