The relationship between reflection coefficient and reflectance is:

From the above equations, the Fresnel reflection coefficient for a perpendicularly polarized wave is derived:

where εr1 and εr2 are the relative permittivities of the incident and reflected media, respectively, and εr is the ratio of εr1 and εr2. In general, the incident medium is air (εr1 = 1), so εr = εr1 = εr2 =1.

In fact, there is also a corresponding Fresnel reflection coefficient for parallel-polarized waves, but since the antenna used in this article is perpendicularly polarized, no derivation is made for it.

Equation (8) only applies to completely smooth surfaces because it is based on specular reflection without scattering, and only ideal surfaces meet this condition. There are no completely smooth surfaces in everyday life. When an electromagnetic wave hits a rough surface, it scatters at angles other than the reflection angle, causing a decrease of energy in the specular reflection. Therefore, the Raleigh roughness factor is introduced in the Beckmann-Kirchhoff theory, as shown in Equation (9):18,19

where λ is the wavelength, θi is the incident angle, hrms is the root-mean-square height (i.e., surface roughness) and J0(∙) is the zero-order Bessel function. When the value inside the brackets approaches 0, J0(∙) approaches one. Here it is assumed that the surface height distribution follows a Gaussian distribution, so sharp edges and shadows can be ignored. Therefore, the corrected reflection coefficient is as follows:


The following describes the vector signal transceiver platform, THz frequency conversion module, measurement system and measurement steps.

Vector Signal Transceiver Platform

The PXIe-5841vector signal transceiver platform integrates a vector signal generator, vector signal analyzer, high-speed serial interface and FPGA-based real-time signal processing and control. It can perform high-speed data acquisition up to 1 GSPS and can up-convert baseband signals to radio frequency signals. It has high speed, high accuracy and low latency, which provide a good foundation for the construction of a THz wireless communication system test platform.

The PXIe-8881 embedded controller is used to solve the problem of baseband digital signal processing. It is in the form of a PXI board and can be well integrated with PXIe-5841. It has a multi-threaded processor inside and supports NI's LabVIEW software development environment as well as various third-party software toolkits such as MATLAB. These advantages greatly improve the flexibility, accuracy, immediacy and compatibility of the baseband digital signal processing process, which complements the high-speed data acquisition function of the PXIe-5841.

THz Frequency Conversion Module

The frequency conversion used is a fully solid-state harmonic mixing electronic frequency conversion scheme, which is a THz communication system based on harmonic mixing heterodyne transmission and reception. The frequency range is 220 to 330 GHz, including the up-conversion (transmission) module and down-conversion (reception) module.

The frequency conversion module is a cascaded structure, including two triplers and one subharmonic mixer (see Figure 1).

Figure 1a

Figure 1b

Figure 1 Schematic diagram(a) and photograph (b) of the 220 to 330 GHz frequency conversion module.

Measurement System

The local oscillator signal is generated by an R&S SMB100A RF and microwave signal generator with a frequency range of up to 40 GHz. Considering the specified local oscillator input power of the frequency conversion module and the loss of the cable, the local oscillator output power is set to 9.5 dBm. The output of the local oscillator is divided into two equal power signals after passing through a power divider and then routed to the local oscillator input ports of the 220 to 330 GHz frequency conversion modules.

The intermediate frequency (IF) signal has a frequency of 2 GHz, an IQ rate of 10 MSPS and a power of – 20 dBm. The DC power supply of the Keysight E3646A provides a 5V voltage for the frequency conversion module, and a DC isolator is added to the IF input port to protect the frequency conversion module. The entire experimental setup is placed on an optical platform with a fixed hole spacing and the module is secured by an optical clamp, which ensures good alignment (see Figures 2 and 3).

Figure 2

Figure 2 Channel measurement platform schematic.

Figure 3

Figure 3 Channel measurement setup.

During the measurement, the signal generator provides a spread-spectrum pseudo-random sequence which is upconverted to the THz band by the up-conversion module for transmission. The received signal is down-converted to baseband and the channel impulse response (CIR) is obtained using the sequence auto-correlation characteristic. A series of channel parameters is obtained from the CIR, based on large-scale path loss fading characteristics in the environment.

Measurement Procedure

The 220 to 330 GHz reflection path (RNLoS) is measured using four types of materials as reflecting surfaces (see Figure 4): wood, plaster, glass and a mirror (plain glass substrate with a metal reflective coating). These are chosen to represent a range of common materials. The incident and reflection paths are fixed at 10 cm and the incident angle varies from 10 to 80 degrees with a 10-degree step size. For each surface and angle, the frequency is swept by changing the local oscillator frequency with a step size of 10 GHz to cover the 230 to 330 GHz frequency range. For comparison, the 20 cm line-of-sight (LOS) path for each frequency is measured as well.

Figure 2

Figure 4 Reflection channel measurement.


Relationship Between Reflection Coefficient and Material, Angle and Frequency

Figure 5 shows the trend of reflection coefficient versus incident angle at different frequencies for different materials. For comparison, the Rayleigh model curve is plotted with a black line. It is consistent with the theoretical trend, with higher fitting accuracy for glass, plaster and wood, while the mirror shows a slight deviation. This may be due to the metallic components on the mirror surface, which have special optical properties, as also mentioned in the literature.

The reflection coefficient of plaster and wood is relatively stable, while that of glass varies greatly with frequency, with a difference of 0.5 between the reflection coefficients at 230 and 290 GHz when the incident angle is 80 degrees.

Figure 5a Figure 5b Figure 5c Figure 5d

Figure 5 Measured reflection coefficients of wood (a), plaster (b), glass (c) and mirror (d) as a function of incident angle and frequency.