Robust Fingerprint Localization Based on Massive MIMO Systems

Xiaojun Wang,Yijie Ren,Weiguang Sun,Xiaoshu Chen,2

1 National Mobile Communications Research Laboratory,Southeast University,Nanjing 210000,China

2 Purple Mountain Laboratories,Nanjing 210000,China

3 Frontiers Science Center for Mobile Information Communication and Security,Southeast University,Nanjing 210000,China

Abstract: Location-based services have become an important part of the daily life.Fingerprint localization has been put forward to overcome the shortcomings of the traditional positioning algorithms in indoor scenario and rich scattering environment.In this paper,a single-site multiple-input multiple-output(MIMO) orthogonal frequency division multiplexing(OFDM) system is modeled,from which an angle delay channel power matrix (ADCPM) is extracted.Considering the changing environment,auto encoders are used to generate new fingerprints based on ADCPM fingerprints to improve the robustness of the fingerprints.When the scattering environment has changed beyond a certain extent,the robustness will not be able to make up for the positioning error.Under this circumstance,an updating of the fingerprint database is imperative.A new fingerprint database updating algorithm which combines a new clustering method and an updating rule based on probability is proposed.Simulation results show the desirable performance of the proposed methods.

Keywords: massive multiple-input multiple-output;fingerprint extraction;robustness;database updating

I.INTRODUCTION

Location-based services have drawn great attention recently [1].Traditional positioning algorithms mainly includes angle of arrival(AOA),time of arrival(TOA),which can provide accurate positioning results in outdoor scenario[2–4].However,most activities of people are carried out in a complex environment now,which makes traditional localization algorithms tend to have poor performance because of the non-line-ofsight(NLOS)propagation and multipath effect[5].

To overcome the limitations of the traditional localization algorithms,fingerprint localization has drawn great attention [6].The main point of fingerprint localization is to transform the localization problem to a model recognition problem by mapping the location to the wireless channel characteristics.A fingerprint database can be set after the fingerprint extracting and collecting,then location can be calculated by matching algorithms.The typical system model of fingerprint localization is shown in Figure 1:

There are mainly two types of fingerprints.The first type is received signal strength (RSS) from access points,the second type is multipath characteristics,which mainly including channel state information(CSI),AOA,power delay profile(PDP).The fingerprint localization based on RSS was firstly used in Radar system [6].Then Horus improved the algorithm and acquired better positioning accuracy [7].Many other works have been done based on RSS later [8–12].A high-adaptability indoor localization(HAIL) approach was proposed based on RSS which has achieved high positioning accuracy [13].Localization based on RSS can be implemented simply with low-cost.But the RSS itself cannot overcome the multipath effect.As a result,the values of the fingerprint vector may vary a lot over the time,which reduces the positioning accuracy.Compared to RSS,the fingerprint based on multipath characteristic can make up for the shortcoming of the RSS [14,15],for it exploits the multipath effect instead of affected by it.In combination of massive MIMO [16,17],better performance can be achieved.A fast localization method was proposed based on massive MIMO,which has significantly saved the time of positioning while keeping certain accuracy[18].

In this paper,a single-site MIMO-OFDM system model is established.Fingerprints are extracted from the wireless channel and then new fingerprints are generated.When the scattering environment has changed to a certain extent,the fingerprint database will be updated according to certain updating rule.The major contributions of this paper are concluded as follows:

1)Three kinds of fingerprints are extracted from the wireless channel,and all three kinds have exploited the multipath effect and can be easily extracted.

2) To improve the robustness of the fingerprints,auto encoder(AE),denoising auto encoder(DAE)and denoising convolution auto encoder(DCAE)are used to generate new fingerprints based on the original fingerprints extracted from wireless channel.

3)In combination of the Euclidean distance and cosine distance,an updating rule based on probability is proposed.

4)Considering the characteristic of ADCPM,a new clustering method based on central AOA (CAOA) is proposed.

The rest of the paper is organized as follows.Section II shows the system model and the channel analysis.In Section III,fingerprints which possess stronger robustness are generated based on AE,and a fingerprint database algorithm is proposed as well.Simulation results are shown in Section IV and the conclusion is given in Section V.

II.MASSIVE MIMO CHANNEL MODEL

The base stations equipped withNtantennas are in the form of uniform linear array (ULA).The interval of antenna iss.Kusers are distributed randomly in the locating area andKsatisfiesNt >>K.The wireless signal propagates through the multipath channel to the base station.The propagation of the wireless signal is shown in Figure 2:

The channel impulse response associated with thepth path of thekth user can be calculated as:

whereap,k ∼CN(0,δp,k) represents the complex gain,φp,k ∈(0,π) represents the AOA,sp,krepresents the physical distance between the transmit antenna and the first receive antenna,e(φp,k)represents corresponding array respond vector andλcis the carrier frequency.e(φp,k)can be expressed as:

Define a phase-shift matrixV ∈CNt×Ntwhich satisfies:

through matrixV,the channel impulse response(CIR) including antenna domain features can be mapped to angle domain [19].Considering that the TOA of each path is different,the CIR of userkcan be calculated as:

whereτp,k=sp,k/vrepresents the TOA of each path andvrepresents light speed.

The channel frequency response (CFR) can be calculated by Fourier transform,which can be expressed as:

wherenp,k=modNcrepresents the propagation delay of thepth path,Ncrepresents the number of subcarriers,Tsrepresents sampling interval,Ngrepresents the number of the sampling points of cyclic prefixes andflrepresents thelth subcarrier.Thus the overall CFR matrix with dimension ofNt×Nccan be expressed as:

III.ROBUST FINGERPRINT LOCALIZATION

Considering the changing environment,robustness is an important factor of the fingerprint localization algorithm.The localization based on the massive MIMO systems is mainly affected by the multipath effect,which means the changes of the scattering environment will affect the positioning accuracy.In this section,ADCPM fingerprint will be extracted from the channel firstly,and then new fingerprints will be extracted to improve the robustness.And to deal with bigger changes of scatters,a fingerprint database updating algorithm is proposed to guarantee the robustness of the localization algorithm.

3.1 ADCPM Fingerprint Extraction

Fingerprint localization requires that the fingerprints extracted from instantaneous CSI should possess wide-sense stationary characteristic,which means a transformation to angle delay domain is needed in advance.The characteristic matrix of the response will be used as fingerprint[20].

Define the angle delay channel response matrix(ADCRM)as follows:

whereU ∈CNc×Ngrepresents unitary DFT matrix,[Zk]i,jrepresents the complex gain of theith AOA and thejth TOA of thekth user.V HandU∗Nc×Ngmap the space domain to the angle domain and delay domain separately.WhenNttends to positive infinity,the element in ADCRM is independent of each other.The statistical channel power of theith AOA andjth TOA is given as:

Considering the complexity of the complex matrix calculation,the ultima fingerprint ADCPM will be defined as the Hadamard product of ADCRM,which can be expressed as:

where⊙represents Hadamard product.Compared to CFR matrixHk,ADCPM makes a full-scale description of channel power,AOA and TOA,which is more suitable as fingerprint.

To reduce the storage burden of database,the fingerprint will be compressed using csr-matrix.The biggestMvalues will be taken and saved to the compressed matrix,which can be expressed as:

whererowiandcoliin the matrix represents the row and the column of non-zero value separately,andvalueirepresents the value of non-zero value.Mis decided by the compression ratio and satisfies:

ADCPM fingerprint shows different features in angle domain and delay domain.Thus,new fingerprints can be extracted separately from corresponding domains,which are named as mean angle channel power vector(MACPV)and mean delay channel power vector(MDCPV).

The MACPV is given by:

and the MDCPV is given by:

whereFrepresents ADCPM matrix,Fang ∈R1×Ntrepresents average channel power vector of angle domain andFdel ∈R1×Ngrepresents average channel power vector of delay domain.The distribution is shown as follows:

where the X axis in the figures represent the angle domain and delay doman separately.Figure 3 shows that fingerprints which are close to each other physically tend to have similar average channel power distribution in angle domain.But the MDCPV does not have the same property as is shown in Figure 4.Moreover,the dimension of MACPV is only decided by the number of antennas,which can reduce the storage burden and the time of matching.Thus MACPV is more suitable as the fingerprint for the following processing.

3.2 Robust Fingerprint Extraction

ADCPM fingerprint can show good performance when the scattering environment is constant,but if the scattering environment is changing,the average positioning accuracy(APE)will be affected as is shown in Figure 5.

To improve the robustness of the fingerprints,further process is necessary.Fingerprints can be processed by many methods,of which neural network is the most widely used.Study[21]has shown the great potential of neural network in processing fingerprints.Thus,neural network is introduced in this paper.

AE is a widely used model of unsupervised learning [22],which can copy the input to the output and then reconstruct the representation by compressing the input to a hidden space representation.Considering the training sample dataset Dn={(x1,t1),··· ,(xn,tn)},where x∈Rdvecandtis the corresponding label.Assuming thatDnis sampled from unknown distributionq(X,T)which satisfies independently identically distribution.Usingxas input,the mapping can be calculated as:

whereW ∈Rdvec′×dvecrepresents the weight vector of the network,brepresents the corresponding bias parameters,s(·) represents nonlinear active function and vectoryis the extracted fingerprint.In this paper,sigmoid function and relu function are used as active function.The expression of sigmoid and relu are given in Eq.(15)and Eq.(16).

After getting vectory,mapping it back to the reconstruction vectorz ∈Rdvec.The mapping can be calculated as:

whereW′andb′represent the corresponding parameters in the inverse mapping separately,which usually satisfiesW′=WT.Thus each training samplexican be mapped toyiand reconstructed tozi.

The parameters are optimized through average reconstruction error(ARE),which is given by:

whereL(·)represents the loss function,which usually adopts square error.The parameters will be optimized and updated in combination with stochastic gradient descent(SGD).

Normally,the AE is in the undercomplete state,which means it can be made to learn the most representative feature by training incomplete representations.After applying the AE to the MACPV fingerprint,ycan be used for matching algorithm in the following process.

However,AE can only learn certain mapping functions,which does not solve the problem of the changing scattering environment.Thus DAE is used in this section to simulate the scenario that the scatters are decreasing.In the mapping process of DAE,for arbitrary inputx,disrupt the input with probabilityPc,which means to randomly selectdvec·Pcelements and make their values remain the same while the others are assigned to 0.Such operation can simulate the scenario that a part of signals fails to arrive at the base station when a part of scatters disappears.To guarantee the randomness,w0will be regenerated each time before the training.The structure of DAE is shown in Figure 6:

The neuron with value equals 1 represents the input of biasbandb′.The mapping fromxtocan be calculated as:

where⊙represents entry-wise and it works on every element in the vector.w0is a one-dimension vector,the value is assigned to 1 with a probability ofPc,and 0 with a probability of 1-Pc.After getting output,calculate the reconstructed outputzusing Eq.(14)and Eq.(17),and update the parameters using Eq.(18).After the processing above,define vectoryas DAE fingerprint.

Given that ADCPM fingerprint is a matrix with high dimension,if reconstruct the ADCPM fingerprint to a one-dimension vector and then import to AE or DAE model,too many parameters will be generated,which is bad for the training model.Convolution neural network (CNN) is widely-used in image classification and objective detecting [23],which can maintain the neighborhood relationship and the spatial locality in high levels.Because of the parameters sharing,data with high dimension can be processed by AE.Thus,another robust fingerprint will be extracted using DCAE[24].

Different from AE and DAE using one-dimension vector as input,DCAE uses matrix as input.Firstly input should be redefined asx,which satisfiesx ∈RNW×NH,whereNWandNHrepresent the dimension of row vector and column vector separately.Then initialize convolution kernels and corresponding bias.Thekth mapping can be calculated as:

where * represents two-dimension convolution operation,Wrepresents the parameter matrix of the convolution kernel.

After the mapping there should be a pooling operation to extract high-order local feature (usually maxpooling or ave-pooling).Max-pooling selects the biggest value while ave-pooling selects the average value in the receptive field.Max-pooling procedure is shown in Figure 7:

Pooling can keep the main feature while reduce the parameters and prevent over-fitting.In addition,corresponding location matrix should be recorded to restore the data to the original size by unpooling.Assume that thekth feature mapping by pooling ish′k,which will then be restored to the original size ofhkby zeropadding.The location of the biggest value stays the same.The new matrix through unpooling is recorded asy′k.The unpooling operation is shown in Figure 8:

Output matrixycan be calculated by deconvolutingy′k,which can be expressed as:

where the convolution kernel usually satisfies=WT.cis the corresponding bias andHrepresents feature mapping cluster.The loss function is calculated based on mean square error.To simplify the calculation,2·NH ·NWis imported to the denominator,which can be expressed as:

then derivative the loss function and update the parameters using SGD.

The CAE fingerprint model usually includes convolution layer,pooling layer,unpooling layer and deconvolution layer.Similarly to the random disturbing to the inputxin the DAE model,CAE fingerprint model can be transformed to DCAE fingerprint model.But different from DAE fingerprint,the input of DCAE is a two-dimension matrix,so the vector in Eq.(19)will be modified firstly.When the training is completed,ADCPM fingerprint will be imported to the DCAE model which then outputs a three-dimension matrixhk′.To reduce the computational complexity and compare with the ADCPM fingerprint more intuitively,hk′will be dimension-reduced as:

whereNumHrepresents the number of feature maps.hfpwill be the input fingerprint for matching,which is renamed as DCAE fingerprint.

3.3 Fingerprint Database Updating

When the scattering environment is changing,DCAE fingerprint can provide better positioning accuracy.However,as is shown above,if the scattering environment has changed to a certain extent,the positioning accuracy will decrease rapidly.Under this circumstance,the fingerprint database shall be updated,the fingerprints of certain reference points shall be recollected to assure the accuracy of the algorithm.

To update the fingerprint database,the criterion of the variation should be set firstly.Assume that the number of scatters before and after the change isNumbeforeandNumafterseparately.The change number of scatters satisfies:

For example,ifNumchange ≥60,then the fingerprint database needs to be updated,otherwise it does not.

Combine the two most common criterions of similarity,which are Euclidean distance and cosine distance,an updating rule based on probability is proposed to decide whether the fingerprint database needs to be updated.

Define the fingerprint distancedbefore and after the change of the environment as:

whereXandYrepresent the two-dimensional fingerprint matrix before and after the change of the scattering environment,∥·∥2represents 2-norm of the matrix.∆dis a small positive number to avoid the denominator to be zero.Theoretically,the similarity probability of the fingerprints is negatively associated with the difference.Thus the fingerprint distancedcan be mapped to corresponding probability value.The mapping function is given as:

whereλis a parameter which is set in advance.The mapping function satisfies probability distribution.The probabilitypis negatively associated withd.Corresponding probability of differentλis shown in Figure 9.

As is shown in the figure above,considering the distancedsatisfies 0≤d <1,whenλ=1/2,the correspondingpvaries in a small range.Whenλ=1/4,the curve is too steep,soλis set to 1/3 in this paper.

When given the fingerprints before and after the change of scattering environment,firstly calculate the similarity probability using Eq.(26).Then decide whether to update the reference point according to the threshold.Assume that theXcoordinate remains the same whileYcoordinate varies from-21m to-1m with an interval of 2m and the threshold set to 0.85.The similarity probability calculation result of ADCPM fingerprint is shown in Figure 10:

When the scatters are decreasing,more reference points will need to be updated.So if better positioning accuracy is needed,the threshold should be set to 0.9 or even bigger value.But if the cost of the algorithm is the primary,then the threshold should be smaller.

The criterion mentioned above is simple and direct.But to record the localization of each scatter will take much effort.To avoid such circumstance,the locating area is usually divided into serval parts in advance.Anchors are set in each sub-region to monitor the changes of scattering environment.Then the reference points in the sub-region are updated according to the similarity probability in Eq.(26).

K-means clustering is a statistical analysis technique which classifies the subjects into relatively homogeneous groups.It can divide the area into serval sub-regions,and makes the data in the same subregion as similar as possible,while the data in different sub-region would be as dissimilar as possible.The‘K’represents the number of the sub-regions,the‘means’represent the average value of the corresponding data in each sub-region.The K-means algorithm is highly efficient,but it will converge to a local optimal value affected by the abnormal data or the value ofK.Thus an area partition algorithm based on CAOA is proposed in this section to make up for the defects of K-means.

Considering that the scattering environment of the user is mainly determined by the nearest scatters around the user,the channel power after scattering is only distributed around few multipath components as is shown in Figure 3.

Define the CAOA of ADCPM fingerprint as:

and considering the angle spread,the range of actual CAOA will be[αm−∆α,αm+∆α],where ∆αrepresents maximum angle offset.For each reference point,calculate the CAOA and use the CAOA as corresponding cluster center.

The results of the clustering are saved in the form of key-value,where ‘key’ represents cluster center and‘value’ represents reference point.To update the fingerprint database,firstly select serval anchors in the corresponding sub-regions,then calculate the similarity probability.If the conditions of updating are satisfied,the fingerprints in the sub-region will be updated.The anchors are selected randomly in the sub-region,and the number of anchors satisfies:

whereαrepresents the density of anchors,Numsub−regionrepresents the number of reference points in the sub-region.The cost of update increases withαgetting larger,but it also increases the confidence.Calculate the similarity probability before and after the change with Eq.(24).Define the number of samples which satisfyPsub < Psub−thrasNumsub−update,wherePsub−thrrepresents the threshold of updating.WhenNumsub−updateis larger than a certain value,the conditions of updating are satisfied,which can be expressed as:

whereβrepresents the probability parameter which satisfies the conditions of updating.

Under the same simulation parameters,and with number of antennasNt=32,grid intervalsg=2m,compression ratioρ=100 .And for K-meansKis set to 7.The clustering results of K-means and CAOA are shown as follows:

As is shown in the figures,compared to the clustering based on K-means,the clustering based on CAOA has shown a clear pattern of distribution.It not only reflects the distribution of the fingerprint features,but also reflects the physical distribution.Additionally,clustering based on CAOA can save much time for it can perform clustering operations directly while Kmeans needs to update the cluster during the whole algorithm process.Combining the new clustering method and the updating rule,a new updating algorithm Central Angle of Arrival-Probability-based Fingerprint Update Criterion(CAOA-PFUC)is proposed,which can improve the efficiency of algorithm while maintain the positioning accuracy.

Table 1.Parameters of locating area.

IV.SIMULATIONS

A massive MIMO-OFDM single site system is established based on MATLAB to simulate the city wireless propagation scenario.The base station equipped with ULA is located in the center of the cell.The parameters of the locating area are shown in table 1:

In the massive MIMO systems,each link from the user to the base station is mainly determined by the nearest scatters surrounding the specified user.For each link,the complex gain and the delay can be calculated based on the tabulated distribution function[25].The AOA is calculated based on the locations of the scatters.For each sub path,the corresponding AOA and delay can be calculated by adding a small delay spread and an angle spread separately based on the first sub path.The parameters of the massive MIMO systems are shown in table 2[25,26]:

Three hidden layers are included in DAE fingerprint model.The corresponding number of neurons of each layer is 64,128 and 64,the training time is set to 1000,learning rate is set to 0.001,Pcis set to 0.65,and relu will be chosen as active function.

Table 2.Parameters of MIMO systems.

DCAE fingerprint model adopts double convolution-pooling operations to extract highorder feature representation.The mapping is based on 32 convolution kernels with the dimension of 3×3.The dimension reduction is based on max-pooling,after which the dimension will be (32,189,32).The training time is set to 150,learning rate is set to 0.001,Pcis set to 0.65,and relu will be chosen as active function.

Normalization will be done during the gradient back propagation.Min-max normalization will be adopted in this paper for it can maintain the sparsity of the matrix.The min-max normalization can be expressed as:

wherexmaxrepresents the maximum value of vectorx,andxminrepresents the minimum.

For matching algorithms,Knearest neighbor(KNN),weightedKnearest neighbor(WKNN),support vector regression (SVR) and gradient boosting tree(GBT)are adopted under the same simulation environment.kof the WKNN and KNN is set to 3.For the parameters of LGB,learning rate is set to 0.1,data sampling rate is set to 0.9,characteristic sampling rate is set to 0.9 and the number of leaf nodes is set to 120.Cubic polynomial is chosen as kernel function and the regularization parameter is set to 0.1.The APE is shown in Figure 13:

The figure above shows that WKNN has the best performance among the four algorithms with APE of 1.11m and 95% reliability for 2m accuracy.Thus WKNN will be used for fingerprint matching.

Table 3.APE of different fingerprints.

To simplify the model,only considering the scenario that the number of scatters decreases and setting the initial number of the scatters to 628.Use the parameters in table 2,and set the compression ratio to 100.The APE based on WKNN is shown in table 3:

Table 4.Simulation results.

As is shown in the table,when the reduction number is 0,MACPV has the best positioning accuracy.The features of the DAE fingerprint are global,which may lead to improper data transformation processing and thus reduce the positioning accuracy.Compared with ADCPM,MACPV fingerprint and DCAE fingerprint have higher positioning accuracy for MACPV keeps the high resolution while eliminating the randomness,while DCAE can extract high-order features while keeps the local features.

As the number of scatters is decreasing,DCAE fingerprint becomes the best fingerprint for positioning.The noise reduction model simulates the scenario by setting values to 0 randomly.Set the reduction number to 120,CDF figure based on for fingerprints above is shown in Figure 15,which confirms that DCAE fingerprint is of more robustness.

Assume that the decreasing number of scatters is 120,parameterα=0.2 andβ=0.6,other parameters are shown in table 1 and 2.Under different thresholdPsub−thr,the simulation results are shown in table 4,whereNumfurepresents the number of reference points to be updated.

As is shown in table 4,when the updating threshold is set to 0,which means the fingerprint database will not be updated,the APE is 4.0m.When the threshold is set to 1,all the reference points are updated,and the APE is 1.2m.Thus,a global update can improve the positioning accuracy,but it will also bring more cost.When the updating threshold is set to 0.7,27.1%of the reference points are updated and APE is 2.1m,which is about half of the original value.When the updating threshold is set to 0.75,48.5%of the reference points are updated and APE will be less than 2m.Larger threshold means better positioning accuracy while smaller means less cost.

V.CONCLUSION

In this paper,four fingerprints are investigated for positioning based on massive MIMO systems.ADCPM extracted from CIR has shown different features in angle domain and delay domain,according to which new fingerprint MACPV and MDCPV are extracted.To simulate actual scenario,the number of scatters is set to decrease in this paper.Thus to improve the robustness of the fingerprint in changing environment,DAE and DCAE are adopted in this paper to extract new fingerprints.Simulation results show that MACPV fingerprint performs best when the reduction number of scatters is 0.But as the number increases,DCAE performs the best,which indicates that DCAE fingerprint is of strong robustness.However,if the scattering environment has changed to a certain extent,the fingerprint database should be updated to guarantee the robustness of the localization algorithm.A CAOAPFUC updating algorithm which combines an updating rule based on probability and a new clustering method is proposed,with proper updating threshold,the algorithm can achieve a balance of the cost and accuracy.

ACKNOWLEDGEMENT

This work was supported by Jiangsu Province Key Research and Development Program (BE2018704),Technical Innovation Project of The Ministry of Public Security(20170001),Fundamental Research Funds for the Central Universities(2242022k30001)and National Science Foundation of China (CN) (Grant No.61871111).