Feasibility Study of Practical AoA Estimation Using Compressed CSI on Commercial WLAN Devices

Wireless local area network (WLAN)-based localization is key for advanced indoor Internet-of-Things and embedded sensor applications. To further improve the accuracy of indoor localization, attention has been focused on WLAN-based indoor localization using channel-state information (CSI) in addition to the existing information provided by received signal strength (RSS). For easy and low cost installation of wireless sensing, wireless sensing based on standardized protocols and commercial WLAN devices, such as IEEE 802.11ac and IEEE 802.11ax, is necessary. Much previous research used the angle of arrival (AoA), but commercial WLAN devices cannot use directly for AoA estimation. Therefore, we propose a practical method for estimating the AoA to solve four problems: 1) compressed CSI, which cannot be used for AoA estimation directly, 2) the antenna wireline, in which the phase changes depending on the length of the wireline, 3) the antenna spacing, in which the distance between antennas places a restriction on AoA estimation, and 4) antenna individuality, in which the antennas used in actual MIMO communication have different characteristics. We implemented the proposed method on IEEE 802.11ac devices and evaluated it in a lecture room and shield tent. The results indicate that the proposed method can estimate AoA with an average error of 9.1° and reduce the estimation error by 85.4 % compared with a straightforward approach.

We focus on the WLAN-based estimation of the angle of arrival (AoA), which is a key piece of information of WLAN-based indoor localization, because it allows the existing WLAN infrastructure to acquire the AoA of WLAN packets. ArrayTrack is the first system to consider AoA derivation in the WLAN infrastructure and a proof-ofconcept test was demonstrated using the Rice WARP FPGA platform [34]. Several WLAN-based wireless localization techniques [14], [15], [17]- [20] have been developed using channel state information (CSI) on IEEE 802.11n [35] with the CSI tool [36], [37]. In particular, Ubicarse [14], SpotFi [15], Chronos [17], MonoLoco [18], and UAT [19] can successfully acquire the AoA from the CSI tool for wireless localization. For example, Chronos [17] performs decimeter-level localization by combining the AoA and time of flight of wireless signals.
The method of this paper advances WLAN-based AoA estimation a step further toward wide deployment as it allows commercial WLAN devices such as IEEE 802.11ac and IEEE 802.11ax to realize highly accurate AoA estimation. WLAN-based AoA estimation in previous studies was based on IEEE 802.11n (WLAN 4), CSI tool, Intel 5300 WLAN cards, Atheros chipsets, and WARP. To deploy WLANbased localization in real environments, we must address how commercial WLAN devices such as IEEE 802.11ac (WLAN 5) and IEEE 802.11ax (WLAN 6) can yield AoA data.
To achieve AoA estimation on commercial IEEE 802.11ac and IEEE 802.11ax devices, we must solve the following four problems. 1) Compressed CSI problem: The AoA estimation system has to recover phase information from the CSI compression format standardized in IEEE 802.11ac and IEEE 802.11ax. 2) Antenna wireline problem: The phase changes depending on the length of the wireline between each antenna and the analog-to-digital (AD) converter. 3) Antenna spacing problem: It is desirable that the distance between adjacent antennas be λ/2 where λ is the wavelength of radio waves. However, the distance in several commercial WLAN devices is larger than λ/2 to improve the multiple-input multiple-output (MIMO) performance because of the need for a low spatial correlation among antennas. 4) Antenna individuality problem: It is desirable that the characteristics of the signals received by each antenna be the same. However, the antennas used in actual MIMO communication have different characteristics due to the effects of housing, circuit boards, and installation environments.
Details on the aforementioned four problems are provided in Section III.
To solve these four problems, this paper proposes the first AoA estimation method for IEEE 802.11ac and IEEE 802.11ax WLAN devices. The compressed CSI problem is solved by restoring the right singular matrix, which contains relative phase information among antennas, from compressed CSI. The antenna wireline problem is solved by calibrating the right singular matrix based on the right singular matrix for an AoA of zero degrees. The antenna spacing problem is solved by using a heuristic algorithm that estimates the number of times the phase is rotated by the AoA and distances between adjacent antennas that are larger than λ/2. The antenna individuality problem is solved by using another heuristic algorithm that selects a combination of antennas to reduce the AoA estimation error. Our solutions are detailed in Section IV. We evaluate the accuracy of the proposed method in a lecture room and shield tent. Compared with a straightforward approach, the proposed method reduced the AoA estimation error by 85.4 %.
The main contributions of the paper are as follows: • We propose an AoA estimation method that is not for any specific Wi-Fi devices. whereas that of the straightforward approach is approximately 62.6 • in a lecture room. The average calculation time of the proposed method is approximately 0.6 s. The rest of this paper is organized as follows. Section III introduces compressed CSI in IEEE 802.11ac and IEEE 802.11ax devices and identifies the problems created by using commercial WLAN devices for AoA estimation. Section IV describes the solutions based on the proposed method for the problems identified in Section III. Section V evaluates the performance of the proposed method in both a shield tent and a lecture room. Section II discusses related work, and finally, Section VI concludes this paper.

II. RELATED WORK
This paper is related to wireless sensing and AoA estimation.

A. WIRELESS SENSING
Studies on wireless sensing can be classified into three categories: 1) Direct use of a physical layer signal 2) Use of raw CSI 3) Use of compressed CSI following IEEE 802.11ac Many studies on wireless sensing through the direct use of a physical layer signal have explored the many possibilities of wireless sensing, such as for device localization [38], [39], device-free user localization [40]- [42], device proximity detection [43], emotion recognition [44], gesture recognition [45], hidden electronics detection [46], human detection through walls [47]- [49], in-body device localization [50], respiratory monitoring [51], [52], heart rate monitoring [51], RF imaging, [48], [53], [54], and touch sensing [55]. For example, Vital-Radio [51] successfully tracked the breathing and heart rates of multiple users simultaneously even when the users were 8 m away from the wireless sensing device. However, the above methods have a deployment cost problem due to the need for special wireless devices such as USRP and millimeter-wave (mmWave) transceivers.
The proposed method is classified as wireless sensing using compressed CSI. As described in III-C, compressed CSI is already applied in commercial IEEE 802.11ac and IEEE 802.11ax devices. Studies on compressed-CSI-based wireless sensing have recently begun. They include position estimation [71] and object detection [72].

B. AOA ESTIMATION
AoA estimation has been studied for military radars since the 1950s. In recent years, several studies on AoA estimation have examined its use in various applications such as beamforming to improve the performance of mobile communications and indoor localization. For example, Ar-rayTrack [12], Ubicarse [14], ToneTrack [16], SpotFi [15], Chronos [17], MonoLoco [18], UAT [19], and LocAP [20] have been employed for indoor localization, the authors of [73], [74] improved the throughput by using beamforming in massive MIMO for mmWave, and BreathTrack [75] has been employed for the tracking of human breath.
Two types of AoA estimation exist: those that use the received signal strength indicator (RSSI) and those that use phase. RSSI-based AoA estimation utilizes multiple RX antennas: the AoA is estimated by calculating the RSSI differences among the antennas. For example, ALRD [76] estimates the AoA using the fact that the difference in RSSI between antennas increases as the AoA increases from 0 • . However, it is difficult to improve the accuracy of AoA estimation using RSSI when the influence of multipath propagation is large, as is true in indoor environments.
Phase-based AoA estimation uses the phase difference acquired by multiple antennas as described in Section III-A. Phase-based AoA estimation assumes that the distance between a TX antenna and an RX antenna is infinity, and all RX antennas in the same array have the same the AoA. Most of the existing studies on AoA estimation [14], [15], [17]- [20], [77]- [80] assume that the antenna arrays are linear, equally spaced, and that the distance between adjacent antennas is less than or equal to λ/2. Various methods have been proposed for estimating the AoA using phase, such as minimum variance distortionless response, MUSIC, and the estimation of signal parameters via rotational invariance techniques. However, this previous research is only available for 802.11n. These methods cannot be uses on commercial WLAN devices directly. Even if these methods are used, the compressed CSI, antenna wireline, antenna spacing, and antenna individuality problems described in Section III need to be addressed when using commercially available IEEE 802.11ac devices to estimate AoA. Figure 1 illustrates the basis of AoA estimation using radio waves, where M is the number of antennas, θ is the AoA, and d is the antenna spacing. In Figure 1, all antennas form a uniform linear array with an equal spacing of d between adjacent antennas. When a radio wave transmitted from a TX antenna is received by multiple RX antennas, the path of the radio wave differs at the RX antenna depending on the AoA. As the phase observed at each RX antenna depends on the path length, the AoA can be estimated using the phase difference among the RX antennas. If the TX antenna is sufficiently far from the RX antennas, we can assume that all the RX antennas receive the radio waves transmitted from the TX antenna at the same AoA. If all AoAs are equal, the phase difference between RX antenna i and RX antenna 1 can be expressed as follows.

A. BASIS OF AOA ESTIMATION
where h i is the phase difference between RX antennas i and 1 (i = 2, 3, · · · , M ), f is the frequency of the radio wave, c is the speed of light, and d(i − 1) sin(θ) is the radio path difference yielded by the distance d(i − 1) between antenna i and antenna 1.
The CSI matrix at an arbitrary subcarrier can be expressed as follows when CSI is used in MIMO transmission in VOLUME 4, 2016 WLAN communication.
where M is the number of RX antennas, and N is the number of TX antennas. CSI * ,1 , which is the CSI from the 1st TX antenna to M RX antennas, is expressed as: where Θ is the phase of RX antenna 1 and a m is the amplitude of RX antenna m. h i , which is the observed phase difference between RX antenna 1 and RX antenna i, is expressed as follows.
>From Equation (1) and Equation (4), we can estimate θ using the phase difference among the RX antennas, as d, f , and c are known.

B. CHALLENGES FOR AOA ESTIMATION USING IEEE 802.11AC AND IEEE 802.11AX WLAN DEVICES
The following four problems must be solved for the practical deployment of AoA estimation on IEEE 802.11ac and IEEE 802.11ax WLAN devices.

C. COMPRESSED CSI PROBLEM
Compressed CSI is a CSI feedback method specified in IEEE 802.11ac [81]. Two types of CSI feedback methods exist: implicit feedback and explicit feedback. Compressed CSI is classified as an explicit feedback method and it cannot be employed for AoA estimation directly because it contains only compressed information. Note that the CSI assumed in this paper has a center frequency offset and sampling frequency offset corrected by the preamble signals specified in WLAN. Figure 2 shows the frame sequence for acquiring compressed CSI. The frame sequence is a type of WLAN communication between an access point and a user device. First, the access point transmits a null data packet announcement (NDPA) frame and a null data packet (NDP) frame to the user device. Second, the user device calculates compressed CSI from the NDP. Finally, the user device transmits compressed CSI to the access point. Compressed CSI is calculated using singular value decomposition (SVD) and a Givens rotation on the CSI matrix [35]. The SVD of CSI is expressed as: where U is a left singular matrix, S is a diagonal matrix with singular values of CSI, and V is a right singular matrix. Compressed CSI is the angle information ϕ, ψ, which corresponds to V compressed using a Givens rotation.
We can acquire as many as V subcarriers.
The following equation represents the relationship between matrix V and angle information ϕ, ψ calculated through a Givens rotation.
D k is a diagonal matrix expressed as follows: G l,k (ψ) is a Givens rotation matrix expressed as where I k−1 is a (k − 1) × (k − 1) identity matrix, and I M ×N is an identity matrix in which zeros are inserted as the missing elements if N ̸ = M . An example of data reduction by compressed CSI is as follows. Let us assume that there are 4 TX antennas, 2 RX antennas, and 52 subcarriers. To extract the CSI, first input the obtained compressed value of the CSI into Equations (7) and (8). Next, the CSI is restored by inputting the calculated value into Equation 6. To extract the CSI, first input the obtained compressed value of the CSI into Equations (7) (4,2) (6,4) (7,5) (9,7) Bits of ( , )   (8). Next, the CSI is restored by inputting the calculated value into Equation (6).
To investigate the amount of data reduction, this study compares the data size of compressed CSI with that of the CSI matrix. The CSI matrix is composed of the signal-tonoise ratio (SNR) and CSI information. The SNR is given as 8 bits per RX antenna. The CSI information contains the amplitude and I/Q signals per subcarrier. The amplitude is 3 bits. The I/Q signals are multiplied by the number of TX antennas and the number of RX antennas, and each I signal and Q signal is 8 bits. Therefore, the total data size of the CSI matrix is 8 Compressed CSI is composed of the SNR and angle information. The SNR is 8 bits per RX antenna. When the transmitter has four antennas and the receiver has two antennas, the angle information is 5 ϕ and 5 ψ. The number of quantization bits of ϕ and ψ differs between the singleuser (SU) and multi-user (MU) feedback types. For SU type feedback, the numbers of quantization bits of ϕ and ψ are (4, 2) or (6,4). From the above conditions, the total data size of compressed CSI is 8×2+(6×5+4×5)×52 = 2616 bits. Thus, compressed CSI compresses the data size to approximately 40 % compared with the original CSI matrix. The importance of compressed CSI will increase with the increase in the number of antennas expected in future wireless communication. Figure 3 shows simulation results of quantization error. We simulated the effect of quantization error on AoA estimation accuracy. For IEEE 802.11ac, the representation bits of ϕ and ψ are (4,2), (6,4), (7,5), and (9,7) [81]. The quantization error of phase difference between antennas is about 11.3 degrees when the representation bits of ϕ and ψ are (4,2) bits. Similarly, it is about 2.8, 1.4, 0.35 degrees, respectively. The AoA estimation error is almost the same as the above phase difference error. We cannot ignore the effect of quantization error, but its effect is relatively smaller than what this paper will show in Section III. The phases of CSI observed at the RX antennas should follow Equation (3). However, each phase changes depending on the length of the wireline from each RX antenna to the AD converter. Therefore, CSI ′ * ,n , which reflects the effects of the length of the wireline between the antenna and the AD converter in Equation (3), is determined as: where τ m (m = 1, 2, . . . , M ) is the phase change dependent on wireline length.

E. ANTENNA SPACING PROBLEM
When a phase is obtained from a radio wave, the correct value of the phase difference can be obtained only when the distance between the RX antennas is less than or equal to λ/2 where λ is the wavelength of the radio wave. The range of h i , which is the phase difference acquired from CSI, is expressed as follows.
We can also express h i as shown in Equation (11) by combining Equation (1) and Equation (10).
However, the distance between the antennas in commercial WLAN devices is made larger than λ 2 to lower the spatial correlation and thus improve the MIMO transmission performance. Figure 4 shows an example of an access point. The λ of 5 GHz is approximately 6 cm. The distance between the access point antennas is larger than 3 cm. When the distance between the RX antennas exceeds λ 2 , the phase difference between adjacent antennas sometimes exceeds 360 • , and the phase difference is truncated to fit between −π and π, making it impossible to estimate AoA correctly.
For example, suppose f is 5.2 GHz, d is 4 cm, and the number of RX antennas is 4. Figure 5(a) shows the correct values of the phase when the AoA is 30 • and the phase of Antenna4 is 0 rad. The vertical axis is the phase and the horizontal axis is the subcarrier index. The phase difference is approximately 2.17 rad. If the phase of Antenna4 is 0 rad, the correct phases of Antenna3, Antenna2, and Antenna1 are approximately 2.17, 4.34, and 6.51 rad, respectively. However, as CSI is a complex number, the acquired phase is truncated between −π and π. Figure 5(b) shows the phase acquired from CSI. If the phase of Antenna4 is 0 rad, the phase of Antenna3 is approximately 2.17 rad, but the phase of Antenna2 is truncated to approximately −1.92 rad, and the phase of Antenna1 is also truncated to approximately 0.26 rad. Figure 5(c) shows a multiple signal classification (MUSIC) spectrum using the phase of Figure 5(b). A peak appears at 30 • , but peaks also appear at 89 • , −30 • , and −80 • .

F. ANTENNA INDIVIDUALITY PROBLEM
Antenna arrays for AoA estimation such as radars are designed assuming that the receiving conditions of the antennas are as equal as possible. However, because of the requirements of MIMO transmission as described in Section III-E, each RX antenna in actual WLAN devices should be expected to have a different receiver condition. Consequently, the phase acquired by each RX antenna in WLAN devices may be individually affected by housing, circuit boards, and the installation environment. When the AoA is estimated using RX antennas with largely different receiving conditions, the estimated value may be significantly different from the correct value.

A. OVERVIEW
To solve the four problems described in Section III, we propose a practical AoA estimation method; this paper focuses on IEEE 802.11ac and IEEE 802.11ax WLAN devices. The proposed method estimates AoA with the following four procedures, which correspond to the four problems described in Section III.
1) Convert the angle information in compressed CSI to the right singular matrix V, which includes the relative phase information among the antennas. 2) Calibrate the right singular matrix V using V at 0 • , which is expected to be known before factory shipment. 3) Calibrate phases using a brute force algorithm to equalize all the phase differences. 4) Select the optimal combination of antennas with kurtosis and the number of peaks using the MUSIC spectrum.

B. SOLUTION FOR COMPRESSED CSI PROBLEM
To solve the compressed CSI problem described in Section III-C, AoAac/ax restores the relative phase difference information from compressed CSI. Note that proposed method assumes that the distance between the transmitter and the receiver is infinity, and the angles of departure (AoD) and AoA are equal. On the basis of the above assumptions, the proposed method utilizes the right singular matrix V including the relative phase information of the CSI from the TX antennas to the RX antennas.
First, the proposed method calculates V through the substitution of ϕ and ψ into Equations (6), (7), and (8). The right singular matrix V is expressed as follows: As we assume that AoD is equal to AoA, the column vector of right singular matrix V is regarded as the relative phase difference from N TX antennas to M Rx antennas. To use V for AoA estimation, the proposed method uses V * ,1 , which is the first column of V as follows based on Equation (5).
where A n (n = 1, . . . , N ) is the amplitude of each element of V. The proposed method extracts h V,i , which is the phase difference between TX antenna 1 and i (i = 2, 3, · · · , N ), using Equation (16) as follows:

C. SOLUTION FOR ANTENNA WIRELINE PROBLEM
To solve the antenna wireline problem described in Section III-D, the proposed method calibrates the right singular matrix V using the offset acquired by V at 0 • before factory shipment. The calibration involves four steps: 1) Acquire the right singular matrixV when the AoA is 0 • before factory shipment. 2) Extract the phase from matrixV. 3) Use the extracted phase to calculate phase offset τ N with the average of the phase at each subcarrier. 4) Calibrate the right singular matrix V using τ N during actual AoA estimation.
Before factory shipment, the proposed method acquires a singular matrixV when the AoA is 0 • , andV * ,1 is formulated as follows: The proposed method calculates τ m as follows: Using Equations (19) and (17), h 0DC,i , which is the calibrated phase difference, is formulated as follows.

D. SOLUTION FOR ANTENNA SPACING PROBLEM
To solve the antenna spacing problem described in Section III-E, the proposed method performs phase restoration and frequency adjustment as follows.

PHASE RESTORATION
When d > λ 2 , the phase restoration is performed using Equation (21).
where h PR,i is the phase after restoration, h 0DC,i is the phase before restoration, and r i is the number of phase rotations. h PR,i is the correct phase difference including the phase rotation between RX antenna 1 and RX antenna i when h 0DC,i is extracted as described in Sections IV-B and IV-C. Note that r i is an unknown number. From Equation (1), the relationship between h i+1 and h i is expressed by Equation (22).
When all the distances between adjacent antennas are equal, we obtain Equation (23) using Equation (21) and Equation (22).
where r max is the maximum number of phase rotations.
r max is calculated with the non-truncated and maximum phase difference between antenna 1 and antenna N . The non-truncated phase difference between TX antenna 1 and TX antenna N is given by Equation (24).
When θ is 90 • , r N is equal to r max . Therefore, Equation (26) is expressed as Equation (27).
As r max is an integer, we obtain Equation (28).
represents the least integer greater than or equal to

FREQUENCY ADJUSTMENT
Even if the phase restoration is performed as described above before AoA estimation, MUSIC treats the phase difference internally as a complex number and truncates the phase difference between −π and π again. To solve the re-truncation problem, the proposed method adjusts the frequency so that r max = 0 using Equation (29).
where h FA,i is the adjusted phase, h PR,i is the phase restored using Equation (21), f raw is the frequency at which the compressed CSI is sent, and f adjust is the frequency to adjust the phase in order to truncate the phase difference between −π and π. By combining r max = 0 and Equation (28), f adjust is calculated using Equation (30).

E. SOLUTION FOR ANTENNA INDIVIDUALITY PROBLEM
To solve the antenna individuality problem described in Section III-F, the proposed method runs a heuristic algorithm to select the combination of antennas that achieves precise AoA estimation. Algorithm 1 shows the proposed antenna selection algorithm. H is a set of calibrated phases as described in Section IV-D, N is the number of TX antennas, s (∈ S) is the MUSIC spectrum, andŝ is the spectrum yielded by the best antenna combination. The function "combinations(H, i)" returns a set of combinations of i phases from H, and it corresponds to nchoosek() in MATLAB and itertools.combination() in Python. The function "findpeaks(s)" returns the number of peaks in MUSIC spectrum s and corresponds to findpeaks() in MAT-LAB and scipy.signal.argrelmax() in Python. The function "kurtosis(s)" returns the kurtosis of MUSIC spectrum s and corresponds to kurtosis() in MATLAB and scipy.stats.kurtosis() in Python. First, Algorithm 1 uses the number of peaks in the MUSIC spectrum for the antenna selection. The presence of multiple peaks indicates that the AoA estimation error is large. When there is only one peak in the MUSIC spectrum, Algorithm 1 uses the kurtosis of the MUSIC spectrum for antenna selection. Figure 6 shows an example of antenna selection. Figure 6(a) is the observed phase of the right singular matrix V for an AoA of 10 • . AoA estimation using the phases of Antenna3 and Antenna4 is more accurate than that gained by using the phases of four antennas. Figure 6(b) is the MUSIC spectrum estimated using the phase of all antennas, and Figure 6(c) is the MUSIC spectrum estimated using    Figure 7 and Figure 9 represents an access point, and PC represents a user device.
In the shield tent, the access point and user device were surrounded by radio wave absorbers. The distance between the access point and the user device was 2.5 m. The access point was an NTT EA-7HW04AP1ES, which supports IEEE 802.11ac, and the user device was a Panasonic Let's note CF-SZ6. There were no obstacles between the access point and the user device. Table 1 shows the evaluation parameters. The radio frequency was 5.2 GHz, the number of antennas at the access point was 4, the antenna spacing of the access point AP PC To evaluate the effect of each solution presented in Section IV for the proposed method, we implemented and evaluated four methods using Python: 1) V: AoA estimation using the MUSIC algorithm and the right singular matrix V restored from the compressed CSI described in Section IV-B. 2) V+0DC: AoA estimation adding 0 • calibration (0DC), which is described in Section IV-C, to the above V. 0DC is a phase calibration method . 3) V+0DC+PRFA: AoA estimation adding phase restoration and frequency adjustment (PRFA), which are described in Section IV-D, to the above V+0DC. 4) Proposed: This is the proposed approach. AoA estimation adding antenna selection (AS), which is described in Section IV-E, to the above V+0DC+PRFA. AoA was estimated on a MacBook Pro Mid 2017 (MPXT2J/A). Figures 11 and 12 show the average AoA estimation errors in the shield tent and lecture room, respectively. The vertical axis is the average AoA estimation error at each angle, and the horizontal axis is the ground truth of the AoA.

B. ACCURACY
In the shield tent, the average AoA estimation errors at all angles of V, V+0DC, V+0DC+PRFA, and the proposed method were approximately 53. that the proposed method achieved the highest accuracy. Additionally, the AoA estimation in the shield tent was more accurate than that in the lecture room. The evaluation results include those obtained in different environment results such as when AP was rotated from −80 • to 80 • . The proposed method remained effective for AoA estimation even in actual environments or AP was rotated. However, at some angles, V+0DC+PRFA was more accurate than the proposed method. For example, at −40 • in the lecture room, the proposed method had an average error of approximately 7.8 • , whereas V+0DC+PRFA had an average error of approximately 3.3 • . Figures 13 and 14 show the average variances of the estimated AoA in the shield tent and lecture room, respectively. The vertical axis is the average variance of AoA estimation at each angle, and the horizontal axis is the ground truth of the AoA.
In the shield tent, the average variances at all angles of V, V+0DC, V+0DC+PRFA, and the proposed method were approximately 668.95, 109. 25 7. In contrast, the average AoA estimation error of the proposed method in the lecture room at 10 • was approximately 9.1 • , but the variance of the proposed method in the lecture room at 10 • was approximately 0.2. We believe that the proposed method yielded an error offset for some unknown reason. We think that the antenna directional and the antenna accuracy of the devices may have affected the AoA estimation error. Then, we evaluated the existing AoA estimation in the same environment. Figure 15 shows the cumulative frequency (CDF) of the proposed method and SpotFi [15]. The vertical axis is the CDF, and the horizontal axis is the AoA estimation error. The median AoA estimation errors of the proposed method in shield tent and lecture room were 7.0 • and 7.2 • , respectively. The median AoA estimation errors of SpotFi in the shield tent and lecture room were 40.5 • and 42.0 • , respectively. From Figure 15, the previous AoA estimation methods cannot solve the problems described in Section III, while the proposed method can. Figure 16 and Figure 17 show the computation times of AoA estimation in the shield tent and lecture room, respectively. The vertical axis is the computation time for AoA estimation, and the horizontal axis is the AoA ground truth. From the figures, we can observe that V, V+0DC, V+0DC+PRFA, and the proposed method calculated the AoA within 1 s, regardless of the AoA ground truth. The average computation times at all angles of V, V+0DC, V+0DC+PRFA, and the proposed method in the shield tent were approximately 0.18, 0.24, 0.31, and 0.50 s, respectively. The average computation times at all angles of V, V+0DC, V+0DC+PRFA, and the proposed method in the lecture room were approximately 0.16, 0.19, 0.26, and 0.46 s, respectively. Additionally, the highest computation cost was observed for the antenna selection algorithm described in Section IV-E. Furthermore, the computation time of MUSIC was neither short nor stable and depends on the propagation path.

VI. CONCLUSION
We proposed a practical method for successfully estimating AoA from the compressed CSI specified by IEEE 802.11ac and IEEE 802.11ax. The proposed method advances the current research toward wide deployment because it can estimate AoA using commercially available IEEE 802.11ac and IEEE 802.11ax WLAN devices without CSI tools such as the Atheros CSI tool, Intel 5300 NIC, or Atheros 802.11n chipsets. This method solves four problems with AoA estimation using compressed CSI and estimates AoA with an average error of 9.1 • . The results of this study not only indicate that we could estimate AoA from compressed CSI but also the possibility of expanding current CSI-tool-based wireless sensing into wide deployment. We believe that the use of compressed CSI will contribute to a future where deploying WLAN access points means making a platform that provides both communication and sensing. Our future work will exploit the channel-state information of multiple links and multiple antennas to improve the AoA estimation accuracy.
TAKASHI WATANABE (S'83-M'87) is a Professor of Graduate School of Information Science and Technology, Osaka University, Japan. He received his B.E., M.E. and Ph.D. degrees from Osaka University, Japan, in 1982, 1984 and 1987, respectively. He joined Faculty of Engineering, Tokushima University as an assistant professor in 1987 and moved to Faculty of Engineering, Shizuoka University in 1990. He was a visiting researcher at University of California, Irvine from 1995 through 1996. He has served on many program committees for networking conferences, IEEE, ACM, IPSJ, IEICE (The Institute of Electronics, Information and Communication Engineers, Japan). His research interests include mobile networking, ad hoc networks, sensor networks, ubiquitous networks, intelligent transport systems, specially MAC and routing. He is a member of IEEE, IEEE Communications Society, IEEE Computer Society as well as IPSJ and IEICE.
SHUNSUKE SARUWATARI received the Dr. Sci. degree from the University of Tokyo in 2007. From 2007 to 2008, he was a visiting researcher at the Illinois Genetic Algorithm Laboratory, University of Illinois at Urbana-Champaign. From 2008 to 2012, he was a research associate at RCAST, the University of Tokyo. From 2012 to 2016, he was an assistant professor at Shizuoka University. He has been an associate professor at Osaka University since 2016. His research interests are in the areas of wireless networks, sensor networks, and system software. VOLUME 4, 2016