We present a study of the robustness in the estimation of the Direction of Arrival (DoA) of Wi-Fi mobile devices using amplitude-monopulse systems, with respect to variations in the transmitted power of Wi-Fi packets and hardware heterogeneity. This variation can be due to different transmission power levels, or due to hardware heterogeneity between different chipsets used in distinct mobiles devices and Wi-Fi readers. In any case, it is shown that the estimated DoA is stable within a mean error of 2.64º, with respect to variations in the measured RSSI. This allows using the RSSI-based monopulse technique to localize Wi-Fi terminals despite the strong heterogeneity of devices and dynamic range variation of transmitted power.
In the last years, Indoor Location System (ILS) is having high popularity in both
academia and industries. Because the proliferation of Wi-Fi infrastructure (Access Points
- AP), the use of Wi-Fi signal for implementing ILS is the most common used [
Regarding antenna arrays for power-based solutions, monopulse configuration can
be used for implementing RSSI-based DoA systems. The antenna array is composed of
pairs of identical tilted directive antennas. These amplitude-monopulse radar
techniques have been recently applied to low-cost localization architectures [
In our previous work [
The objective of the proposed system is to estimate the DoA of Wi-Fi signals transmitted from mobile devices in the horizontal plane, i.e. the azimuth angle, and then infer the position by intersecting the estimated azimuthal angles of the HAD readers.
The DoA location architecture is sketched in Fig.1(a). The mobile device (in our
prototype three models of smartphones), is linked to a Wi-Fi router and it is transmitting
Wi-Fi frames on a regular basis. Every time the smartphone sends a Wi-Fi frame, each
HAD reader sniffs the frame by means of a commercial MiMo 3X3 Wi-Fi card with
AR9380 Atheros chipset [
The digital monopulse functions for each HAD reader are calibrated and characterized
individually inside an anechoic chamber. A HAD reader is separated 3 meters from a
smartphone. The smartphone continuously transmits Wi-Fi frames, which are measured
by the WiFi reader to obtain the RSSI levels at both and channels for different
angles of arrival . The digital monopulse function of each reader, using both and
channels, is computed from the RSSI digital data received at each antenna as a function
of rotating angle θ:
Ψ ( ) =
Δ
Σ
( )
( )
=
Even though the two panel antennas are ideally identical, in practice they may have
slight different radiation patterns and peak gains. Therefore, it is of key importance to
calculate a calibration coefficient KD from measured RSSI levels from each antenna at
the perpendicular direction =0º. In [
The monopulse function gives a value between (-1,1) without ambiguity in the FoV. As depicted in Fig. 2(a), the digital monopulse functions of readers 1 and 2 are quite similar within a FoV of (-30º,30º). The differences are due to the individual antennas radiation patterns and gains, which are not perfectly symmetrical, and also due to imperfections on the mechanical tilting angle. Nevertheless, both digital monopulse functions provide a null value at boresight direction (θ=0º), i.e. when each HAD reader is perpendicular to the smartphone.
In order to estimate the DoA a measured monopulse value is obtained from the RSSI reads coming from any unknown direction: Ψ = − + ∙ ∙ (2)
Fig. 2. RSSI values per antenna and angle for HAD Readers 1 (a) and 2 (b). c) Digital monopulse functions for a FoV (-30º,30º) for each HAD Reader
Then, a simple numerical search is performed to obtain the estimated angle EST which minimizes the following monopulse comparison error function: . = ⎯⎯ |Ψ() − Ψ |(3) 2.3
This work has two main goals: i) to demonstrate the robustness of DoA estimation for different devices applying the Wi-Fi monopulse technique; ii) to provide a step forward for an indoor positioning system based on DoA employing an array of WiFi monopulse readers. Therefore, several test experiments have been performed using an anechoic chamber with two readers installed in their respective tripods. Within the anechoic chamber, the readers were placed at one side 25 cm detached from the isolating material and separated 2 meters between them.
Six reference points (called A, B, C, D, E, and F) have been selected to test the devices. These points are ranging from 3 to 4 meters away from the readers. Fig. 3(b) illustrates the experimental set-up, the dimensions of the anechoic chamber, and the exact position of the readers. Table 1 summarizes the theoretical angles (1 and 2), and the Cartesian coordinates X,Y of each one of the six reference points employed in the test experiment.
Point #
A B C
In an environment of indoor location of mobile terminals, we will demonstrate how the monopulse function works well with the two most common problems related to RSSI fluctuations: i) Hardware heterogeneity: the proposed system will be able to estimate the DoA of any terminal regardless of the absolute level of power transmitted; and ii) variability of the power transmitted over time for a given terminal, these variations are produced by the transmitter electronics, and they will induce changes in the level of RSSI detected by the reader.
Fig.4 illustrates an example of the results of the measurement campaign carried out for smartphone (a) Xiaomi Redmi Note 1 LTE at point A, (b) for Motorola Moto G LTE device at point B and (c) for Huawei P10 Lite at point F. The subscripts indicate reader number and in the case of RSSI the antenna for each reader. The upper part plots the four levels of RSSI (a pair of antennas in each of the two readers), the central figure indicates the evolution of the estimated DoA from the monopulse functions characterized in Fig.2 and the measured RSSI levels following Eqs. (2)-(3). Finally, in the lower part, the corresponding Cartesian X-Y location coordinates are obtained by the crossing of the estimated angles 1 and 2 as it was described (see Fig.3(b)).
Regarding the 15 dB of difference between the two readers (see Fig. 4 (b) and Fig 2 (y-axis)), it can be explained for the different hardware used in each sniffer. They are assembled using different models of embedded PC. Moreover, the antenna radiation pattern and gains are not identical, and the different losses produced by coaxial cables and RF connectors produce the differences in the RSSI acquired. Based on the results obtained, we can draw the following conclusions: The RSSI measure presents temporal variations in the four measurements (RSSIi Reader j; i, antenna j = 1,2), although the experimental conditions remain unchanged (remember that the experiments are carried out in an anechoic chamber). RSSI measured levels are consistent with the reader characterization of Fig.2 (see reference point A), showing a difference in the RSSI measures of about 5 dB between the antennas of both HAD readers. The estimated DoA in both cases also presents temporal variations, but the result remains stable. In addition to the small variations of the RSSI in all cases, abrupt or more significant variations also occur, as is highlighted in the range indicated with a circle, where several RSSI peaks are displayed. In Fig.4(a), considering all the received frames and taking the average value, the monopulse function estimates a mean DoA of approximately 1 = -12º and 2 = -7º (according to Table 1, real DoA is 1 = -16º and 2 = -13º), which results in a mean distance error of almost 0.5m. Fig. 4(b), again, the temporal variability of RSSI can be shown, and the conclusions obtained previously remain valid. The RSSI changes, which can affect one or both sniffer (as the last of the peaks indicated, which shows that it is mainly due to variations in transmitted power). Focusing on each reader separately, the RSSI measure is similar, and the calculated DoA is close to 0 °, as indicated by the prediction shown in Fig. 3(b) for point B. Similar results are observer for Huawei P10 Lite at point F in Fig. 4(c).
Regarding the quantification error in the reading of the RSSI, it is inherent to the use
of cost-effective hardware, and therefore, it cannot be avoided [
Angular Angular Er- Angular Er- Angular Angular ErError R1 ror R1 de- ror R2 de- Error R2 ror R2 dedevice #2 vice #3 vice #1 device #2 vice #3 4.7546 -0.2056 -0.8006 5.9239 4.0406 -0.8368 0.4920 0.6990 -1.7629 -2.6744 -5.4890 -6.0807 0.3059 0.2531 0.5451 0.3013 -1.4754 -5.0044 -2.6314 1.1798 3.2429 -0.4639 0.4115 1.4531 2.5108 0.9850 -2.7876 -0.3103 2.9819 2.5963 0.1771 0.3002 5.3202 -0.6230 0.3081 -5.3031 0.3659 -1.6781 0.6265 0.1137 6.847 -1.3054 4.0331 -6.5155 1.9350 -1.6220 0.8321 0.3918 Fig. 6 compares the representation of the estimated X,Y position for 150 samples: Fig. 6 left shows the result of averaging the RSSI received from five frames, giving rise to 150 position estimates. On the other hand, Fig. 6 right shows the direct estimate from the RSSI of 150 chosen randomly from the total, comparing this way the same number of samples. The mean error, in the case of averaging the RSSI levels of the acquired frames, has lower dispersion that in the case of using raw RSSI samples. The colormap, from red to blue, indicates the number of samples determined in each point. If a point is red-color, 60 samples are determined in these coordinates.
Table 2 shows the mean angular and mean distance error of the 150 positions estimated from the total of Wi-Fi frames acquired in each of the reference points averaged every 5 frames. The angular error in degrees indicates the difference between the theoretical expected DoA of each reader and the computed one. The error (in meters) shows the mean Euclidean distance from the known reference point position to the estimated. 5
This work has studied the use of monopulse techniques for the estimation of the angle of arrival (DoA) as part of a positioning system of Wi-Fi mobile devices. The combination of RSSI information, directive panel antennas, and the amplitude-monopulse technique allow the use of commodity hardware and the implementation of a cost-effective system. Several experiments have been carried out using different smartphones, operating with several versions of operating systems, in order to analyze the effect of the heterogeneity of hardware and software to the transmitted power in the estimation of the direction of arrival. The measured results have confirmed that in spite of the fluctuations in RSSI measurements, the use of the monopulse system estimates the DoA with an error of less than 6º, confirming the robustness of the system. Future work will focus on extending the study to a more realistic indoor positioning environment. 6
This work has been funded by the project “2I16SA000050-GEODA. Servicios de Geomarketing y Big-Data” from Consejería de Desarrollo Económico, Turismo y Empleo de la Región de Murcia and by Spanish national projects TEC2016-75934-C4-4-R and TEC2016-76465-C2-1-R.