Beamformed Fingerprint Learning for
Accurate Millimeter Wave PositioningJoão Gante∗ Gabriel Falcão† Leonel Sousa∗∗ INESC-ID, IST, Universidade de Lisboa, Portugal

Abstract—With millimeter wave wireless communications, theresulting radiation reflects on most visible objects, creatingrich multipath environments, namely in urban scenarios. The
radiation captured by a listening device is thus shaped by the
obstacles encountered, which carry latent information regarding
their relative positions.
In this paper, a system to convert the received millimeterwave radiation into the device’s position is proposed, making useof the aforementioned hidden information. Using deep learningtechniques and a pre-established codebook of beamforming
patterns transmitted by a base station, the simulations show that
average estimation errors below 10 meters are achievable inrealistic outdoors scenarios that contain mostly non-line-of-sight
positions, paving the way for new positioning systems.
Index Terms—5G, Beamforming, Deep Learning, mmWaves,
Outdoor Positioning.

I. I NTRODUCTION
Through 5G related research, the door to the so called
millimeter wave (mmWave) frequencies reopened, unlocking
a huge chunk of untapped bandwidth [1]. With mmWaves,the propagation changes dramatically: the resulting radiation
has severe path loss properties and reflects on most visible
obstacles [2]. To counteract the aforementioned characteristics, beamforming (BF) is usually employed in systems containing multiple-input and multiple-output (MIMO) antennas,
enabling steerable and focused radiation patterns.
With that recent focus on mmWaves, new positioning
systems based on these frequencies were proposed [3]. The
achievable accuracy in controlled conditions is remarkable,with sub-meter accuracy in indoor [4] and ultra-dense line-ofsight (LOS) outdoor scenarios [5]. Nevertheless, in order tobe useful in outdoor scenarios, a mmWave positioning system
must also be able to deal with devices in non-line-of-sight(NLOS) locations.
The works developed in [6]–[9] attempt to address thisconcern, being capable of locating devices in both LOS
and NLOS situations. The method in [6] applies compressedsensing on information gathered from static listeners, whilein [7] multiple access points are used to create a location
fingerprint database of received powers and angles-of-arrival(AoA). In [8], the authors use multiple BF transmissions andan iterative algorithm to estimate the position and orientationof the device. Nevertheless, the methods proposed in [6]–[8]have difficulties complying with typical outdoor situations:This work was supported by national funds through Fundação para a
Ciência e a Tecnologia (FCT) with reference UID/CEC/50021/2013, and FCT
Grant No. FRH/BD/103960/2014.

Base Station

DeviceA

BF Pattern 1
BF Pattern 2

Broadcast
Radiation...

arXiv:1804.04112v1 [eess.SP] 11 Apr 2018

† Instituto de Telecomunicações, Department of Electrical and Computer Engineering, University of Coimbra, Portugal

BF Pattern B

Received
Power isSampledB

Sampled Data

CNN
InferenceC
ResultPosition
Fix

D

Fig. 1. Overall scheme of the proposed system. The device samples thereceived power from radiation transmitted using a fixed set of beamforming
patterns, resulting in a unique data arrangement that can then be translated
into its position.

[6] and [7] assume that each device is always in range ofmultiple static transceivers, while [8] struggles with NLOS
locations, requiring multiple transmission paths reflecting inat least three different surfaces. Finally, the method proposedin [9] overcomes the aforementioned restrictions by creating afingerprint database of uplink pilots transmitted to a distributed
massive MIMO base station (BS), and then resolving theposition using a Gaussian process regression, obtaining a rootmean-square-error (RMSE) of 35m.
For a mobile mmWave receiver connected to a BS, the received power delay profile (PDP) for a given BF configuration
is determined by the receiver’s location. Therefore, if a BStransmits short pulses employing a sequence of directive BF
patterns, so as to cover all possible angles of transmission,
each position covered by the system will likely have a uniquepattern in terms of received power over time. In this paper,
we discuss how to obtain said patterns and propose to apply
convolutional neural networks (CNN) so as to learn them,providing geolocation to devices with mmWave capabilities.
By piggybacking on the (planned) infrastructure and hardware, the implementation cost can be kept low. To simulate
the feasibility of the proposed system, a propagation dataset isgenerated using ray-tracing simulations on accurate 3D maps.
Ultimately, by being able to provide accurate positioningin outdoors NLOS scenarios, this technique can be used
to complement the existing mmWave positioning techniques,
resulting in an enhanced experience for the user.

y = Hf x + z,(1)

where H ∈ CNR ×NS is the channel matrix, f ∈ CNS ×1
denotes the currently selected beamforming, x ∈ C is the
waveform to be detected, and z ∈ CNR ×1 is the noise.
In order to avoid losing information due to destructive
interference, the transmissions using those codebook entries
should have a minor time interval between them (Tguard ), toaccount for longer paths with multiple reflections.
Phase B: To capture the detail inherent to the radiation
power over time patterns, the system must be able to measure
the transmitted pulses at a high rate. As the data patterns must
be consistent regardless of the target device, the sampling rate
must be equal for all the receivers, and those receivers must be
synchronized with the BS. Furthermore, if BF at the receiveris also included in the system, a specific array gain must also
be set for all receivers (to ensure consistency). In that case, thereceiver would also have to define a BF codebook to searchover all AoAs with similar gain, containing BRx entries, andit would have to sample the original transmission BRx times,
storing the maximum measured value for each data point. The
acquired data from transmit BF b, db , can thus be written as
db [n] =max

i=1,...,BRxyi (nT ),n = 0, 1, . . . , N − 1,

(2)

X=194.0 Y=-114.0

X=125.0 Y=19.0

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Sample Number

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With the use of mmWaves on MIMO systems, the resulting
multipath propagation is defined by the used BF and theexisting obstacles. For 5G BSs, which are expected to belocated in elevated positions of urban scenarios, most of the
obstacles are static for a significant amount of time, as they are
predominantly buildings. Therefore, successive measurementsof the received radiation pattern at a given position are
expected to remain comparable until a significant change inthe surrounding area occurs.
In order to infer the position from the hypothetical information contained in the received radiation, two requirements
have to be respected: i) the adopted transmitter BFs must
be constant, to culminate in an equivalent set of transmitted
radiation patterns, and ii) the target devices must be able
to detect the transmitted radiation with the same detection
scheme, to gather the required information.
To comply with both requirements, the system depicted
in Fig. 1 is proposed. It contains four distinct phases, aslabeled in the diagram, whose details are described bellow.
Phase A will broadcast pulse waveforms using constant setof radiation patterns, while phase B focuses on measuring theresulting radiation at the target device. After all the required
measurements are performed and transmitted to the BS, phase
C infers the device’s position, which will be relayed back to
the device in phase D.
Phase A: Since mmWave transmissions must employ directive (and therefore, narrow) beam patterns, a fixed codebook
with BT x BFs is proposed, so as to fully cover all possible
angles of transmission. Assuming a BS with NS antennas, thefrequency-domain signal at the NR mobile devices antennasy ∈ RNR ×1 can be written as

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Sample Number

II. P ROPOSED S YSTEM D ESCRIPTION

0

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Beamforming Index

80

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Beamforming Index>-50dBm-100dBm

40

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X=64.0 Y=-97.080-150dBm
020
Beamforming Index

no_data

Fig. 2. Noiseless data samples from the experimental simulations, before
removing low-power entries due to the detection threshold. Adjacent beamforming patterns have a high probability of having similar patterns.

where T is the sampling period and N is the number ofsamples to gather per BF. To be effective, T (and the pulse
duration) must be smaller than 100 ns, as it will examinedin the following section. Nowadays smartphones can connect
to LTE networks with bandwidths exceeding 10 MHz, so,in order to use the proposed system, no additional hardware
should be required at a device with mmWave capabilities.
Phases C and D: Upon obtaining the required data from all
the BFs in the codebook (d), performing inference on a trained
CNN will result in a position estimation. The proposed system
can thus be considered fingerprint-based, since the CNN mustbe trained with data from the possible positions. The inference
can either be performed on the device, or at the base station(after transmitting the required data from the device, andthen reporting the result back to it). However, performing theinference at the device has its limitations, since a CNN caneasily have millions of weights. In that case, the device would
have to download (and store) all those weights each time it
connects to a new BS, or when a network is retrained. For
those reasons, we propose to perform the inference at the BS,
as depicted in Fig. 1
III. DATA A NALYSISThe accuracy resulting from the proposed system ultimately
depends on the learning capabilities of the inference block.
The system performance is thus determined by two factors:
the data obtained in phase B and the learning method used inphase C.
As mentioned in section II, the used pulse duration inphase A and the measurement mechanism selected for phase
B should be able to provide a temporal resolution exceeding
100 ns. In such conditions, the received radiations will arrivein clusters with voids large enough to be reliably detected[11], and the resulting data will be sparse (as it is observablein Fig. 2). The ability to distinguish these voids provides
meaningful shape to the resulting data, enhancing the learning
capabilities. In fact, as it will be observable in section V, theposition of the acquired non-zero samples in the data yields

TABLE I
R AY-T RACING S IMULATION PARAMETERS
Parameter Name
Carrier Frequency
Transmit PowerTx. Antenna Gain
HPBW
Transmitter Downtilt
Codebook Size
Receiver Grid Size

Value
28 GHz45 dBm24.5 dBi (horn antenna)
10.9◦
10◦
32 (155◦ arc with 5◦ between entries)
160801 (400 × 400 m, 1 m between Rx,
1 m above the ground)

TABLE IIC ONVOLUTIONAL N EURAL N ETWORK AND DATA PARAMETERS
Parameter Name
Convolutional Layers (CL)Legend:Transmitter

Fig. 3. Ray-tracing simulation in the NYU area, using the parameters intable I with a transmit power of 30 dBm. The results shown correspond tothe maximum received power for all possible transmit BFs. In [10], it was
shown that this simulation matched the experimental measurements in [11].

more information than their magnitude, especially in noisy
environments (where the fluctuations are more likely to bevisible at the amplitude level). Therefore, a binary detectionof the signal’s existence can be used, further reducing therequirements for the proposed system.
When visualizing the sampled data, it is possible to represent it in a three dimensional space: time, power and BS BF
index. It is interesting to notice a visual pattern in the data,when the sequence of BF indexes correspond to a continuous
sweep over the azimuth. If that resulting data is plotted asa 2D image, where the axis are the time and the BF index,
the formed image will likely have short lines over the BF
dimension, as seen in the examples in Fig. 2. In other words,
this means that physically adjacent BF patterns will likely
have similar clusters to the same location, and thus carry someredundant information. As result, adding an increasing number
of BF patterns to phase A will have diminishing returns on
the position inference accuracy.
The inference in the proposed system can be classified asa regression problem, since it will be transforming data toa continuous set of results (i.e., the device position). Due
to performance, suitability, and noise-resisting capabilities forpattern recognition problems, CNNs were selected as learning
mechanism [12]. Using a CNN, the system should be able
to cope with the non-linearities introduced by reflections andother propagation artifacts. For the CNN cost function, theminimum mean square error (MMSE) was selected, i.e.,
Tp̂MMSE (d) = argminp̂ E{(p̂ − p) (p̂ − p)},(3)

Hidden Layers (HL)HL Activation Function
Output Layer
Optimizer Function
Learning Rate
Training Epochs
Dropout Rate
Samples per Tx. BF
Assumed Rx. Gain
Detection Threshold
Data Preprocessing
Added NoiseValue
1 (8 1 × 3 filters,
followed by 2 × 1 max-pooling)
7 (1024 neurons each)
Rectified Linear Unit
2 Linear Neurons (2D position)
ADAM
10−5 (×0.99 decay each epoch)
1000
0.5
82 (4.1 µs @ 20 MHz)
10 dBi−100 dBm
Row Normalization / Binarization
σ = [0, 10] dB (Log-Normal)

where p̂ denotes the estimated position given the input data
d. The usage of this cost function can be interpreted as aminimization of the squared distance between the real position
p and its estimate.
IV. S IMULATION A PPARATUS
To simulate the proposed system accuracy, a dataset using
mmWave ray-tracing simulations in the NYU area was created,
containing fingerprint data from 160801 positions. These raytracing simulations were created with the Wireless InSite
3.0.0.1 ray-tracing software [13], using the high precisionopen-source 3D map made available by the New York City Department of Information Technology & Telecommunications[14], as well as the specifications depicted in table I (mostly
inherited from [11]). In [10], it was shown that the ray-tracing
simulations (presented in Fig. 3) matched the experimental
measurements obtained in [11].
Even though actual BF is not performed in the ray-tracing
simulations (due to software inability), a physically rotatinghorn antenna produces similar directive radiation patterns.
The received power over time data was sampled at 20MHz
over 4.1 µs (which contained 99% of the non-zero entries).
Combined with the 32 transmit directions, this resulted in
2624 floating-point elements per location entry, as represented
in Fig. 2. Regarding the BF at the receiver, a 10 dBi gain
was considered, akin to the mmWave mobile device tested in[15], which is able to cover most of the receive directions
employing a codebook with 16 elements. The resulting data
was labeled with the corresponding bidimensional position, in
a area centered at the base station.

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When noise is considered in the proposed system, it isadded to the ray-tracing data following a log-normal distribution. This happens before discarding any data entry below
the detection threshold of −100 dBm (selected due to thethermal noise for the considered bandwidth). If the simulated
system considers a binary detection of the received signal,
the simulation data is transformed after adding the noise andpassing through the detection threshold. This data is thensampled for each position that contains at least one non-zero
entry, so as to create a training set (for each CNN training
epoch, a new training set is generated). Since the system is
expected to be used to predict positions for which it alreadyhas samples, the test set is generated as the training set. Whenevaluating the average results, a total of 10 test sets are used.
The selected CNN follows a traditional architecture, whose
hyperparameters were selected after empirical tests, also taking
in account the total execution time (the training takes less than
8 hours in a Nvidia GTX 780 Ti, using Google’s TensorFlow
framework). The system can thus be summarized as depicted
in table II1 .
V. S IMULATION R ESULTS
When working with the proposed system, the data format must be carefully selected, since it manages a trade-off
between achievable performance and hardware requirements.
While employing a binary detection of the received radiation
is far simpler, obtaining the information regarding the powerof said radiation could help to pinpoint the receiver. In Fig.
4, the proposed system accuracy is plotted against multiple
noise levels, for the original (floating-point) simulation data
and for a binary version of the same data. For the assessedbinary dataset, the average error rages from 6.2 m (noiselessavailable

Zoomed CDF, excluding the last 10%

0.6

95th percentile:
31.6179

Fig. 4. Average and 95th percentile prediction errors for the proposedsystem, for multiple log-normal modeled noise levels, depicted by its standard
deviation (σ). For larger noise values, using binary data resulted in improved
performance.

1 The
simulation code and used data are
https://github.com/gante/mmWave-localization-learning

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CDF

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Error (m)

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Fig. 5. CDF of the prediction errors, considering binary data samples and anoise σ of 6 dB. The least accurate predictions are very inaccurate, and thus
the average error is larger than the median error.

data) to 12.1 m (σ = 10 dB), with a 95th percentile error
never exceeding 35.3 m. As for the floating-point dataset, theaverage error rages from 4.3 m to 13.6 m, with a maximum
95th percentile error of 40.4 m. Therefore, from the obtained
results, it is possible to conclude that using binary data isactually helpful for the CNN at higher noise regimes.
In Fig. 5, the cumulative distribution function (CDF) for thebinary dataset with moderate noise (σ = 6 dB) is shown. From
the CDF, its is observable that the least accurate predictions arevery inaccurate, explaining the significant difference between
the median and the average errors (6.1 m and 10.6 m, respectively). For this configuration, the predictions have a RMSE of
22.1 m, which denotes superior performance when comparedto the RMSE of 35 m obtained in [9] (which also considers
a lower noise, with σ = 5 dB). However, it is important topoint out that the numerical simulations performed in [9] do
not contain NLOS positions.
To explain the inaccurate predictions, Fig. 6 plots the error
against the number of detected (non-zero) entries per sample,
for the aforementioned dataset and noise parameters. The
general trend is a lower average error with an increasing
number of detected entries per sample. Furthermore, it isimportant to notice that when a sample contains fewer than
10 non-zero entries, the average prediction error soars dueto the lack of information in the received data, explaining the last percentiles of the CDF. Therefore, due to themmWave propagation characteristics, the presence of multiple
paths between the transmitter and the receiver enhances theinformation perceived by the proposed system, resulting in
improved predictions. Furthermore, since additional sources of
information improve the system performance, the presence of
non-zero entries originating from other BSs should increase
the prediction accuracy, making the proposed system fit for
dense BS deployment schemes.
Finally, in Fig. 7 the average prediction error per position

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Fig. 6. Prediction error and sample count per number of detected non-zero
entries in a sample, considering binary data samples and a noise σ of 6 dB. As
observed, when few entries are detected, the prediction error soars, explaining
the least accurate predictions shown in Fig. 5.

is shown, considering once again a binary dataset with anoise σ of 6 dB. Comparing these results to Fig. 3, it ispossible to conclude that the system is always able to return apositioning prediction, as long as the mobile user is covered by
the mmWave network. Moreover, it is interesting to notice thatthe prediction quality is not dictated by the received power:
for instance, inside the building block at (75, 50), the mobile
receiver is expected to have a weak signal and a high-quality
position estimate. This can be easily explained due to a uniquedata pattern, which is identified by the CNN. As a final key
remark, it is clearly observable that being in a NLOS position
is not a constraint to obtain an accurate positioning prediction.
VI. C ONCLUSIONS
Throughout this paper, a system that is able to predict a device geolocation through mmWave transmissions and CNNs is
proposed. This system will be able to function whenever there
is 5G coverage, and should require no additional hardware indevices that have mmWave reception capabilities.
In the preliminary simulations performed, the average estimation error can drop below 10 meters, in a scenario containing mostly NLOS positions, outperforming the existingalgorithms for such positions. Therefore, by providing accurate
estimates for NLOS positions, where other sub-meter-accuracy
mmWave positioning algorithms struggle, the proposed system
can be seen as a enabling component of the mmWave positioning techniques ecosystem, enhancing the end-user experience.
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