This paper investigates the advantages and drawbacks of using the amplitude monopulse technique to estimate the Direction of Arrival (DoA). The experimental setup consists of two-panel antennas and is utilized with three distinct tilting configurations to examine the efect on accuracy in estimating DoA. Experiments are done in an analog domain inside an anechoic chamber, and noise is applied to the results to simulate the efects of the real environment.
To analyze optimum design for monopulse antenna system, three distinct tilting angles are utilized. The setup of antennas is illustrated in Figure 1. Figure 1a shows tilting antenna under an angle = 1∘ . It corresponds to a cutof point between two radiation patterns at perpendicular angle = 0∘ . The second scenario is shown in Figure 1b. The tilted angle of the antenna is = 6∘ and the crossover level of the main beams is -3 dB which is typically used for monopulse antenna systems [8, 9, 10, 14, 15]. The last scenario can be seen in Figure 2c. It is tilted under an angle = 12∘ which produces a cutof point at perpendicular angle at -6 dB. For our experiments, we used two-panel antenna of size 20cm × 20cm with 14 dBi peak gain. Because we want to study how our three scenarios will behave in the WiFi 2.4 GHz analog domain, a frequency of 2437 MHz, which corresponds to channel 6, was chosen.
The concept of a monopulse array utilizing two antennas is a configuration where two separate antennas are employed to generate two steering beams pointing in mirrored spatial directions. The beams are typically designed to intersect at a specific angle, such as the Half-Power Beam Width (HPBW) point, to optimize the accuracy of the direction estimation [8, 9, 10, 14, 15]. It corresponds to a cutof point of -3 dB in the perpendicular angle = 0∘ .
To obtain amplitude monopulse function from our measured amplitude of both beams in the whole angle = [− 90∘ , 90∘ ] we used formula [8, 9] = Δ ( ) Σ ( ) = 1( ) − · 2( ) 1( ) + · 2( ) where 1 and 2 is the received power of antenna A1 and antenna A2. Because antennas are not perfect, the gain patterns can be unbalanced, and it have to be corrected by correction factor calculated as follows
1( = ∘ ) = 2( = ∘ ) → () = 1( ∘ ) − 2( ∘ )().
Analog measurements have been performed in the anechoic chamber at a radial distance of 3 m
between transmitter and receiver, corresponding to the far-field region [14].
(
The block diagram of the analog measurement setup is shown in Figure 2a. It consists of two-panel antennas and one reference antenna connected via coaxial cable to a vector network analyzer (VNA). Since VNA has only two ports, one is connected to a reference antenna, and only one of the two-panel antennas is measured at a time. So, measurements must be repeated for the second antenna of the two-panel antennas with the same conditions to obtain the monopulse pattern. VNA and turn table were connected to a PC with Matlab, which contains a script to control these devices. The whole setup is shown in Figure 2b. The purpose of analog measurement in the anechoic chamber is to determine how the radio signal behaves in optimal conditions (no reflection and multipath) and calibrate the radiation patterns for the amplitude-monopulse comparison technique [9].
The radiation patterns of the three diferent monopulse configurations are shown in Figure 3. The
minimum tilting angle is set to 1∘ , which creates a crossover value between the two tilted beams of
only -1 dB, as shown in Figure 1a. In such monopulse configurations, the closer the beams are, the
higher the resulting Field of View (FoV), as demonstrated in Figure 4. Figure 3b presents the measured
beams of the second tilted array configuration (see Figure 1b). In this case, the optimal monopulse
configuration with -3 dB crossover level between adjacent beams -HPBW point according to (
At this point, one could think that the optimum monopulse antenna design is the one with the maximum FoV. However, if the slope of the MF is less steep, as it happens for the red MF in Figure 4, lower angular sensitivity for angle estimation is obtained. This will imply lower DoA accuracy, as will be shown with experiments.
Since the analog measurements were performed in an anechoic chamber (ideal environment), no noise
or multipath efects were presented. To better evaluate the DoA estimation accuracy, the noise was
added to our measurements based on [16] for three signal-to-noise ratio (SNR) scenarios: 54, 64, and 74
dB. We create 100 samples of received power per degree for each tilted configuration and SNR. Then,
the DoA was estimated using the same procedure described in [9]. The monopulse function for each
antenna design shown in Figure 4 is used. Later, degree sample with noise is used for calculating
monopulse value ( ) by the following formula
(
1 | ( ) − | ︂) .
The highest peak of ( ) inside FoV is estimated DoA. For the purpose of evaluate the performance, the DoA was calculated for each degree, antenna configuration, and SNR. Figure 5 shows the angular DoA estimation error for each SNR and tilted array configuration. Because FoV is a zone without ambiguities, the angle error outside of FoV increases. So, only angular error inside FoV was taken into account. As we can see, the DoA estimated error increases with lower SNR and decreases with higher SNR. This is due to the greater noise at lower SNR. As expected, the tilted array configuration with crossover -1 dB gains a higher error in DoA estimation than the configuration with a cutof point of -6 dB. Due to less step in MF, little changes in received signal make a more varying highest peak in APS. The results of DoA estimation performance are summarized in Table 1. It compares diferent FoV with three SNR scenarios. The best results, a smaller DoA estimation error, are obtained with the tilted array with SNR: a) 54 dB, b) 64 dB, c) 74 dB. configuration of crossover point at -6 dB and the highest SNR 74 dB. The worst DoA estimation error was obtained with a tilted array configuration of -1 dB and the lowest SNR 54 dB. It is clearly visible in Figure 5.
This paper studied the impact of diferent tilting antenna array configurations for DoA estimation using the analog monopulse technique. Experiments were performed in an anechoic chamber to calibrate the system and obtain monopulse function. Subsequently, noise based on three diferent SNRs was applied to the measured data to simulate real environment signal changes. The results show that with a higher angle we obtain a smaller FoV but the estimation of DoA is more accurate. On the other hand, with a lower angle , the FoV is greater at the cost of lower precision in DoA estimation. SNR also has a significant impact on the accuracy of DoA estimation. The results are more accurate with higher SNR. Future work will focus on extending the study to real environment measurement, including the digital domain.
This work was supported in part by the Slovak Scientific Grant Agency (VEGA) Grant Agency through the Research of a Location-Aware System for Achievement of QoE in 5G and B5G Networks under Project 1/0588/22, and in part by the Spanish National projects TED2021-129196BC42 and PID2022136590OB-C42.
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