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A simple and exact closed-form equation to determine a penetrated ray path in a ray tracing is proposed for an accurate channel prediction in indoor environments. Whereas the penetrated ray path in a conventional ray tracing is treated as a straight line without refraction, the proposed method is able to consider refraction through the wall in the penetrated ray path. Hence, it improves the accuracy in ray tracing simulation. To verify the validation of the proposed method, the simulated results of conventional method, approximate method, and proposed method are compared with the measured results. The comparison shows that the proposed method is in better agreement with the measured results than the conventional method and approximate method, especially in high frequency bands.

In recent years, a lot of indoor wireless applications have been proposed and researched to satisfy various demands such as high data rates, low power consumption [

The ray tracing technique which is based on geometrical optics (GO) and uniform theory of diffraction (UTD) is capable of calculating an electromagnetic field at a receiving point by adding multipath waves coherently. These multipath waves with different amplitudes and phases depending on wave propagation mechanisms cause deep power fading and/or intersymbol interference (ISI) [

In indoor environments, the penetration through the building wall is one of the important wave propagation mechanisms. In conventional ray tracing, the building wall has been treated as a semi-infinite half-space, and then the electric field for the penetrated ray path is calculated with the Fresnel transmission coefficients because finding the exact penetrated ray path in ray tracing is complex and time-consuming [

Comparison between an assumed ray path in conventional ray tracing and an actual ray path for penetration through the wall.

To overcome this path error within the ray tracing framework, a few studies were carried out. In [

In this paper, a closed-form equation to determine the penetrated ray path through the wall with finite-thickness in the ray tracing is proposed. This proposed equation is not only an exact solution for the penetrating ray path because it is derived from Fermat’s principle [

The paper is organized as follows. The proposed method is described in Section

Figure

Figure

Geometrical representation of penetrating ray path through the wall.

According to Fermat’s principle, the derivative of the optical path length from the transmitting point (A) to the receiving point (D) must be zero to have the shortest path [

Then, four possible solutions for

Among the above solutions,

To validate the proposed method, an experiment was performed at an empty office room on the sixth floor of the engineering building at Yonsei University. As shown in Figure

Experimental site.

To generate the fading including the penetrating ray path, the transmitter (Tx) was placed in the middle of a corridor outside the office room and the receiver (Rx) was placed in the office room and moved along the paths (1–8), which are 5 m in length and equally spaced at 50 cm intervals. The metal door was open resulting in reflection. Hence, the reflecting ray from metal door and various multi-path waves after penetration through the wall were superposed and caused the fading.

Figure

Measurement system.

Transmitter

Receiver

Figure

Measured received signal strength (fading effect).

700 MHz

7 GHz

Figures

Comparison of fading effect along path 2 for measured and simulated results at 700 MHz.

Comparison of fading effect along path 2 for measured and simulated results at 7 GHz.

Comparison of RMS errors between measured results and simulated results.

700 MHz

7 GHz

In this paper, a new method to calculate the penetrating ray path with refraction in the wall exactly and simply is proposed. For this objective, a closed-form equation is derived from Fermat’s principle; hence, it has a simple form and can consider refraction when the ray penetrates through a wall. To validate the proposed method, the measured results and simulated results in terms of fading effect are compared. As a results, the significant improvement in accuracy for the proposed method is verified, especially in high frequency bands. Therefore, the proposed method is very helpful for channel analysis of indoor wireless communication using high frequency bands such as millimeter-wave WPAN application.

This research was funded by the Ministry of Science, ICT & Future Planning MSIP, Republic of Korea, in the ICT R&D Program 2013.