Localization based on standard wireless LAN infrastructure using MIMOOFDM channel state information
 Tanee Demeechai^{1}Email author,
 Pratana Kukieattikool^{1},
 Thang Ngo^{2} and
 Tae Gyu Chang^{2}
https://doi.org/10.1186/s136380160645x
© Demeechai et al. 2016
Received: 15 July 2015
Accepted: 31 May 2016
Published: 10 June 2016
Abstract
An indoor localization method using multiple input, multiple output orthogonal frequency division multiplexing (MIMOOFDM) channel state information (CSI) is proposed as a method that can be implemented on wireless local area networks of a current standard without affecting their protocol structures and that does not require a training process for adaptation to indoor environments. In the proposed method, the CSI obtained by the MIMOOFDM receivers of all access points upon successful reception of a data packet from a mobile terminal (MT) is processed in order to determine the location of the MT. The proposed method analyzes the multipath effect that appears in the CSI as multiple complex sinusoids by using the matrix pencil method in order to extract only terms that are contributed by direct paths from the MT to the access points. Localization is achieved using the directpath terms on the basis of the maximum likelihood principle.
Keywords
Indoor localization MIMOOFDM Channel state information Multipath propagation Matrix pencil method Maximum likelihood principle1 Introduction
Indoor localization is a hot research topic in the field of wireless communication owing to its capability to provide a wide range of locationbased services for increasingly ubiquitous smart mobile devices. For indoor environments, wireless local area network (WLAN) technology based on the IEEE 802.11 standards is widely employed around the world for providing data connections to mobile devices. Therefore, this paper focuses on indoor localization methods based on WLAN technology. Specifically, the purpose of this paper is to propose a localization method that can be implemented using the infrastructure of a WLAN without affecting its protocol structure. The proposed method will simultaneously exploit and be constrained by WLAN characteristics whereby WLANs are trending toward asynchronous networks of multiple input, multiple output orthogonal frequency division multiplexing (MIMOOFDM) access points (APs) [1].
Although many studies have investigated localization [2–6], it is not straightforward to apply their results to the problem of interest without requiring dedicated infrastructure or affecting the WLAN protocol structure. A few localization methods based on the IEEE 802.11 standards have been proposed in the literature [7–9] and implemented commercially. However, most of these methods use the received signal strength indicator (RSSI) as data for location determination [7, 8]. The use of the RSSI usually requires a disincentive process of measurementbased training for adaptation to everchanging environments because the RSSI is very sensitive to both largescale shadowing and smallscale multipath fading prevalent in indoor environments. Recently, a method that uses channel state information (CSI) available through a network interface card [10] has been proposed [9]. Compared to the RSSI, the CSI is less sensitive to multipath fading. Nevertheless, the method proposed in [9], which is based on singleantenna APs, requires a disincentive measurementbased training process. The method proposed in the present paper uses the CSI obtained by the MIMOOFDM receiver of each AP as data for location determination, without any measurementbased training process for adaptation to everchanging environments. The details of the proposed method are described in subsequent sections.
2 Proposed localization method
According to the proposed method, the CSI obtained by the MIMOOFDM receivers of all APs upon successful reception of a data packet from a mobile terminal (MT) is processed in order to determine the location of the MT. We assume that the MT uses only one antenna, i.e., one spatial stream, for transmitting the data packet for localization. Therefore, the packet’s preamble part for estimating the CSI by the OFDM receiver of each AP will consist of only one VHTLTF (see [1], Fig. 22–4). It may be noted that, while the standard [1] defines four OFDM signal models, classified according to the bandwidth as the 20, 40, 80, and 160MHz models, the duration of the VHTLTF symbol equals 4 μs including the 800ns guard interval for all the models.
The localization method involves removing multipath reflection components in the CSI and searching for the best location on the basis of a likelihood metric. Because removing multipath reflection components in the CSI is an important step, the characteristics of indoor multipath propagation and the CSI are discussed first; then, the algorithm of the proposed method is described in detail.
2.1 CSI from MIMOOFDM receivers as location information
This uncertainty of t _{ q } is another source of variation of the CSI, which must be properly treated when the CSI is used for localization.
where \(\phantom {\dot {i}\!}g_{\textit {\text {n,q}}}=h_{\textit {\text {n,q}}}e^{j2\pi f_{0}t_{\textit {\text {n,q}}}}\). We may note from (6) that for an AP antenna, the estimated CFR as a function of k is the sum of multiple sinusoids plus noise. In addition, it is the relationship between ϕ _{0,m,q },1≤m≤M _{ q }, characterizing the sinusoids of the shortest paths to the array elements, that will contain the location information of the MT, if the shortest paths are the direct paths.
2.2 Proposed algorithm
The proposed algorithm consists of two major steps. The first step is to obtain CFRs that are effective for localization by minimizing irrelevant contributions from multipath reflection and the uncertainty of the OFDM time synchronizer. The second step is to search for the best location on the basis of a likelihood metric.
2.2.1 Obtaining an effective CFR
where w _{ m,q } denotes the average of w _{ k,m,q } across k. Note that the effective CFR consists of the contribution from the shortest path and additive noise. Therefore, the effective CFR will carry information of the MT location if the shortest path is actually the direct path. Hence, the main assumption of the proposed algorithm is that direct paths between the MT and the APs exist with considerable amplitudes compared to the amplitude of the additive noise.
In the proposed algorithm, the effective CFRs for an AP are obtained by first obtaining reflectionrich CFRs for contiguous subcarriers from the CSI, then obtaining parameters of the sinusoids in the reflectionrich CFRs, and finally transforming the reflectionrich CFRs to obtain the result.
2.2.1.1 Obtaining a reflectionrich CFR for contiguous subcarriers
According to the underlying standards [1], a CFR can be obtained from the CSI only for used OFDM subcarriers that are discontiguous. The proposed algorithm obtains the CFR for contiguous subcarriers by simply using linear interpolation to compute the CFR for unused subcarriers whenever they are between two used subcarriers. The linear interpolation method is clearly simple, but we consider whether it can effectively preserve the slowoscillation characteristics of the shortestpath sinusoid. Hence, according to the standard signal models [1], the resulting CFR is contiguous for −K≤k≤K, where the values of K for the 20, 40, 80, and 160MHz signal models are 28, 58, 122, and 250, respectively.
2.2.1.2 Obtaining parameters of sinusoids
A sinusoid as a function of k, expressed by a e ^{ j ω k }, is characterized by its frequency ω and its complex amplitude a. To estimate the frequencies of all the sinusoids in the CFRs of the qth AP, we adopt the matrix pencil method (MPM) [12, 13] because this constant amplitude multiplesinusoid estimation problem is equivalent to the directionofarrival estimation problem with fully coherent sources, which is directly addressed by the MPM. Moreover, the MPM method has been shown to be the most suitable method among various superresolution methods [13].
Here, the value of L will be selected on the basis of the simulation results for this range.
where S ^{R} is obtained from S by setting all the singular values in S that are smaller than ρ s _{max} to zero, where ρ is a small positive parameter (0<ρ<1), and s _{max} is the maximum singular value in S. Hence, N _{U} equals the rank of the resulting S ^{R}. A suitable value of ρ depends on how often and by how much the directpath amplitude is lower than the strongestpath amplitude. It also depends on the MPM performance in separating the paths from others. In addition, it can depend on the additive noise level. However, the noiselevel effect may be minimal in practice because the algorithm always obtains the CSI from a detected data packet for which the signal must be of a detectable quality. As the effect of ρ on the algorithm performance is so complex analytically, the value selected in this paper will be based on a simulation study.
Then, the frequency values of the N _{U} sinusoids are obtained from Y ^{R} as follows. First, the eigenvalues of \(\mathbf {Y}_{1}^{+}\mathbf {Y}_{2}\) are evaluated, where (·)^{+} denotes the MoorePenrose pseudoinverse, and Y _{1} and Y _{2} are matrices of size (2K−L+1)×M _{ q } L, obtained by deleting the last and first rows of Y ^{R}, respectively. Then, the N _{U} frequency values ω _{0},ω _{1},.., \(\omega _{N_{\mathrm {U}}1}\) are obtained as the angles of the obtained N _{U} eigenvalues.
2.2.1.3 Transforming a reflectionrich CFR
2.2.2 Search for the best location
is computed for every location of interest, and the best location ζ ^{∗} is obtained as \(s(\zeta ^{*})=\max _{\zeta } s(\zeta)\).
2.3 Some remarks
2.3.1 AOAbased localization
We may note that the location metric (21) is a sum of metrics, each of which is contributed by the data of an AP, i.e., \(s(\zeta)= \sum _{\forall q} s_{q}(\zeta)\), where \(s_{q}(\zeta)=\sum _{\forall m} G_{\textit {\text {m,q}}}e^{j(2\pi /\lambda) r_{\textit {\text {m,q}}}^{(\zeta)}}^{2}\). The metric contributed by the data of an AP has an interesting property that may be described as follows. Note that the metric s _{ q }(ζ) can be equivalently expressed by \(s_{q}(\zeta)=\sum _{\forall m} G_{\textit {\text {m,q}}}e^{j(2\pi /\lambda) [r_{\textit {\text {m,q}}}^{(\zeta)}r_{1,q}^{(\zeta)}]}^{2}\). Then, since \(r_{\textit {\text {m,q}}}^{(\zeta)}r_{1,q}^{(\zeta)},\forall m\) will not considerably change if ζ moves along on the same AOA to the qth AP, s _{ q }(ζ _{1})≈s _{ q }(ζ _{2}) if ζ _{1} and ζ _{2} are along similar AOAs to the qth AP. Then, we can conclude that the metric contributed by the data of an AP contains information of the AOA to the AP.
The usefulness of the effective CFR obtained by (16) may be noted as follows. Thus far, we have assumed that the direct path exists and all paths also have distinctive delays. However, paths can actually have indistinguishable delays. Then, a problem could arise when some scattered paths of considerable amplitudes have delays close to the delay of the direct path, while they also have AOAs considerably different from that of the direct path. In this case, the effective CFR will possibly contain also the AOA information of the scattered paths that can degrade the location estimation of the proposed algorithm. Therefore, the proposed algorithm requires significant scattered paths with delays close to the delay of the direct path to also have AOAs close to the AOA of the direct path. This could be realistic if the placement of the AP antenna array is not close to any significant reflective materials. Such placement also seems to be a good practice for other AOAbased localization systems.
2.3.2 Effect of MT velocity
It may be interesting to assess the effect of the MT velocity on the performance of the proposed algorithm. In this regard, we consider that there are two issues caused by MT movement that may affect the performance. One issue is the location shift of the MT that may change the real multipath configuration of the channel during the OFDM training symbol. The other issue is the Doppler shift of the directpath term in the estimated CSI. The location shift should be of no concern because the duration of the training symbol is just 4 μs, which means that a moving speed of 900 km/h is required to observe a location shift of 1 mm. The 1mm shift does not seem to significantly change the multipath configuration, and the 900km/h speed is infeasible in indoor environments.
Regarding the Doppler shift, it should be noted that movement of the MT during a packet transmission would cause a directiondependent spectral shift of the radiating wave. Hence, the spectral shift of one transmission path arriving at the receiver could be different from the spectral shifts of other paths. This effect is not as simple as that of the local oscillator frequency offset between the transmitter and the receiver, where the effect is equivalent to causing identical spectral shifts for all paths. However, the directiondependent spectral shifts could only change the phases of the sinusoidal terms in (6) and therefore could not affect the frequency estimation of the MPM. In addition, the spectral shift of the directpath term could only rotate g _{0,q } in (6) through a certain angle and therefore could not change the MT location information in ϕ _{0,m,q },1≤m≤M _{ q }.
However, the Doppler shift is known to cause intercarrier interference in OFDM data detection. It will also affect the CSI estimation that is conventionally based on detecting the data carried by the training symbol. For a successfully detected data packet, we can expect that such interference is insignificant. Therefore, in this paper, we assume that the effect is negligible. Nevertheless, we believe that it merits a detailed analysis that should be conducted in a separate study.
2.4 CRLB for twodimensional systems with lineartype arrays
We may use (27) and (30) to compute the CRLB as a function of g _{0,q },1≤q≤Q, which are random variables. In this paper, by considering such variability, the CRLB is then obtained by averaging the computed CRLBs across the simulated values of {g _{0,q }1≤q≤Q}.
3 Numerical results and discussions
3.1 Multipath propagation model
In this paper, we estimate the performance of the proposed algorithm on the basis of computer simulation using statistical indoor channel models. In addition, because our algorithm is AOAbased, we require a relevant channel model to provide specifications of the AOA characteristics in addition to the power delay profile of the multipath. As we find that only the IEEE 802.11 TGn channel models [17] are available in detail and meet our requirements, we base our performance evaluation on only such models.
NLOS and LOS characteristics of models D and E of [17]
Model D  Model E  

Firsttap kfactor (dB)  NLOS  \(\infty \)  \(\infty \) 
LOS  3  6  
RMS delay spread (nm)  NLOS  50  99 
LOS  47  95  
Maximum delay spread (nm)  NLOS  390  730 
LOS  390  730 
However, we note that the described LOS model consists of LOS and NLOS parts, with the first tap of the NLOS part being set to have the same delay as (but arbitrarily different AOA from) the LOS. This seems to be unrealistic if the placement of the AP antenna array is not close to any significant reflective materials. Such placement seems to be also a good practice for other AOAbased localization systems. Assume that such placement has been done successfully for every array, although absorptive materials may be required in some cases. Then, it would be more realistic if a scattered path with a delay close to that of the LOS also had its AOA statistically close to that of the LOS. Accordingly, we modify the TGn channel models for our purpose by (i) setting the mean AOA of the NLOS first tap to equal the AOA of LOS and (ii) introducing a new parameter σ _{0} as the AS of the NLOS first tap. The impact of this parameter on the algorithm performance will be studied by simulation.
The TGn channel models include six model subtypes with RMS delay spread in the range of 0 to 150 ns. We use the LOS models D and E in this paper because according to [18], the associated delay spreads are representative of typical office environments for model D and typical large open spaces and office environments for model E. In addition, such environments are expected to be targets of a wide range of indoor locationbased services. The characteristics of the two models in terms of the firsttap kfactor, the RMS delay spread, and the maximum delay spread (\(t_{N_{\mathrm {P}}1,q}t_{0,q}\)) are summarized in Table 1, while additional details can be found in [17]. Note that each LOS model is multipathrich while having a direct path that is nondominant because changing from the NLOS model to the LOS model of the same subtype can just slightly reduce the RMS delay spread of the channel.
3.2 Common assumptions and search method
In this paper, the search for the best location on the basis of the metric of (21) is conducted in three rounds. In the first round, the metrics are computed for regular grid points over the 400 m^{2} square region with a gridpoint spacing of 1 m, and the firstround optimum location is then determined. In the (n+1)th round, the metrics are computed for regular grid points over the (\({l_{n}^{2}}\)) m^{2} square region centered at the nth round optimum location with a gridpoint spacing of l _{ n }/20, and the (n+1)thround optimum location is then determined, where l _{ n }/2 equals the gridpoint spacing in meters for the nth round. Note that the gridpoint spacing for the last round, representing the effective resolution of the search space, is 10^{−2} m.
3.3 Selection of algorithm parameters
The performance of the proposed algorithm depends on its parameters L and ρ. We realize that obtaining optimal values of the parameters may require a separate elaborate study. In this paper, we only select certain values for demonstrating the basic working performance of the proposed algorithm and for comparing the proposed algorithm with previous methods. This is done for each standard signal model [1] as follows.
First, we select a tentative value of L to be the middle value of the range (10). Therefore, the selected values for the 40, 80, and 160MHz OFDM signal models are 49, 102, and 209, respectively.
Then, we iterate the simulation experiments by fixing the value of ρ to the tentative one and performing simulations for evaluating the performance in terms of L. According to the results, the performance does not vary significantly with L. Therefore, the tentative values of L and ρ stated above are adopted in this paper.
3.4 Implications of σ _{ 0 } and CSI interpolation
3.5 Comparison with other methods
The performances of the proposed method, the RSSIbased method [8], and the CSIbased method [9] were compared under the same statistical channel conditions. The CSIbased method [9] and the RSSIbased method are similar but differ in terms of the observation data that they use. The RSSIbased method uses the RSSI as observation data, whereas the CSIbased method [9] uses a norm computed from the CSI as observation data. We will refer to the RSSIbased method [8] and the CSIbased method [9] as the RSSI method and the CSI norm method, respectively. Both methods require the localization algorithm to be trained before use or testing. In the training process, usually referred to as fingerprinting, the PDF of the observation data conditioned on the MT location is obtained from the training data for each reference location. In the use phase, the location is determined as a weighted average of the reference locations according to the observation data and the trained model. For the performance comparison, the LOS models D and E are used with the following simulation conditions. The MT transmitted power is 10 dBm, the AP receiver NF is 4 dB, and each LOS model has σ _{0}=4°. In addition, B=160 MHz and M=2. The MT locations for testing are rectangular grid points spanning the 400 m^{2} region with a gridpoint spacing of 1 m, except for the center points of the four antenna arrays. The set of reference locations for the RSSI and CSInorm methods is the same as the set of MT locations for testing. Because the RSSI and CSInorm methods assume observation data from a single antenna, the RSSI and CSInorm averaged across the antennas in the array are respectively used as the observation data for the two methods in this paper. The training data for each reference location consist of 500 independent samples of the observation data, while the test data for each grid point consist of 10 other independent samples.
3.6 Effect of infrastructure conditions
Localization performance in terms of B and M when the MT transmitted power is 10 dBm, expressed as rootmeansquare error in meters and also in percent maximal length of a straight line within the localization region
M=2  M=4  

B (MHz)  40  3.9 m; 13.79 %  2.8 m; 9.90 % 
80  2.0 m; 7.07 %  1.8 m; 6.36 %  
160  1.2 m ; 4.24 %  1.1 m ; 3.89 % 
It can be noted from Fig. 9 that the 90 % confidence level error bound, i.e., the error when the cumulativeprobability is 0.9, increases approximately from 1.2 to 1.6 and 3.5 m when the number of usable APs is reduced from 4 to 3 and 2, respectively. The performance seems to degrade steadily if the number of usable APs is greater than two. However, the performance with two APs is still better than the performances of the RSSI and CSInorm methods with four APs, as shown in Fig. 5, from which we may note that the 90 % confidence level error bounds are around 4.5 and 3.8 m for the RSSI and CSInorm methods, respectively. For the proposed method, the preferable number of usable APs seems to be three or greater, while having only two usable APs may still be viable in some applications.
Regarding the localization performance in terms of the MT location, it is interesting to note from Fig. 10 that the RMSE is locally large for locations on the line connecting the two usable APs. This can be explained by noting that the locations on such a line correspond to the case where the equivalent Fisher information matrix expressed in (30) is singular. Intuitively, the singularity indicates that the available information is not sufficient for estimation, i.e., the location information contribution in the observation data is not sufficient for deducing a location. Therefore, the localization performance in the singularity case here is extremely vulnerable to the AWGN. It may be noted from Figs. 11 and 12 that having more usable APs effectively relieves the singularity problem, especially for locations farther away from the two underlying APs. In contrast, having more usable APs is less effective in relieving the problem for locations close to an AP, possibly because the equivalent Fisher information matrix for such a location is largely dominated by only the contribution of that AP.
4 Recommendations for further study

Validation with real measurements: In this paper, the localization performance of the proposed algorithm was evaluated on the basis of statistical indoor channel models specifically obtained for benchmarking data communication systems. It is much more relevant to evaluate the performance on the basis of real measurements or a statistical indoor channel model specifically obtained from real measurements for benchmarking AOAbased localization systems. Therefore, performance validation with real measurements is very important.

Other superresolution methods: Estimating the frequencies of all the sinusoids in the CFRs plays a major role in obtaining an effective CFR for the proposed algorithm. Although the MPM is used in this paper because it directly addresses the problem of interest, we believe that other superresolution methods should also be studied in this regard.

Using a priori knowledge in estimation: In this paper, estimating the parameters of all the sinusoids in the CFRs plays a major role in obtaining an effective CFR. Such estimation has been performed without considering a priori knowledge about the parameters, i.e., their statistical models. Note that such knowledge may be used to improve the estimation performance in general, as discussed in [16]. Applying such knowledge to the proposed algorithm is an interesting direction for further study.

Optimal parameters for the algorithm: In this paper, the values of the algorithm parameters L and ρ were selected for simply demonstrating the basic working performance of the proposed algorithm. Actually, the optimal values could depend on variable conditions of the radio channel and infrastructure. These effects are also worthy of further study.

Problem of NLOS: In addition to bandwidth availability and multipleantenna configuration, an essential requirement for the proposed algorithm to work is the availability of LOS in the radio channel. In this regard, the availability required is just sufficient for triangulation. This requirement is the same as for the ultrawidebandbased localization regime [19, 20]. Several methods for mitigating the problem of LOS availability have been presented in the literature. These methods are based on the detection of channel condition. By applying the detection of channel condition, we may simply ignore an AP if the detection result declares unavailability of LOS. We could then expect performance degradation on the basis of the results shown in Fig. 9, or encounter an outage if the number of usable APs is less than two. We note that the signal processing results obtained using the proposed method are employed as observation data for the detection of channel condition. However, a detailed study of such detection is beyond the primary scope of the present paper and it is therefore recommended for future work.

AOA bias induced by diffraction: In the present study, the effect of diffraction caused by building components, such as walls, is ignored. If not properly managed, this effect may degrade the performance of the proposed algorithm by introducing a bias into the AOA of a direct path, as well as the performance of the ultrawidebandbased localization regime by introducing a bias into the time of arrival of a direct path. Therefore, further investigation is required to efficiently mitigate such a bias.

MT velocity effect: As discussed in Section 2.3.2, a detailed analysis of the effect of MT velocity on the localization performance should be carried out in a future study.

Simple way to obtain the effective CFR: Note that a _{ n,m } obtained using the proposed algorithm by solving (13) is an estimation of \(\phantom {\dot {i}\!}g_{\textit {\text {n,q}}}e^{j\phi _{\textit {\text {n,m,q}}}}\). Therefore, according to (7), a _{0,m } is also an estimation of G _{ m,q }. Then, it might be better to save computation by using a _{0,m } as G _{ m,q }, instead of obtaining G _{ m,q } from (16). This issue also requires further investigation in order to observe its possible effects on the localization performance.
5 Conclusions
A new localization method based on an asynchronous network of MIMOOFDM access points was proposed. This method can be implemented on WLANs of a current standard without affecting their protocol structures. The method involves first obtaining effective CFRs, in which irrelevant contributions from scattered paths and the uncertainty of the OFDM time synchronizer are minimal, and then searching for the most likely location. The proposed method does not require a training process for adaptation to everchanging environments. The availability of direct paths is sufficient for triangulation, as in the ultrawidebandbased localization regime. Further, significant scattered paths with delays close to the delay of the direct path are required to have AOAs close to the AOA of the direct path.
Declarations
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Authors’ Affiliations
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