1

Improving the Performance of OTDOA based
Positioning in NB-IoT Systems
Sha Hu† , Axel Berg‡ , Xuhong Li† , and Fredrik Rusek†
of Electrical and Information Technology, Lund University, Lund, Sweden
‡ ARM, Lund, Sweden
† {sha.hu, xuhong.li, fredrik.rusek}@eit.lth.se, ‡ axel.berg@arm.com

arXiv:1704.05350v2 [] 5 Sep 2017

† Department

Abstract—In this paper, we consider positioning with observedtime-difference-of-arrival (OTDOA) for a device deployed in longterm-evolution (LTE) based narrow-band Internet-of-things (NBIoT) systems. We propose an iterative expectation-maximization
based successive interference cancellation (EM-SIC) algorithm
to jointly consider estimations of residual frequency-offset (FO),
fading-channel taps and time-of-arrival (ToA) of the first arrivalpath for each of the detected cells. In order to design a low
complexity ToA detector and also due to the limits of lowcost analog circuits, we assume an NB-IoT device working at
a low-sampling rate such as 1.92 MHz or lower. The proposed
EM-SIC algorithm comprises two stages to detect ToA, based
on which OTDOA can be calculated. In a first stage, after
running the EM-SIC block a predefined number of iterations,
a coarse ToA is estimated for each of the detected cells. Then in
a second stage, to improve the ToA resolution, a low-pass filter is
utilized to interpolate the correlations of time-domain PRS signal
evaluated at a low sampling-rate to a high sampling-rate such as
30.72 MHz. To keep low-complexity, only the correlations inside
a small search window centered at the coarse ToA estimates
are upsampled. Then, the refined ToAs are estimated based on
upsampled correlations. If at least three cells are detected, with
OTDOA and the locations of detected cell sites, the position of
the NB-IoT device can be estimated. We show through numerical
simulations that, the proposed EM-SIC based ToA detector is
robust against impairments introduced by inter-cell interference,
fading-channel and residual FO. Thus significant signal-to-noise
(SNR) gains are obtained over traditional ToA detectors that do
not consider these impairments when positioning a device.

I. I NTRODUCTION
Observed-time-difference-of-arrival (OTDOA) is a downlink (DL) positioning method first introduced in long-termevolution (LTE) in Rel. 9 [1], [2]. The positioning-referencesignal (PRS) is transmitted in the DL to enhance positioning
measurements at receiver nodes to ensure sufficiently high
signal quality and detection probability. The PRS is distributed
in time and frequency resources over a subframe and a number
of consecutive positioning subframes are allocated with a
certain periodicity. In a PRS subframe where PRS is present,
no data but only control signaling is transmitted which reduces
the interference from neighbour cells [1]. In order to further
reduce inter-cell interference, the network can mute PRS
transmission of certain e-NodeBs (termed PRS muting). When
PRS is not available, cell-specific-reference-signal (CRS) can
also be used to detect the OTDOA.
As is well-known, low-cost and power-efficient transceiver
circuits are important for a device working in narrow-band
Internet-of-things (NB-IoT) systems, which needs to operate

Fig. 1. Positioning with PRS signals from 3 e-NodeBs based on OTDOA,
where the ToA (τ0,0 , τ1,0 and τ2,0 ) of the first arrival-paths are detected at
an NB-IoT device, and then reported back in the uplink (UL) for e-NodeBs
to estimate the position of the device.

for 10 years with its built-in battery. Therefore, using an analog
RF circuitry that supports sampling-rate up to 30.72 MHz to
obtain good resolution of time-of-arrival (ToA) is expensive
and infeasible for a low-end NB-IoT device. Although the
device can interpolate the received samples in digital domain
to have a high sampling-rate, intensive computations of PRS
correlation consume lots of the battery-power. Hence, in this
work we consider an NB-IoT device that only works at a low
sampling-rate such as 1.92 MHz, and instead of upsampling
the received samples we interpolate the PRS correlations in a
small search window to improve the ToA resolution.
In order to position an NB-IoT device, PRS signals from at
least three cells need to be detected as depicted in Fig. 1. To
enhance the hear ability from multiple cells, the positioning
subframes are designed with no data transmission in the
physical-downlink-shared-channel (PDSCH). However, due to
the time-delays, the PRS signal from different cells can still
cause strong interference to other cells, which degrades the
ToA detection performance. For instance, consider an NB-IoT
device that is very close to one e-NodeB; this causes dramatical interference to other cells which results in a positioning
failure since only one PRS signal from the closest cell can
be detected. Therefore, a successive interference cancellation
(SIC) technique is needed for the ToA detection. Although
PRS muting can avoid collisions of PRS signal, it increases
the latency of positioning process linearly in the number of
cells involved and is infeasible for a dense cell-deployment.
Besides inter-cell interference, the residual frequency offset

2

One and two PBCH antenna ports

R6
(FO) due to an imperfect FO estimate based on NB-IoT
R6
synchronization signals also causes performance degradation
R6 R0
R
R
0
6
of the coherent additions of correlations in the ToA detection
process. Moreover, although an NB-IoT device is expected
R6
R6
to have a low speed and the channel can be assumed constant
R6
R6 R0
R0
over one PRS subframe, the wireless fading-channel still needs
R6
to be estimated for the SIC process and the coherent additions
R6
of correlations.
R6 R0
R6 R0
In this paper, we consider OTDOA based positioning in LTE
based NB-IoT systems where only one physical resource block
R6
R6
(PRB) is used for data-transmission (180 KHz). We propose an
R0
R6
R6 R0
expectation-maximization based successive interference can…...
…...
l=0
l=6 l=0
l=6
ns is even
ns is odd
cellation (EM-SIC) algorithm to estimate the fading-channel,
residual FO and ToA of the first arrival-path for each of the
PRS subframe
detected multiple cells. The EM-SIC algorithm based ToA
Fig. 2. The PRS pattern in one PRB for normal CP and one or two PBCH
detector works on received time-domain samples at a low antenna ports for a cell with PCI=0 in LTE. The PRS is transmitted on antenna
sampling-rate, to firstly obtain coarse estimates of the ToA port 6 which is labeled as R6 , while the normal CRS is sent on antenna port
for all detected cells. Then, the resolution of estimated ToA 0 and labeled as R0 . The frequency shift is given by mod (PCI, 6).
is refined with upsampled correlations inside a search window the baseband time-domain PRS signal is obtained through
centered at the coarse ToA estimates using interpolations. To inverse Fast-Fourier-Transform (IFFT) according to
further improve the accuracies of ToA estimates, we use an
N/2−1
j2πnk
1 X
iterative multi-path detection (MPD) algorithm to detect the
Sp,ℓ [k]e N
sp,ℓ [n]= √
ToA of the first arrival-path by taking into account the property
N k=−N/2
of the auto-correlation function (ACF) of time-domain PRS


j2πn(kp,ℓ+6)
j2πnkp,ℓ
1
signal. We show through numerical results that, the proposed
N
,
Sp,ℓ [kp,ℓ ]e N +Sp,ℓ [kp,ℓ +6]e
=√
N
EM-SIC algorithm based ToA detector renders significant
(2)
signal-to-noise (SNR) gains compared to traditional OTDOA
detectors that do not thoroughly consider the impairments where N is the IFFT size, and Sp,ℓ [k] is the mapped PRS signal
introduced by the inter-cell interference, ACF of the time- generated in (1) on the ℓth OFDM symbol of the pth cell. In
domain PRS signal, fading-channel and residual FO.
total we consider P cells for OTDOA based positioning, and
kp,ℓ is the lower frequency index where the corresponding PRS
signal
is transmitted on the ℓth symbol of the pth cell.
II. PRS AND OTDOA BASED P OSITIONING IN NB-I OT

S YSTEMS
A. PRS Generation and Subframe Mapping
We consider an LTE based single-input-single-output
(SISO) NB-IoT system, where the PRS signal is generated
based on physical cell identity (PCI), and mapped to resource
element (RE) over a time-frequency grid as described in [2].
The number of consecutive PRS subframes can be either 1,
2, 4 or 6, which are transmitted periodically in the DL. The
period of one positioning occasion can be configured to every
160, 320, 640 or 1280 milliseconds (ms). In the considered
NB-IoT system, we assume a narrow-band data-transmission
over one PRB. The QPSK-modulated PRS signal is generated
as [2]
1
1
zns ,ℓ = √ (1 − 2c[2m]) + j √ (1 − 2c[2m + 1]).
2
2

(1)

where ns is the slot number within a radio-frame, ℓ is
the OFDM symbol number within one slot, and m = 0, 1
represents the two PRS symbols in each PRS OFDM symbol.
The pseudo-random sequence c[m] is generated by a length31 Gold sequence whose initial state depends on PCI, ns , ℓ
and the cyclic-prefix (CP) type. According to the PRS mapping
pattern such as shown in Fig. 2, the QPSK symbols are mapped
to REs. As there is no data transmission in the PRS subframe,

B. Received Signal Model
In LTE, the unit of ToA for OTDOA based positioning is
Ts = 1/Fs where Fs = 30.72 MHz. In the considered NB-IoT
system, we assume a sampling-rate F̃s with a typical value
1.92 MHz, which is much lower than Fs . Denote the true
ToA of the ith channel-tap from the pth cell as τp,i , and the
ToA measured in number of samples as
np,i = ⌊τp,i F̃s ⌋.

(3)

Then, the received signal from the pth cell corresponding to
the ℓth PRS OFDM symbol and ith path of the fading-channel
at time-epoch n can be modeled as

0 ≤ n < np,i
0,
yp,i [n+ℓM ] = hℓp,i [n]sp,ℓ [n−np,i ], np,i ≤ n < np,i +M (4)

0,
np,i + M ≤ n < M̃

where sp,ℓ [n] is the time-domain PRS signal (including CP)
generated in (2) with M being its length with the samplingfrequency F̃s , and M̃ equals M plus the number of samples
corresponding to the maximal ToA for all P cells. The channel
hℓp,i [n] comprises two parts: the ith tap of the fading-channel
hp,i which we assume to be constant over one PRS subframe,
and a phase-rotation caused by the residual FO, which equals
hℓp,i [n] = hp,i ej2π

ǫp (n+ℓM )
N

.

(5)

3

Processes in each block

Input samples

Stage 1: The strongest path esma on for
P cells with EM-SIC algorithm

Interpola on
of R1[n]

Stage 2: Correlaon intepolaon
and ToA esmaon
First-path
detecon

EM-SIC Block
cell P-1

Interpola on
of Rp-1[n]

Residual FO
es amte

Interpolaon
of R0[n]

…...



First-path
detec on

First-path
detec on

Correlator

EM-SIC Block
cell 1

…...

EM-SIC Block
cell 0

Add the subracted
PRS signal back

Time-domain
received samples

OTDOA based posi oning



Channel
es mate

Regenerate
PRS signal

ToA esamte

Esmated NB-device posion

Puriﬁed samples

Fig. 3. ToA Detection structure with proposed EM-SIC algorithm.

where ǫp is the residual FO of the pth cell normalized by
the subcarrier frequency-spacing (15 KHz). Then, the superimposed received samples for all P cells reads
y[n] =

sym Lp −1
P
−1 N
X
X
X

p=0 ℓ=0

yp,i [n+ℓM ] + w[n],

(6)

i=0

where w[n] is modeled as AWGN with zero-mean and variance
σ 2 , and Lp is the maximal number of channel-taps for the pth
cell. The signal-to-noise (SNR) is defined as SNR = σs2 /σ 2
where σs2 is the averaged power of signal sp,ℓ [n]. We denote
the number of OFDM symbols in one subframe as Nsym , and
the number of OFDM symbols carrying PRS as NPRS . From
Fig. 2, Nsym and NPRS are equal to 14 and 8, respectively.
For simplicity, we let ℓ̃(s) (0 ≤ s < 8) denote the sth OFDM
symbol that contains PRS. In order to position an NB-IoT
device1 , the device needs to detect ToA of the first arrivalpath for (at least three out of) the P cells, that is, detect np,0 .
C. ToA Detection of the First Arrival-Path
In order to detect the ToA, for each cell a cross-correlation
between the received samples and the PRS signals sp,ℓ [n] is
implemented, and the correlations are calculated as
y[k]s∗p,ℓ [k

k=n

− n].

Then, the delay np,0 can be estimated according to


7
P




Rp,ℓ̃(s) [n]


s=0
 7
 > η1 .
np,0 = argmin
P


n


 max

Rp,ℓ̃(s) [n]
n

7
M̃−M−1
X X
η2
R
[n] .
n
M̃ −M −1 n=0 s=0 p,ℓ̃(s)
s=0
(9)
For both (8) and (9), η1 and η2 are a predefined thresholds
that can be adapted for different scenarios. The condition (9)
decides if the PRS signal is detected while the condition (8)
provides the estimation of the ToA. A drawback of decision
conditions (8) and (9) is that, the presence of residual FO
degrades the performance of coherent addition of Rp,ℓ̃(s) [k]
over all PRS symbols, and a non-coherent addition renders
inferior performance compared to coherent addition.

max

(

7
X

Rp,ℓ̃(s) [n]

)

>

D. Cramér-Rao Lower Bound (CRLB)
According to (4), under AWGN channel (hp,i = 0 for i 6= 0)
without residual FO, the CRLB for estimating np,0 can be
shown to be [4]
var(np,0 ) ≥

σ2 N 2
7 NP
−1
P
8π 2
n2 Sp,ℓ̃(s) [n]

2

s=0 n=0

n+M−1
X

Rp,ℓ [n] =

However, (8) is not executed unless the following is satisfied

(7)

=

σ2 N 2


2  , (10)
7
P
2
2
kp,
+
k
+6
8π 2
ℓ̃(s)
p,ℓ̃(s)
s=0

(8)

s=0

1 Although considering CRS can further improve the positioning performance, in this paper we only consider 8 OFDM symbols on which the PRS
are transmitted for positioning. The same principle can be applied to CRS
assisted positioning.

which shows that the CRLB for estimating np,0 depends on
the subcarrier index kp,ℓ̃(s) where the PRS signal is transmitted. Note that, the value of kp,ℓ̃(s) changes slightly with
different FFT shift operations in practical implementations of
(2). Although the CRLB is usually difficult to attain unless
under the AWGN channel and without impairments caused by
interference or FO, it still provides an insight for designing
the optimal PRS mapping-pattern of the NB-IoT system.

-8

0

-9

-2

-10

-4

Normalized PDP [dB]

Normalized PDP [dB]

4

-11
-12
-13

-6
-8
-10

-14

-12

-15

-14

-16
100

101

102

delay [Ts]

103

-16
0

5

10

delay [16Ts]

Fig. 4. The normalized power-delay-profile (PDP) of ETU channel with
sampling period Ts and 16Ts , respectively.

III. P ROPOSED EM-SIC A LGORITHM
P OSITIONING

FOR

several times to achieve a better performance. As shown in
[7] and observed in numerical simulations, 2-3 iterations can
harvest the major gains.
As the sampling-period at 1.92 MHz is 520 nanoseconds
(ns) which corresponds to a maximal resolution of 156 meters
(m) with a single cell, the resolutions of ToA estimates are
poor in the first stage. Noting that the Fourier transform of a
correlation is the power-spectral-density (PSD) which is bandlimited to one PRB, to further improve the resolutions, in the
second stage the correlations are interpolated to 30.72 MHz
(of a resolution 9.75 m). Then, ToA of the first arrival-path is
estimated based on upsampled correlations using an iterative
MPD approach. After that, the refined ToA estimates are sent
to the OTDOA based positioning module which generates an
estimate of the position of the NB-IoT device.

OTDOA

In this section, we elaborate the proposed EM-SIC algorithm
based ToA detector, which jointly considers mitigating the
inter-cell interference, estimating the residual FO and the
multi-path fading-channels, and detecting ToA of all cells.
A. ToA Detection and OTDOA Positioning Structure
In Fig. 3 we depict the detector structure with the EMSIC algorithm for OTDOA based positioning of the NB-IoT
device, which essentially comprises two stages. In the first
stage, coarse estimations of ToA of the first arrival-path of all
P cells are obtained with iterative EM-SIC blocks, and the
correlations are coherently summed-up after the residual FO
correction. Then in the second stage, the ToA estimates are
refined with interpolated correlations. Note that, as explained
earlier, we assume that the EM-SIC algorithm works with the
received samples at a low sampling-rate, and as depicted in
Fig. 4, the multiple-path components of fading-channel are
merged together at a low sampling-rate such as 1.92 MHz.
Therefore, for the EM-SIC algorithm in the first stage it is
sufficient to only consider the strongest path.
In the first stage, for each cell an EM-SIC block is applied
to firstly cross-correlating the time-domain PRS signal with
the received samples to obtain the correlations Rp,ℓ̃(s) [n].
Then, the residual FO is estimated by cross-correlating the
correlations Rp,ℓ̃(s) [n] among the 8 PRS symbols in each
subframe. After the FOC, the strongest channel-path is found
at the delay that maximizes the coherent addition of the
correlations, and the corresponding channel-tap is estimated
with LMMSE filtering. Finally, with the estimated FO and
channel-tap, the time-domain PRS samples are regenerated and
removed from the received signal for each of the cells. The
same operations are implemented in a successive way until
all P cells have been processed. Then in the next EM-SIC
iteration, before computing the correlations Rp,ℓ [n], for each
cell the PRS signal subtracted from the previous iteration is
added back. Such an EM-SIC based estimation algorithm was
first used to decompose the superposed signals for iterative
channel estimation and then also applied for PDSCH detection
with inter-cell interferences in LTE systems, which was shown
to work well [7]. The EM-SIC in the first stage can be repeated

B. Stage 1a: Correlation Per OFDM Symbol
As the operation in the EM-SIC block is the same for
each detected cell, we elaborate the operations for the pth
cell. At a first step, the cross-correlation Rp,ℓ [n] in (7) is
computed within the maximal delays M̃ − M for each of
the 8 OFDM symbols carrying PRS signal and for all the P
cells independently. Before summing Rp,ℓ [n] over 8 OFDM
symbols, we first need to estimate and correct the FO to
improve the detection performance.
C. Stage 1b: Residual FO Estimation
Since there have been FOC operations using the NB-IoT
synchronization signals (NPSS and NSSS) at the synchronization steps, the residual FO can be considered relatively small
such that the coherent addition inside one OFDM symbols
is still applicable. As there are in total 8 OFDM symbols
transmitted, the FO ǫp can be estimated based on Rp,ℓ̃(s) [n].
Note that, as depicted in Fig. 2, the maximal separation
between two OFDM symbols carrying PRS is 10 OFDM
symbols. Therefore, the largest residual FO, normalized by the
subcarrier frequency-spacing, that can be estimated is ±0.05.
To estimate the residual FO, we cross-correlate Rp,ℓ̃(s) [n] at
each delay n, and the best-linear-unbiased-estimator (BLUE)
for ǫp [n] is
ǫ̃p [n] =

4
X

w(m)φ(m, n)

(11)

m=1

where φ(m, n) equals
φ(m, n) =

7−m
X

N
2πM (8 − m) s=0

n
o
∗
arg Rp,ℓ̃(s) [n]Rp,
[n])
ℓ̃(s+m)
ℓ̃(s+m) − ℓ̃(s)

,

(12)
and the operation arg{·} returns the angle which belongs to
[−π, π). The combining coefficients w[m] are set to
w = [0.4762 0.3095 0.1667 0.0476],

(13)

computed according to [8, eq. (16)], and achieves the minimum estimation error (MSE) with 8 PRS OFDM symbols.

With ǫ̃p [n] estimated in (11), we implement FOC and coherently add the correlations for 8 PRS OFDM symbols to obtain
7
X
M (ℓ̃(s)−ℓ̃(0))
N
Rp [n] = Rp,ℓ̃(0) [n]+ e−j2πǫ̃p [n]
Rp,ℓ̃(s) [n]. (14)

Normalized Corr.

5

s=1

1
PRS Correlation at 30.72 MHz
PRS Correlation at 1.92 MHz
Interpolated PRS Correlation

0.5
0
-0.5
-800

-600

-400

-200

0

200

400

600

800

5

10

15

20

delay [Ts]

Then, the residual FO estimate for the pth cell is set to

(15)

where the index ñp is found such that
Rp [ñp ] = max {|Rp [n]|} .

(16)

n

NMSE [dB]

0

ǫ̂p = ǫ̃p [ñp ],

-100

-200
-20

Then, the condition (9) is verified to decide whether there is a
PRS signal received from the pth cell. If (9) is not satisfied, the
detector directly moves to process the next cell and removes
the pth cell from current EM-SIC iteration.

-15

-10

-5

0

delay [Ts]

Fig. 5. The normalized correlations and normalized mean-squared-error
(NMSE) of the interpolations for one PRS OFDM symbol (without CP) on
time-domain under SNR=0 dB at sampling-rate 1.92 and 30.72 MHz, and the
interpolated correlations based on 1.92 MHz and with W = 20, respectively.

E. Stage 2a: Interpolate the Correlations
D. Stage 1c: Channel Estimation and Interference Cancellation
As we assume that the fading-channel is approximately
constant within one subframe, the channel estimate for the
strongest channel-path of the pth cell is
7 ñp +M−1
1 X X ỹ[k+ ℓ̃(s)M ] −j2π ǫ̂p (k+ℓ̃(s)M )
N
ĥp =
e
,
8M s=0
sp,ℓ̃(s) [k− ñp ]

(17)

k=ñp

where without loss of generality, we assume sp,ℓ [k] 6= 0 for
all k. The purified received samples ỹ[k] after removing the
regenerated PRS signal from the first p cells equals
ỹ[k+ ℓ̃(s)M ] = y[k+ ℓ̃(s)M ]
p−1
X
ǫ̂q (k+ℓ̃(s)M )
N
, (18)
−
h̃q sq,ℓ̃(s) [k− ñq ]e−j2π
q=0

where the refined channel estimate h̃p with LMMSE filter is
h̃p =

ĥp
1 + σ̃p2 /|ĥp |2

,

(19)

and the noise density σ̃p2 is estimated according to
σ̃p2 =

7 ñp +M−1
1 X X
ỹ[k+ ℓ̃(s)M ]
8M s=0
k=ñp

−ĥp sp,ℓ̃(s) [k − ñp ]e−j2π

ǫ̂p (k+ℓ̃(s)M )
N

2

. (20)

After all PRS symbols are estimated and removed from y[k],
the data ỹ[k] is sent to the EM-SIC block for processing
the next cell. As the PRS signal from the pth cell has been
removed from ỹ[k], the detection performance of the remaining
cells is improved, especially under the case that the received
signal power from the pth cell is stronger than the others.
The EM-SIC algorithm (comprising the processes in Sec.
III B-D) is repeated for the remaining cells until the ToAs
have been estimated for all cells. Once done, the received
signal ỹ[k] ideally comprises only noise and remaining PRS
signals. Hence, at the beginning of the next EM-SIC iteration
for each cell, the regenerated and subtracted signal in (18)
corresponding to that cell is added back to ỹ[k] for a refined
detection as depicted in Fig. 3.

As the PSD of the PRS signal is band-limited inside one
PRB, we can therefore interpolate the correlations Rp [n] to
a higher sampling-rate to improve the resolutions of estimated ToAs. With the coarse estimates obtained from the low
sampling-rate samples output from the first stage (after SIC
and FOC process), the upsampled correlations R̂p [m] can be
interpolated using a sinc-function according to

W
X
sin π m
n
V −
,
(21)
R̂p [m] =
Rp [n]
π m
V −n
n=−W

where V is the upsampling rate, and W specifies the window
size for searching around the coarse ToA estimate ñp . As can
be seen in Fig. 5, with Rp [n] calculated at sampling-rate 1.92
MHz, setting W = 20 is sufficient to capture the main-lobe of
the normalized PRS correlation function. With setting V = 16,
the interpolated correlations at 30.72 MHz is also depicted
which is shown to be accurate at an SNR of 0 dB.
F. Stage 2b: Iterative MPD
After obtaining the upsampled correlations R̂p [m], we can
perform the ToA detection of the first arrival-path. Directly
comparing the maximal value of R̂p [m] to a predefined
threshold as in (8) results in poor performance due to the
strong correlations of the PRS signal as shown in Fig. 5. For
instance, with an AWGN channel, the ToA estimate should
be the index corresponding to the maximal correlation value.
However, with a threshold η1 < 1, the detection (8) provides
a ToA estimate which is smaller than the true ToA. In order
to cope with fading-channels the threshold η1 needs to adapt
accordingly which is a difficult design task. Instead we utilize
a similar method as in [6] to implement iteratively MPD of
the fading-channel taking into account the ACF of the PRS
signal. We claim that a first path is found at position ñp,0 if
R̂p [ñp,0 ] = max
n

n

R̂p [m]

o

>

M̂ −1
γ X

M̂

R̂p [m] ,

(22)

m=0

where M̂ = V (2W + 1) is the length of R̂p [m], and γ is a
predefined peak-to-average (PAR) threshold.
Then we update R̂p [m] as
R̃p [ñp,0 +k] = R̂p [ñp,0 +k] − R̂p [ñp,0 ]R0 [k],

(23)

6

ñp = min {ñp,i },

(24)

i

which is the estimated ToA of the detected first arrival-path.
Note that, when path delays of the fading channel are
smaller than the main lobe of ACF depicted in Fig. 5, the
peak ñp,0 found in (22) can be an artificial peak caused
by overlapping of ACFs corresponding to different channel
taps. Therefore, a more accurate ToA estimator shall jointly
detect the multi-path components of the fading-channel, which
increases the complexity and is out of the scope of this paper.
IV. N UMERICAL R ESULTS
In this section, we provide numerical results to show the
promising performance of proposed EM-SIC based ToA detection for positioning of NB-IoT devices.
A. ToA Detection Performance with 3 Cells
Firstly we consider ToA detection with 3 cells with PCIs
equal to 0, 1 and 2 at sampling rate 1.92 MHz. The ToA np,0
(0 ≤ p ≤ 2) is set to 320, 480 and 640 Ts , and the transmit
powers of the three cells are set to 0, -4 and -8 dB, respectively.
We first evaluate the ToA detection performance without
residual FO under AWGN channel, in which case the channel
estimation degrades to received power detection. As shown in
Fig. 6, compared to a ToA detector without IC, the proposed
EM-SIC algorithm provides substantial SNR (measured by
the ratio of the transmit power of the strongest cell and the
noise density) gains up to 10 dB for the cell that has the least
transmit power.
In Fig. 7 we repeat the tests under ETU-3Hz channel, and
set the normalized residual FO for the three cells to 0.02, 0.01
and 0.01, respectively. As can be seen, the proposed EM-SIC
detector renders significant detection improvements compared
to the detector that does not apply FOC or SIC processes.
1
0.9
0.8
0.7

Pd

0.6

0.8

0.35

Pd with error-tolerance +/-2 samples

Cell 0
Cell 0, EM-SIC
Cell 1
Cell 1, EM-SIC
Cell 2
Cell 2, EM-SIC

0.4

0.3
0.25
0.2
0.15
0.1
0.05
0
-20

-10

0

10

20

SNR [dB]

0.4
0.3
0.2
0.1
-15

-10

-5

0

5

SNR [dB]

Fig. 6. The detection probability under AWGN channel with 3 cells running
the proposed EM-SIC detector only once .

0.5
0.4
0.3
0.2
0.1
0
-20

-10

0

10

20

SNR [dB]

C. OTDOA based Positioning Performance
In Fig. 10 and Fig. 11 we plot the cumulative distribution
function (CDF) of the horizontal positioning error under
TABLE I
S IMULATION PARAMETERS FOR OTDOA- BASED P OSITIONING .
Parameter

Value

Number of e-NodeBs
Inter-cite distance
Frequency band
Channel model
Number of e-NodeB antenna
Number of device antenna
Macro transmit power

6
1.732 km
900 MHz
AWGN, ETU
1
1
46 dBm for 1.92 MHz
-174 dBm/Hz for AWGN
-184 dBm/Hz for ETU
L = 120.9+37.6 log10 (d)
8 dB
Between e-NodeBs: 0.5
Between sectors of e-NodeB: 1.0

Shadowing correlation

10

0.6

Cell 0
Cell 0, EM-SIC
Cell 1
Cell 1, EM-SIC
Cell 2
Cell 2, EM-SIC

B. ToA Detection Performance in Practical Scenarios
Next we consider an NB-IoT system with simulation parameters listed in Table I, and the OTDOA based positioning
performance is evaluated with 6 cells with a deployment
geometry depicted in Fig. 8. We uniformly generate 200 NBIoT devices associated to the cell with PCI 8. In all simulations
we set the thresholds η2 = 0.8, η2 = 3 and γ = 7 and make no
efforts to further optimize them for each individual channel
condition. At the beginning of all detecting methods we use
(9) to decide whether PRS signal is present or not, and the
false alarm probability of detecting the PRS are similar for all
evaluated detectors.
In Fig. 9 we evaluate the probability density function
(PDF) of the ToA estimation error when only transmitting the
PRS from the cell with PCI 8 and disabling the other cells
under AWGN channel. The estimation errors are calculated
by subtracting the true ToA with estimated ToA values. As
can be seen, the FOC and upsampling using interpolations
improves the accuracy of the ToA estimation significantly.

Path loss model [9] (d in km)
Shadowing standard deviation

Cell 0, no IC
Cell 0, EM-SIC
Cell 1, no IC
Cell 1, EM-SIC
Cell 0, no IC
Cell 2, EM-SIC

0.7

Fig. 7. The detection probability under ETU-3Hz channel for 3 cells with
the proposed EM-SIC detector with 2 global iterations.

Thermal noise density

0.5

0
-20

0.45

Pd

where R0 [k] is the normalized ACF of time-domain PRS
signal with delay k. Then we check again if (22) holds by
replacing R̂p [m] with R̃p [m]. If so, we claim that a second
valid path is present at position ñp,1 where the maximum of
R̃p [n] is attained, and then we update R̄p [ñp,1 +k] again by
subtracting the impact of the ACF of the PRS signal according
to (23). We repeat this process iteratively until the condition
(22) is violated, and denote the detected channel-path delays
as ñp,i . Then, the ToA estimate ñp for the pth cell is set to

Number of PRB / PRS occasion
/ consecutive PRS subframes
PRS Muting
Normalized residual FO

1 /1 /1
False
Uniformly drawn in [-0.03, 0.03].

7

1
-1500

0.9
0.8
1

13

0

12

0.7

-500

500

6

7

4

0.6

14

CDF

x [m]

2

8

3

4

15

16

8

0.5
0.4
0.3

1500

17

9

10

5

0.2

no IC, 67% localized
EM-SIC w/o FOC and w/o upsampl., 88% localized
EM-SIC w. FOC and w/o upsampl., 97% localized
proposed EM-SIC, 97% localized

0.1
11
2500

0
0

3000
-3000

-2000

-1000

0

1000

2000

50

100

150

200

250

300

350

400

450

500

Horizontal error [m]

3000

y [m]

Fig. 8. The geometric deployment of the 6 e-NodeBs (marked as magenta
circles and each of them comprises 3 sectors) and 200 NB-devices (marked
as red triangles) that are associated to the cell with PCI 8.

Fig. 10. The OTDOA based positioning performance and localization ratio
under AWGN channel.
1
0.9

3
0.8

no IC
EM-SIC w/o FOC and w/o upsampl.
EM-SIC w. FOC and w/o upsampl.
proposed EM-SIC

2.5

0.7

CDF

0.6

PDF [%]

2

0.5
0.4

1.5

0.3
0.2

no IC, 56% localized
EM-SIC w/o FOC and w/o upsampl., 76% localized
EM-SIC w. FOC and and w/o upsampl., 85% localized
proposed EM-SIC, 86% localized

1
0.1
0

0.5

0

50

100

150

200

250

300

350

400

450

500

Horizontal error [m]
0
-4

-3

-2

-1

0

1

2

3

4

ToA error [16Ts]

Fig. 9. The PDF of ToA estimation errors. The iterative MPD performs better
than the threshold based detection (8) under AWGN channel.

AWGN channel and ETU-3Hz channels, respectively. The
localization percentages of different detection methods are
also shown in the legends, where we claim a successful
positioning only when at least three cells are detected and
the positioning error-distance is less than 500 m. As can
be seen, under both channels the proposed EM-SIC detector
performs much better than a traditional no IC detector that
does not consider the impairments of the interference, residual
FO and fading-channels. Moreover, as can be seen, the FOC
and upsampling processes greatly improve the positioning
performance under AWGN channels, while under EUT-3Hz
channel, the gains in positioning accuracy introduced by FOC
and upsampling processes are marginal due to inaccurate ToA
estimates. Nevertheless, with FOC process the localized ratio
is still greatly improved, while the upsampling process further
slightly improves that.
V. S UMMARY
We have considered the observed-time-difference-of-arrival
(OTDOA) based positioning for an NB-IoT device with multiple cells. We have proposed an expectation-maximization
based successive interference cancellation (EM-SIC) detector
to jointly consider the fading-channel, residual frequency offset (FO), and time-of-arrival (ToA) of the first arrival-path. To
design a low complexity ToA detector, the EM-SIC algorithm
works with received time-domain samples at a low samplingrate. The resolution of estimated ToA is further refined by

Fig. 11. The OTDOA based positioning performance and localization ratio
under ETU-3Hz channel.

upsampling the correlations obtained at the low samplingrate inside a small search window to a higher sampling-rate
with interpolation. Numerical simulations have shown that,
the proposed EM-SIC ToA detector performs robustly against
impairments introduced by inter-cell interference, fadingchannel and residual FO, which shows significant signal-tonoise (SNR) gains compared to traditional ToA detectors that
do not thoroughly consider these impairments.
R EFERENCES
[1] S. Fischer, “Observed time difference of arrival (OTDOA) positioning
in 3GPP LTE,” White Paper, Qualcomm Technologies Inc., Jun. 2014.
[2] 3GPP TS 36.211, “Evolved Universal Terrestrial Radio Access (EUTRA): Physical channels and modulation,” Release 14, Dec. 2016.
[3] J. Liu and S. Feng, “RSTD performance for small bandwidth of OTDOA
positioning in 3GPP LTE,” IEEE Veh. Tech. Conf. (VTC-Fall), Las
Vegas, Sep. 2013, pp. 1-5.
[4] W. Xu, M. Huang, C. Zhu, and A. Dammann, “Maximum likelihood
TOA and OTDOA estimation with first arriving path detection for 3GPP
LTE system,” Trans. Emerging Tel. Tech., vol. 27, no. 3. pp. 339-356,
Mar. 2016.
[5] S. M. Kay, “Fundamentals of statistical signal processing, volume I:
Estimation theory,” Prentice Hall signal processing series, 1993.
[6] H. Rydén, A. A. Zaidi, S. M. Razavi, F. Gunnarsson, and I. Siomin,
“Enhanced time of arrival estimation and quantization for positioning in
LTE networks,” IEEE Int. Symp. on Personal, Indoor and Mobile Radio
Commun. (PIMRC), Valencia, Sep. 2016, pp. 1-6.
[7] S. Hu, G. Wu, B. Priyanto, F. Rusek, S. Kant, and J. Chen, “Iterative
interference cancellation method”, Patent US20140369300A1, filed on
Aug. 2014.
[8] M. Morelli and U. Mengali, “An improved frequency offset estimator
for OFDM applications,” IEEE Comm. Lett., vol. 3, no. 3, pp. 75-77,
Mar. 1999.
[9] 3GPP TSG RAN WG1, R1-168310, “WF on simulation assumption for
NB-IoT positioning,” Gothenburg, Sweden, Aug. 22-27, 2016.

