# Multi Ray Model for Near-Ground Millimeter Wave Radar
## 4 Experimental Results  
The multi-ray effects were demonstrated using a short-range wireless link operating at millimeter wavelengths. A W-band transmitter and receiver were placed next to each other, with directional antennas looking at a target located on a motorized movable rail system. Due to the physical limitations of the system, the distances and heights were scaled down to imitate a radar operating on a vehicle. The antennas were placed at a height of 100 mm above a table, which served as a reflective surface, as shown in Figure 4. In order to ensure that the diffuse component in the scattering pattern is very small, a smooth table was used. The table roughness was well below the Rayleigh criterion \(\lambda/(8\text{cos}\theta_{0})\) for all incident angles \(\theta_{0}\) along the varying distance to the target (where \(\lambda=3\) mm at 94 GHz). Various objects were placed on top of a rod attached to the rail, serving as moving targets along the axial line. This experiment examined the effect of changing the distance between the transmitter and the scattering object, which reflects the signal to the receiver. Several types of reflecting object were used to examine their impact on the rays returned.  
The experiment was conducted at a frequency of 94 GHz. The transmitter was based on a Gunn diode, producing continuous power of 50 mW of constant envelope wave. The receiver was based on direct detection, with a diode serving as a square law detector. The voltage attained from the detector was amplified by a video amplifier with a gain of 10 dB in order to match the detected signal to a recording oscilloscope (see Figure 5). The typical bandwidth of the amplifier was about 50 kHz. The transmitting and receiving antennas were both horns, with a gain of 24 dBi, operating in the same vertical (TM) polarization.  
In the first experiment, we demonstrated the reflection from a round plate. The plate diameter was 235 mm, and it was located close to the table, as shown in Figure 5. In this scenario, the plate formed a right angle with the table. This served as a specific reflector, causing only three possible ray paths between the transmitter and receiver.  
Figure 4: Multi-ray experiment setup. The transmitter and the receiver adjacent to each other.  
The experiment was carried out repeatedly, while the target moved on the radial axis back and forth between distances of 400-1500 mm. The received power was recorded, and graphs were drawn as a function of the distance. Figure 6 shows the normalized received signal strength vs. the distance to the target. A comparison between analytical calculations and experimental results was performed via the locations of peaks and dips of the signal strength measured along the distance, corresponding to constructive and destructive interferences. It can be seen that the power peaks and dips follow the two-ray model, where path 4 in Equation (4) is omitted.  
Figure 5: Multi-ray experiment with round plate.  
Figure 6: Received power in two-ray model: (**a**) Analytical calculation. (**b**) Experimental results for three similar experiments.  
A four-ray model was demonstrated by using a metal cylinder as a reflecting target. We used a 48 mm diameter cylinder with a length of 330 mm that was located 90 mm above the table (see Figure 7). As in the previous experiment, the object moved continuously in an axial line at distances between 400 mm and 1500 mm. In this case, the cylinder reflected the incident radiation at many angles, resulting in all four possible paths between the transmitter and receiver.  
The measured power was recorded and is presented in Figure 8. Inspection of the results reveals agreement between the theoretical four-ray model calculation and the experimental measurements.  
Figure 8: Four-ray model: (**a**) Analytical calculation. (**b**) Experimental results for three similar experiments.  
Figure 7: Multi-ray experiment with a metallic cylinder as a target.