---
title: 'FIND: Fine Indoor Wi-Fi Localization'
url: https://www.emergentmind.com/topics/find
type: topic
---

# FIND: Fine Indoor Wi-Fi Localization

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 [2103.05329]. 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 [2103.05329]. 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 [2103.05329]. 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 [2103.05329]. 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 [2103.05329].

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 [2103.05329]. A motorized turntable carries the four-antenna array, and the platform angle \(\theta\) is controlled and logged to provide ground-truth DoA [2103.05329].

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 [2103.05329]. 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 [2103.05329]. 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 [2103.05329].

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 [2103.05329]. 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 [2103.05329]. 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 [2103.05329]. The retained active subcarriers are \(k=-122,\dots,-1,1,\dots,122\) for each chain \(i=1,\dots,4\) [2103.05329]. This yields a dense multi-antenna, multi-subcarrier snapshot of the channel for each packet.

The SNR estimate, denoted \(\gamma\), plays two roles in the system. First, it supports quality filtering, allowing algorithms to down-weight or discard packets with low \(\gamma\). Second, it can be used as a weight in covariance estimation when forming the sample covariance matrix \(\widehat{R}\), so that higher-quality snapshots contribute more strongly [2103.05329].

For each method evaluated in the paper, the input is a \(4\times N\) matrix of snapshots \(X\), where each snapshot is a \(4\times 1\) vector of frequency-domain samples on one subcarrier, or a value averaged across subcarriers [2103.05329]. 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 [2103.05329]. The common steering-vector model assumes a uniform linear array with inter-element spacing \(d\) and carrier wavelength \(\lambda\), with steering vector
\[
a(\theta) = [1, e^{-j2\pi(d/\lambda)\sin\theta}, e^{-j2\pi(2d/\lambda)\sin\theta}, e^{-j2\pi(3d/\lambda)\sin\theta}]^\top.
\]
This model maps azimuth \(\theta\) to the phase progression expected across the four antennas [2103.05329].

Conventional Beamforming, identified in the paper with Bartlett beamforming, uses the power spectrum
\[
P_{\rm CBF}(\theta) = a(\theta)^{H}\,\widehat{R}\,a(\theta),
\]
with
\[
\widehat{R} = \frac{1}{N}\sum_{n=1}^N x_n x_n^{H}.
\]
Its complexity is reported as \(O(G\cdot M^2)\) per search over \(G\) candidate angles and array size \(M=4\), and its accuracy is described as limited by a broad main lobe, with resolution of about \(30^\circ\) on four elements [2103.05329].

MUSIC uses the eigendecomposition
\[
\widehat{R} = E_s \Lambda_s E_s^{H} + E_n \Lambda_n E_n^{H},
\]
where \(E_n\) spans the noise subspace, of dimension \(M-1\) for one source [2103.05329]. Its pseudospectrum is
\[
P_{\rm MUSIC}(\theta) = \frac{1}{a(\theta)^{H}E_nE_n^{H}a(\theta)}.
\]
The complexity is \(O(M^3 + G\cdot M^2)\), and the paper characterizes its angular resolution as high, down to a few degrees even on small arrays [2103.05329].

ESPRIT avoids angular scanning. The array is partitioned into two overlapping subarrays of size \(M-1=3\), forming \(X_1\) and \(X_2\) from rows \(1\dots3\) and \(2\dots4\) of \(X\), and the shift-invariance equation \(X_2 \approx \Phi X_1\) is solved by least squares [2103.05329]. Eigen-decomposition of \(\Phi\) yields phase factors \(e^{-j2\pi(d/\lambda)\sin\theta}\). Its complexity is \(O(M^3)\) once, with no angle scanning, i.e. \(O(1)\) at runtime for the scan stage, and its single-source accuracy is described as similar to MUSIC but orders faster at runtime [2103.05329].

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 \(\phi_i(k)\) caused by hardware, including feedlines and RF chains [2103.05329]. 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 \(\theta_0\), for example \(0^\circ\) [2103.05329]. Under this configuration, CSI measurements \(H_i^{\rm cal}(k)\) are collected for all RF chains and subcarriers.

For each RF chain \(i\) and subcarrier \(k\), the phase offset is defined as
\[
\phi_i(k) = \arg[H_i^{\rm cal}(k)] - \arg[a_i(\theta_0,k)],
\]
where
\[
\arg[a_i(\theta_0,k)] = -2\pi(i-1)(d/\lambda)\sin\theta_0.
\]
The calibration coefficient is then
\[
c_i(k)=e^{-j\phi_i(k)}.
\]
Subsequent packets are corrected by
\[
H_i^{\rm corr}(k) = H_i^{\rm raw}(k)\cdot c_i(k).
\]
After calibration, the per-chain phase responses are aligned so that only propagation-induced phase differences remain [2103.05329].

The paper reports that Figure 2 shows nearly constant \(\phi_i\) across different array positions in the anechoic chamber after this procedure [2103.05329]. 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 \(\theta\) spans from \(-90^\circ\) to \(+90^\circ\) in \(5^\circ\) steps, corresponding to 37 positions, and approximately 80,000 frames are collected, around 2,000 per angle [2103.05329]. In the classroom laboratory, \(\theta\) spans from \(-60^\circ\) to \(+60^\circ\) in \(5^\circ\) steps, corresponding to 25 positions, and approximately 300,000 frames are collected, around 12,000 per angle, with mild multipath [2103.05329]. In both cases, the turntable logs the ground-truth angle [2103.05329].

For each packet, the dataset stores raw I/Q of all preamble fields, calibrated CSI \(H_i^{\rm corr}(k)\), packet SNR \(\gamma\), and true \(\theta\) [2103.05329]. The details section also describes the open dataset as approximately 380k packets [2103.05329]. 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 [2103.05329].

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 [2103.05329].

| Algorithm | Anechoic Median / 90% | Classroom Median / 90% |
|---|---:|---:|
| CBF | \(12^\circ\) / \(25^\circ\) | \(18^\circ\) / \(40^\circ\) |
| MUSIC | \(3^\circ\) / \(7^\circ\) | \(6^\circ\) / \(15^\circ\) |
| ESPRIT | \(4^\circ\) / \(9^\circ\) | \(8^\circ\) / \(18^\circ\) |

Figure 4 is reported to plot the full CDFs of \(|\theta_{\rm est}-\theta_{\rm true}|\), demonstrating that MUSIC consistently outperforms the other methods in both controlled and multipath conditions, at the cost of higher computational load [2103.05329]. 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 [2103.05329].

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 [2103.05329]. 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 [2103.05329].

## 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 [2103.05329]. Second, precise DoA estimation can enable Reconfigurable Intelligent Surfaces controllers to steer reflected beams toward mobile users [2103.05329]. 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 [2103.05329]. Finally, the released dataset and calibration data are presented as a research tool for algorithmic comparisons under identical channel conditions [2103.05329].

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 [2103.05329]. 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 [2103.05329].

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 [2103.05329].

Source: https://www.emergentmind.com/topics/find