FIND: Fine Indoor Wi-Fi Localization

• FIND is a fine indoor localization system that uses Wi-Fi access points and a four-antenna SDR prototype to estimate signal direction of arrival in real time.
• It integrates full preamble capture, raw I/Q data processing, and a calibration method to correct hardware-induced phase shifts, ensuring consistent channel state information.
• Experimental evaluations using methods like MUSIC and ESPRIT show superior angular resolution in both anechoic and classroom settings, enabling effective DoA estimation.

Searching arXiv for the specified FIND paper and closely related indoor localization / Wi-Fi DoA work to ground the article. FIND is a fine indoor localization system that uses Wi-Fi Access Points to estimate the Direction of Arrival (DoA) of Wi-Fi signals, implemented as a software-defined-radio prototype that receives Wi-Fi frames in the 80 MHz band with four antennas and extracts data in both frequency and time domains to calculate DoA of Wi-Fi signals in real time (Khorov et al., 2021). It is presented as a prototype that retrieves from frames all preamble fields in the time domain, Channel State Information, and signal-to-noise ratio, and it is accompanied by a calibration method for constant phase shifts between receiving paths caused by hardware imperfections, together with calibration data and datasets gathered in an anechoic chamber and in a classroom (Khorov et al., 2021). In this form, FIND occupies a dual role: a real-time measurement system for Wi-Fi angle estimation and a research instrument for comparing DoA algorithms under identical acquisition conditions.

1. System definition and hardware architecture

FIND is built around an NI USRP-2955 SDR receiver with four RF channels, denoted RX0 through RX3, sharing a common LO (Khorov et al., 2021). Its antenna subsystem is a uniform linear array of four omnidirectional Wi-Fi antennas, spaced at half-wavelength for the 2.4 GHz band, approximately $6.25$ cm in the current prototype, while the hardware nominally supports up to $6$ GHz (Khorov et al., 2021). The system operates on an 80 MHz Wi-Fi channel in IEEE 802.11ac VHT mode and captures the full set of 242 VHT subcarriers (Khorov et al., 2021).

The computational pipeline is divided between an onboard FPGA and a host PC running LabVIEW 2020. The FPGA implements preamble detection, coarse frequency offset correction, and buffering of I/Q samples, whereas the host handles CSI computation, SNR estimation, calibration, and DoA processing (Khorov et al., 2021). A motorized turntable carries the four-antenna array, and the platform angle $\theta$ is controlled and logged to provide ground-truth DoA (Khorov et al., 2021).

A defining design choice is full-preamble capture. FIND demodulates and stores the I/Q samples of all Legacy preamble fields—L-STF, L-LTF, and L-SIG—together with the VHT extension, namely VHT-SIG-A, VHT-STF, and VHT-LTF (Khorov et al., 2021). From the VHT-LTF field, the system computes fine-grained channel estimates on all 242 data subcarriers for each of the four RF chains, and during the L-STF and L-LTF periods it computes per-packet SNR by comparing known training symbols to received samples (Khorov et al., 2021). The paper states that, by offloading packet detection and frequency-offset correction to the FPGA, the system sustains line-rate 80 MHz capture and CSI output at hundreds of packets per second, enabling practical real-time DoA estimation (Khorov et al., 2021).

This combination of SDR hardware, synchronized multi-channel reception, and host-side processing suggests that FIND was designed not merely to estimate a single angle but to expose multiple signal representations relevant to subsequent algorithmic work.

2. Signal representations and processing pipeline

The time-domain pipeline begins when the FPGA detects the short-training field, L-STF, and aligns the receiver to the packet start (Khorov et al., 2021). Coarse CFO is removed by correlating repeated L-STF symbols, and the full I/Q trains of L-LTF and VHT-STF are then streamed to the host for applications that require raw time-domain data (Khorov et al., 2021). The explicit retention of raw preamble fields distinguishes FIND from systems that only preserve already-processed channel estimates.

In the frequency domain, each VHT-LTF symbol, consisting of two OFDM symbols, is transformed by FFT to produce per-subcarrier channel estimates

$H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$

where $Y_i(k)$ is the received symbol on subcarrier $k$ at RF chain $i$, and $X_{\rm ref}(k)$ is the known training sequence (Khorov et al., 2021). The retained active subcarriers are $k=-122,\dots,-1,1,\dots,122$ for each chain $i=1,\dots,4$ (Khorov et al., 2021). This yields a dense multi-antenna, multi-subcarrier snapshot of the channel for each packet.

The SNR estimate, denoted $6$0, plays two roles in the system. First, it supports quality filtering, allowing algorithms to down-weight or discard packets with low $6$1. Second, it can be used as a weight in covariance estimation when forming the sample covariance matrix $6$2, so that higher-quality snapshots contribute more strongly (Khorov et al., 2021).

For each method evaluated in the paper, the input is a $6$3 matrix of snapshots $6$4, where each snapshot is a $6$5 vector of frequency-domain samples on one subcarrier, or a value averaged across subcarriers (Khorov et al., 2021). This representation places the four-element array geometry at the center of subsequent DoA estimation.

3. Array model and DoA estimation methods

FIND evaluates three common DoA estimators on its four-element array and 80 MHz Wi-Fi signal: Conventional Beamforming, MUSIC, and ESPRIT (Khorov et al., 2021). The common steering-vector model assumes a uniform linear array with inter-element spacing $6$6 and carrier wavelength $6$7, with steering vector

$6$8

This model maps azimuth $6$9 to the phase progression expected across the four antennas (Khorov et al., 2021).

Conventional Beamforming, identified in the paper with Bartlett beamforming, uses the power spectrum

$\theta$0

with

$\theta$1

Its complexity is reported as $\theta$2 per search over $\theta$3 candidate angles and array size $\theta$4, and its accuracy is described as limited by a broad main lobe, with resolution of about $\theta$5 on four elements (Khorov et al., 2021).

MUSIC uses the eigendecomposition

$\theta$6

where $\theta$7 spans the noise subspace, of dimension $\theta$8 for one source (Khorov et al., 2021). Its pseudospectrum is

$\theta$9

The complexity is $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$0, and the paper characterizes its angular resolution as high, down to a few degrees even on small arrays (Khorov et al., 2021).

ESPRIT avoids angular scanning. The array is partitioned into two overlapping subarrays of size $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$1, forming $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$2 and $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$3 from rows $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$4 and $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$5 of $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$6, and the shift-invariance equation $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$7 is solved by least squares (Khorov et al., 2021). Eigen-decomposition of $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$8 yields phase factors $H_i(k) = \frac{Y_i(k)}{X_{\rm ref}(k)},$9. Its complexity is $Y_i(k)$0 once, with no angle scanning, i.e. $Y_i(k)$1 at runtime for the scan stage, and its single-source accuracy is described as similar to MUSIC but orders faster at runtime (Khorov et al., 2021).

The algorithmic comparison in FIND is therefore structured around a familiar trade-off: lower resolution and lower sophistication for CBF, higher angular resolution for MUSIC, and scanning-free estimation for ESPRIT.

4. Calibration of hardware-induced phase offsets

A central contribution of FIND is a calibration method that removes per-chain, per-subcarrier constant phase offsets $Y_i(k)$2 caused by hardware, including feedlines and RF chains (Khorov et al., 2021). The calibration measurement is performed in an anechoic chamber using a single-antenna, line-of-sight transmitter placed directly facing the array at a known angle $Y_i(k)$3, for example $Y_i(k)$4 (Khorov et al., 2021). Under this configuration, CSI measurements $Y_i(k)$5 are collected for all RF chains and subcarriers.

For each RF chain $Y_i(k)$6 and subcarrier $Y_i(k)$7, the phase offset is defined as

$Y_i(k)$8

where

$Y_i(k)$9

The calibration coefficient is then

$k$0

Subsequent packets are corrected by

$k$1

After calibration, the per-chain phase responses are aligned so that only propagation-induced phase differences remain (Khorov et al., 2021).

The paper reports that Figure 1 shows nearly constant $k$2 across different array positions in the anechoic chamber after this procedure (Khorov et al., 2021). This suggests that the model treats the dominant hardware distortion as a stable additive phase term indexed by RF chain and subcarrier, rather than a rapidly varying impairment. A plausible implication is that the calibration can serve as a reusable front-end correction for algorithmic comparisons performed later in controlled and mildly multipath environments.

5. Dataset design and experimental protocol

FIND provides two principal measurement scenarios. In the anechoic chamber, the platform angle $k$3 spans from $k$4 to $k$5 in $k$6 steps, corresponding to 37 positions, and approximately 80,000 frames are collected, around 2,000 per angle (Khorov et al., 2021). In the classroom laboratory, $k$7 spans from $k$8 to $k$9 in $i$0 steps, corresponding to 25 positions, and approximately 300,000 frames are collected, around 12,000 per angle, with mild multipath (Khorov et al., 2021). In both cases, the turntable logs the ground-truth angle (Khorov et al., 2021).

For each packet, the dataset stores raw I/Q of all preamble fields, calibrated CSI $i$1, packet SNR $i$2, and true $i$3 (Khorov et al., 2021). The details section also describes the open dataset as approximately 380k packets (Khorov et al., 2021). The paper states that all calibration data, as well as the gathered dataset with various DoA in an anechoic chamber and in a classroom, are provided to facilitate further research in indoor localization, intelligence surfaces, and multi-user transmissions in dense deployments (Khorov et al., 2021).

The combination of controlled anechoic measurements and classroom measurements with mild multipath gives the dataset a comparative structure. It allows identical algorithms to be studied first under near-ideal propagation and then under a more realistic indoor channel. Because the same acquisition platform exposes time-domain preamble fields, CSI, and SNR, the dataset is also suitable for methodologies that do not rely exclusively on one representation.

6. Quantitative results and comparative behavior of DoA estimators

The paper summarizes performance in terms of median and 90th-percentile absolute DoA errors for the three estimators in both scenarios (Khorov et al., 2021).

Algorithm	Anechoic Median / 90%	Classroom Median / 90%
CBF	$i$4 / $i$5	$i$6 / $i$7
MUSIC	$i$8 / $i$9	$X_{\rm ref}(k)$0 / $X_{\rm ref}(k)$1
ESPRIT	$X_{\rm ref}(k)$2 / $X_{\rm ref}(k)$3	$X_{\rm ref}(k)$4 / $X_{\rm ref}(k)$5

Figure 2 is reported to plot the full CDFs of $X_{\rm ref}(k)$6, demonstrating that MUSIC consistently outperforms the other methods in both controlled and multipath conditions, at the cost of higher computational load (Khorov et al., 2021). ESPRIT is described as similar to MUSIC for a single source but orders faster at runtime, while CBF remains the least accurate because of its broad main lobe and limited resolution on a four-element array (Khorov et al., 2021).

These results establish a clear ranking within the paper’s evaluation setup: MUSIC gives the lowest angular errors, ESPRIT follows closely with lower runtime complexity at inference, and CBF trails both in the anechoic chamber and in the classroom (Khorov et al., 2021). The change from the anechoic chamber to the classroom also indicates a degradation consistent with mild multipath, though all three methods remain operational within the tested angular ranges.

A common misconception in this area is that full-band CSI alone is sufficient for a fair comparison of Wi-Fi DoA estimators. FIND’s design complicates that assumption. Because the platform stores all preamble fields in the time domain, calibrated CSI, and per-packet SNR, it makes available several forms of packet-level evidence that may affect estimator behavior or preprocessing choices (Khorov et al., 2021).

7. Applications, significance, and scope

The paper identifies several application domains. First, by fusing DoA from multiple APs running FIND, client devices can be localized with decimeter-level accuracy indoors, supporting asset tracking or augmented reality (Khorov et al., 2021). Second, precise DoA estimation can enable Reconfigurable Intelligent Surfaces controllers to steer reflected beams toward mobile users (Khorov et al., 2021). Third, in dense MU-MIMO Wi-Fi, access points can spatially separate clients more effectively if they know the precise incoming angles, improving throughput in 802.11ax/be (Khorov et al., 2021). Finally, the released dataset and calibration data are presented as a research tool for algorithmic comparisons under identical channel conditions (Khorov et al., 2021).

Within the scope defined by the paper, FIND is not introduced as a complete indoor positioning stack. It is an SDR-based platform for fine indoor localization through real-time DoA estimation, with an emphasis on acquisition fidelity, calibration, and reproducible comparison of algorithms (Khorov et al., 2021). Its significance lies in combining full 80 MHz CSI, time-domain samples, per-packet SNR, and a calibration method in a single publicly documented prototype (Khorov et al., 2021).

This suggests two broader implications. First, reproducibility in Wi-Fi localization research depends not only on publishing algorithms but also on releasing synchronized raw measurements, calibration procedures, and ground truth. Second, the architecture of FIND makes it relevant beyond single-user localization, because the same measurement primitives can inform work on intelligence surfaces and multi-user transmissions in dense deployments, which the paper explicitly names as downstream research areas (Khorov et al., 2021).