Compact test ranges are used for collimating incoming plane waves to a focus point and vice versa to generate nearly plane waveforms in a short distance . Therefore, these devices can be used to simulate far-field conditions at a relatively near distance. A device under test is placed in the quiet zone (QZ), where the phase and amplitude of the field are nearly constant, whereas the measurement device is placed in the focal point. For the angular testing of radar systems, multiple targets are necessary. As the radar is placed in the QZ for the quasi-plane wave, the targets have to be placed at the focal point. However, this is not directly possible, leading to an offset of the target antennas T1 and T2 as shown in Fig. . Therefore, disturbing effects will occur. For example, as the plane wave criterion is only fulfilled when the target is in the focal point, phase and amplitude deviations of the field will increase with an increasing distance of T1 and T2 from the focal point. Furthermore, the signal still reaching the targets will become weaker as the reflector collimates the incoming waves from the QZ to the focal point. However, in the calculations, these effects are neglected in order to get a simple estimation. The utilized test setup is based on a paraboloid reflector with the equation 1x=y2+z24F, with x, y, and z corresponding to Fig.  and F=0.6 m being the focal length. It is an offset reflector with blended rolled edges and an overall size of 0.6 m by 0.6 m. After calibration, the reflector yields an amplitude deviation of ±0.36 dB and a phase deviation of ±2.89° over a circular QZ with a 20 cm diameter, tested by a 60 mm radius sphere. These parameters fulfill the requirements from of ±5° phase and ±0.5 dB amplitude deviation over the QZ.

Two short-circuited standard 10 dBi rectangular horn antennas are used as targets. Both antennas are mounted on a movable cart controlled by a computer. The maximum distance between the antennas is 30 cm. The antennas are pointed towards the reflector and have an elevation angle of 46.3° and are positioned on a straight line through the focal point as depicted in Fig. .

The radar used in the test cases is a Radarbook2 from INRAS and is depicted in Fig. . It is an FMCW radar system at 77 GHz and consists of 2 TX and 16 RX antennas arranged in a linear array, resulting in 32 virtual antennas. To evaluate the target parameters, a fast Fourier transform (FFT) over the chirps and the antenna array is performed. A simple estimation for the angular resolution of such a radar system can be found in and is Δθ=2/N in radians, leading to Δθ=3.7°. The radar is positioned in three different setups in the QZ. Firstly, the TX antennas are centered in the QZ, secondly, the RX antennas are centered in the QZ, and thirdly, the radar itself can be centered in the QZ. Other positions are also possible, of course.

A ray-tracing simulation is performed to verify the calculation as shown in . The radar system is replicated in the simulation to generate results comparable to those of the measurement. Windowing of the received signals was neglected at the cost of sidelobes in the FFT, as it would reduce the angular resolution.

As the most intuitive positioning of the radar is centered in the QZ, this setup will be analyzed here. Additionally, some effects occurring at the other mentioned positions will be scrutinized. The simulation is done for various angles between 1 and 7°. Some results are presented in Fig. , where the white lines provide the theoretical angle obtained by calculations. As can be seen in Fig. a and b, only one target appears for angle differences smaller than the angular resolution of the radar system of 3.7°. Finally, in Fig. c and d, the targets can be separated, and the simulation is a good match to the calculation. The simulation results for the RX and TX-centered setups are similar, as already shown by .

It has to be mentioned that for simulated angles smaller but close to the radars' angular resolution, there is a possible setup where two targets are visible. This effect is shown in Fig. , where the simulation results for targets at ±1.5° are depicted with the RX antennas centered in the QZ. As the angular resolution of the radar is smaller than the angular distance of the targets, only one target is expected to be visible. Nevertheless, two targets appear at the angles -2.36 and 2.58°. This is an effect of the interference generated by the two targets and is analyzed further in Sect. .

The measurement setup is depicted in Fig. . Additional absorbers are added while measuring to reduce unwanted reflections. Both radar and antennas are movable along linear axes. As the E-band flange of standard waveguide antennas is too large to allow small angles, the antennas are modified and have a 90° waveguide bend before the flange. Comparing the measurements in Fig.  to the simulation results in Fig. , it is notable that they are very similar. Even the ghost target in Fig. d is observable. The target separation is slightly better in Fig. c than in the simulation. Similar to the simulation, when the angle is lower than the resolution ability of the radar, two targets instead of one appear for the RX antennas centered case, as depicted in Fig.  for targets at ±1°. In this case, the appearing targets have angles of -2.92 and 2.47°.

Table  shows the results for the radar-centered setup. As can be seen, the calculation and simulation match with small deviations very well. The simulation and measurement at 1 and 1.5° should yield results at 0° but show some offset. As the values are equal for both cases, this may be caused by the accuracy of the angular FFT. The measurements where two targets appear also show some deviations and are shifted slightly to lower angles. Applying a window function in the signal processing will compensate for this shifting effect, as depicted in Fig.  for an angle of 5.5°. However, only the simulated results get compensated for completely, whereas the measurement is still shifted to lower angles after windowing, which implies that the positioning and alignment of the radar and antennas to the compact test range can be improved. As the windowing decreases the angular resolution of the radar, it was not applied to the measurements and simulations in this work.

The ghost target appearing in the simulations and measurements for large angles is analyzed here. Overall, the ghost targets occur due to the sidelobes of the FFT. Additionally, simulations and measurements show that the magnitude of this target is also influenced by the radar position. Presumably, there are positions where the signal strength at the antennas is influenced in a manner that antennas towards the edges have a lower weighting in the FFT. However, it is not convenient to search for a radar position where these ghost targets do not appear. Therefore, applying a window function to the results is an option to reduce this effect at the cost of lower angular resolution. Fortunately, the ghost targets only appear at angle differences that are at least twice as high as the angular resolution, which enables the application of a windowing function.

Two main problems occur regarding the phase of the transmitted signal. First of all, a phase error will be introduced due to the offset of the targets to the focal point of the mirror compared to an ideal compact test range. Secondly, the physical position of the targets is not the same as their virtual position. Comparing a free-range test setup and a compact test range setup with identical target angles, the phase difference between the signals of all transmit antennas at a target should be equal to achieve identical results. This effect is simulated and depicted in Fig. . It is clearly visible that there is a deviation between the case with a reflector and without a reflector. However, compensating for this effect in the simulations has no influence on the results. Furthermore, the MIMO array has one redundant antenna element, which can be used to mitigate the phase errors occurring due to this reflection.

The target splitting at small angles, as depicted in Figs.  and , is an effect of the interference pattern generated by the two targets. The pattern over the QZ and the part received by the radar is depicted in Fig. . As can be seen, the radar receives an interference pattern with two nearly identical local maximum values, which are not equal to the absolute interference maxima. However, when the maximum values of the measured pattern are used for computing the distance between the sources , the resulting angle is slightly higher than the actual angle, which results in the wrong radar images. Fortunately, this error can easily be mitigated by windowing. Another option is to move the radar slightly along the x axis to introduce a higher difference between the local maximum values.

Due to the offset of the targets to the focal point of the reflector, the incoming angle varies over the QZ. The simulation results for the antenna T1 are depicted in Fig. . For simplification, only the furthest left and right rays are depicted. For reference, the vertical ray is utilized. As shown in Fig. a, the angle variation over the radar aperture is below 0.04° for all measured angles. When the aperture is increased to the size of the QZ or twice the size of the QZ as depicted in Fig. b and c, respectively, the maximum angle deviation increases as expected. As the simulation borders are fixed and the antennas move to the borders, the deviation of one of the rays declines with increasing angle until the position is equal to the simulation border. Due to this angle variation, some errors in the absolute angle measurement appear. This error can not be compensated for in this test setup, as it results from the geometrical conditions. However, for angles below 2°, the deviation is below 2.5%, which does not strongly affect the results.