Multi-Environment based Meta-Learning with CSI Fingerprints for Radio Based Positioning Anastasios Foliadisy Mario H. Casta neda Garcia Richard A. Stirling-Gallacher Reiner S. Thom ay

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Multi-Environment based Meta-Learning with CSI

Fingerprints for Radio Based Positioning

Anastasios Foliadis∗†, Mario H. Casta˜

neda Garcia∗, Richard A. Stirling-Gallacher∗, Reiner S. Thom¨

a†

∗Munich Research Center,Huawei Technologies Duesseldorf GmbH, Munich, Germany

†Electronic Measurements and Signal Processing,Technische Universit¨

at Ilmenau, Ilmenau, Germany

{anastasios.foliadis, mario.castaneda, richard.sg}@huawei.com, reiner.thomae@tu-ilmenau.de

Abstract—Radio based positioning of a user equipment (UE)

based on deep learning (DL) methods using channel state

information (CSI) ﬁngerprints have shown promising results.

DL models are able to capture complex properties embedded

in the CSI about a particular environment and map UE’s CSI

to the UE’s position. However, the CSI ﬁngerprints and the DL

models trained on such ﬁngerprints are highly dependent on a

particular propagation environment, which generally limits the

transfer of knowledge of the DL models from one environment

to another. In this paper, we propose a DL model consisting of

two parts: the ﬁrst part aims to learn environment independent

features while the second part combines those features depending

on the particular environment. To improve transfer learning,

we propose a meta learning scheme for training the ﬁrst part

over multiple environments. We show that for positioning in

a new environment, initializing a DL model with the meta

learned environment independent function achieves higher UE

positioning accuracy compared to regular transfer learning from

one environment to the new environment, or compared to training

the DL model from scratch with only ﬁngerprints from the

new environment. Our proposed scheme is able to create an

environment independent function which can embed knowledge

from multiple environments and more effectively learn from a

new environment.

Index Terms—Wireless, Positioning, CSI, Deep Learning,

Meta-Learning, Transfer Learning

I. INTRODUCTION

One of the main requirements of future communication

networks is accurate user positioning. The precise position

information can aid future applications and improve their

performance. Accurate positioning in wireless networks is

enabled by the support of multiple antennas and large available

bandwidths of current and future communication standards.

Generally, classical positioning methods adopt a 2-step

approach. First, some relevant parameters are extracted from

the measured channel state information (CSI), e.g. angle of

arrival (AoA), time of arrival (ToA), etc. In the second step,

the parameters are appropriately combined to obtain a position

estimate. The function that extracts the channel parameters can

be considered environment independent, while the mapping

of the parameters to the position inherently depends on the

propagation characteristics of the particular environment.

Recently there has been an increased focus on using deep

learning (DL) to aid positioning by leveraging the ability to

collect large amounts of data. Speciﬁcally, DL based position-

ing methods can exploit the information that is embedded in a

multi-path channel between the user equipment (UE) and the

base station (BS), which can be considered a unique ﬁngerprint

of the user’s location. For instance, a neural network (NN)

can be trained on a database of uplink CSI ﬁngerprints of

different positions of a UE along with the respective UE’s

location labels. The NN can later be used for estimating a

UE’s position, by mapping the CSI of the UE to an estimated

UE’s position.

DL based positioning methods have shown promising re-

sults, achieving sub-meter accuracy in some indoor and out-

door environments [1]. The main beneﬁt of using DL in

comparison to classical positioning approaches is that it can

be employed in environments with non line of sight or with

severe multipath where classical positioning methods may

be impaired or fail. On the other hand, one of the major

downsides of employing DL based positioning methods with

ﬁngerprints is that the knowledge that is acquired by training

a NN on a particular environment is generally not directly

applicable to other environments. In other words, a change in

the environment may cause the model to completely fail or

signiﬁcantly reduce its positioning accuracy. The effect that a

potential change in the environment has on the NN model’s

performance is explored in [2].

The most straightforward way to address a change in

the environment is to train a new DL model for the new

environment. A more efﬁcient approach though, is to simply

ﬁne-tune a previously trained model on ﬁngerprints from the

new environment. This process is called transfer learning and

it’s a way of re-using the knowledge of the initial model for

the new environment. The idea behind transfer learning is that

the initial layers of a NN learn to extract relevant features from

the input data, while the ﬁnal layers combine those features

in a task speciﬁc way. By re-training the model, only a subset

of its parameters need to be majorly adjusted, which speeds

up training, can improve performance and requires a reduced

amount of training data. In [3] it is shown that ﬁne-tuning a

model using data from a new environment can even outperform

a model that is trained from scratch on data only from the new

environment. Transfer learning across real environments and

between simulated and real environments is examined in [4].

Motivated by the two step approach of classical positioning

methods, we propose a DL model to support transfer learning,

that analogously consists of two parts. For the proposed

DL model, we aim that the initial layers extract location-

related features from the measured CSI from a UE, in a

arXiv:2210.14510v1 [eess.SP] 26 Oct 2022

way that it is independent of the environment. The latter

layers of the proposed DL model then combine the features

in an environment dependent way to obtain the UE’s position

estimate. To strive to have the initial layers to be independent

of the environment, we propose a multi-environment meta

learning scheme to train the ﬁrst part of the DL model with

data from multiple different environments. The second part

of the DL model would then be trained to be environment

speciﬁc. This is in contrast to the approach presented in [5],

where the second part of the DL model is trained on different

received signal strength (RSS) datasets. In the context of deep

learning the process of applying an initial learning scheme

with the goal of improving transfer learning is included under

the umbrella term of Meta-Learning [6].

In this paper we show that by training the two part DL

model using the multi-environment meta learning scheme we

observe improved positioning accuracy when transferring and

ﬁne-tuning to a new environment. In addition, the positioning

performance of the models in each of the initial environments

is not reduced. Our proposed approach enables simultaneous

training of multiple models for different environments while

further improves transfer learning to a new environment.

II. MULTI-ENVIRONMENT META-LEARNING

We consider an uplink setup with NRantennas at the BS and

NTantennas at the UE. The UE transmits a reference signal

on NCsubcarriers within an orthogonal frequency division

multiplexing (OFDM) symbol. The received uplink signal is

used to estimate the CSI between the UE and the BS. The

estimated channel over the NCsubcarriers between the k-

th receive antenna and the m-th transmit antenna can be

described as:

hk,m = [hk,m

0, hk,m

1, ..., hk,m

NC−1]T∈CNC.(1)

Furthermore, we deﬁne the measured channel ˜

Hmbetween

the m-th transmit antenna of the UE and the BS as:

Hm= [h1,m,h2,m, ..., hNR,m]∈CNC×NR.(2)

The CSI ﬁngerprint is then obtained by stacking the ˜

across the UE’s transmit antennas:

H= [ ˜

H1,˜

H2, ..., ˜

HNT]T∈CNA×NC,(3)

where NA=NR·NT. This is eventually processed according

to the phase difference between antennas as described in [1]

by considering the ˜

Hwith NAantennas. This results in a

3-dimensional matrix, i.e. H∈RNA×NC×3, where the third

dimension includes the magnitude, the sine and cosine of the

phase difference between antennas as separate stacked 2D

matrices.

The matrix His then considered as a ﬁngerprint of the UE’s

position. For DL based positioning using CSI ﬁngerprints,

the input of the NN consists of the CSI ﬁngerprint Hof

a measured uplink channel between a UE and the BS. The

aim of the NN is to estimate the UE’s positiong based on the

CSI ﬁngerprint, i.e. the ouput of the NN is the estimated UE’s

positon. Towards this end, a database is created that consists

of processed CSI measurements for different UE’s positions

along with the respective UE’s position label p∈R2.

A. Multi-environment Learning

It is evident that such training method would generally result

in the model’s parameters being dependent on the environ-

ment, i.e. f(H) = ˜

p. This fact inhibits the models ability to

clearly differentiate between environment independent feature

extraction and environment dependent feature combination.

Due to this, a possible transfer learning algorithm can’t fully

exploit environment independent knowledge that the model

has acquired.

Our proposed multi-environment meta learning approach is

shown in Fig. 1. Nseparate models are trained based on Ndif-

ferent source environments, where the n-th model fθ,n(Hn)

is parameterized by the common parameters θand the n-th

environment speciﬁc parameters nfor n= 1,2, ..., N. We

consider a function that extracts channel features znfrom the

estimated ﬁngerprint Hnof the n-th environment. By deﬁning

fθ,n(Hn) = gn(φθ(Hn)) and training the parameters θof

the initial layers φθ(·)on data from multiple environments we

are forcing θto be the same regardless of the environment and

the models are encouraged to learn a common environment

independent function φθ(·). The latter layers of the model

gn(·)combine the output of the φθ(·)function znin a way

that embeds the distinct propagation information of the n-th

environment , i.e. ˜

pn=gn(zn), since they are only trained

on data from that particular environment. The channel features

znare unknown and are implicitly learned by the DL-model.

B. Meta-Learning

By training the DL model φθ(·)using the multi-environment

learning scheme we essentially create a function which has

already learned how it can extract relevant features from a

new target environment as well. In other words, the model

has already ”learned how to learn”. In the context of meta-

learning, the purpose of multi-environment training is to learn

a general purpose algorithm that can generalize across different

source environments and enable each new target environment

to be learned better [6].

The meta-objective that is optimized using the multi-

environment meta-learning shown in Fig. 1 is as follows:

min

θ,nX

Ln(fθ,n(Hn)),(4)

where Lnis the MSE loss of the n-th model for the n-th

environment. By minimizing this objective when training the

DL models, the weights of the layers gn(·)are updated based

only on the MSE loss Ln(fθ,n(Hn)) of the n-the model,

while the common weights of φθ(·)are updated based on the

summation of the individual losses (4). This effectively fulﬁlls

our intention of training the parameters θon data from all N

environments and the parameters nonly from data from the n-

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Multi-EnvironmentbasedMeta-LearningwithCSIFingerprintsforRadioBasedPositioningAnastasiosFoliadisy,MarioH.CastanedaGarcia,RichardA.Stirling-Gallacher,ReinerS.Thom¨ayMunichResearchCenter,HuaweiTechnologiesDuesseldorfGmbH,Munich,GermanyyElectronicMeasurementsandSignalProcessing,TechnischeUniversit...

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Multi-Environment based Meta-Learning with CSI Fingerprints for Radio Based Positioning Anastasios Foliadisy Mario H. Casta neda Garcia Richard A. Stirling-Gallacher Reiner S. Thom ay

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