Comparative Results for Positioning with
Secondary Synchronization Signal versus Cell
Specific Reference Sig nal in LTE Systems
Kimia Shamaei, Joe Khalife, and Zaher M. Kassas
University of California, Riverside
BIOGRAPHIES
Kimia Shamaei is a Ph.D. candidate at the University of California, Riverside and a member of the Autonomous
Systems Perception, Intelligence, and Navigation (ASPIN) Laboratory. She received her B.S. a nd M.S. in Electrical
Engineering from the University of Tehran. Her current resea rch interests include analysis and modeling of signals
of opportunity and software-defined radio.
Joe J. Khalife is a Ph.D. student at the University of California, Riverside and a member of the ASPIN Laboratory.
He received a B.E. in Electrical Engineering and an M.S. in Computer Engineering from the Lebanese American
University (LAU). From 2012 to 2015, he was a research assistant at LAU. His research interests include o pportunistic
navigation, autonomous vehicles, and software-defined radio.
Zaher (Zak) M. Kassas is an assistant professor at the University of California, Riverside and director of the ASPIN
Laboratory. He received a B.E. in Electrical Engineering from LAU, an M.S. in Electrical and Computer Engineering
from The Ohio State University, and an M.S.E. in Aerospace Engineering and a Ph.D. in Electrical and Computer
Engineering from The University of Texas a t Austin. From 2004 through 2010 he was a research and development
engineer with the LabVIEW Control Design and Dynamical Systems Simulation Group at National Instruments
Corp. His research interests include estimation, navigation, autonomous vehicles, a nd intelligent transportatio n
systems.
ABSTRACT
The achieva ble positioning precision using two different reference signals in long-term evolution (LTE) systems,
namely the secondary synchronization signal (SSS) and the cell-spec ific refere nc e signal (CRS), is presented. Two
receiver architectures are presented: SSS-based and CRS-base d. The CRS-based receiver refines the time-of-arrival
(TOA) estimate obtained from the SSS signal by estimating the channel frequency response, yielding a more precise
TOA estimate. Experimental results of a ground vehicle navigating with each of the presented receivers are given
showing a fivefold reduction in the positioning root-mean square erro r with the CRS-based receiver over the SSS-based
receiver.
I. INTRODUCTION
Signals of opportunity (SOPs) a re an attractive navigation source in global navigation satellite system (GNSS)-
challenged environments [1, 2]. The literature on SOPs answers theoretical questions on the observability and
estimability of the SOPs landscape for various a priori knowledge scenarios [3, 4] and prescrib e receiver motion
strategies for accurate receiver and SOP localization and timing estimation [5–7]. Moreover, a number of recent
experimental results have demonstrated receiver localization and timing via different SO Ps [8–14]. Cellular SOPs
are particularly attractive due to their high carrier-to-noise ratio and the large number of base transceiver stations
in GNSS-challenged environments. Navigation fr ameworks and receiver architectures were developed for cellular
code division multiple access (CDMA), which is the transmission standard of the third generation of cellular signals.
Experimental results showed meter-level a ccuracy fo r CDMA-based navigation [15].
In recent years, long-term evolution (LTE), the fourth ge ne ration cellular transmission standard, has received con-
siderable attention [16–20]. This is due to spec ific desirable characteristics of LTE signals, including: (1) higher
transmission ba ndwidth compared to previous g e ne rations of wireless standards and (2) the ubiquity of LT E net-
works. The literature on LTE-based navigation has de monstrated several exper imental results for positioning using
real LTE s ignals [16–18, 20]. Moreover, several software-defined receivers (SDRs) have been proposed for navigation
Copyright
c
2017 by K. Shamaei, J. Khalife, and Z. M. Kassas Preprint of the 2017 ION ITM Conference
Monterey, CA, January 30–February 2, 2017
with real and laboratory-emulated LTE signals [21–23]. Experimental results with real LTE sig nals showed meter-
level accuracy [23]. These SDRs rely on estimating the time-of-arrival (TOA) fr om the first peak of of the estimated
channel impulse response (CIR).
There are three possible reference sequences in a received LTE signal that can be used for navigation: (1) primar y
synchronization signal (PSS), (2) secondary synchronization signal (SSS), and (3) cell-specific reference signal (CRS).
First, the PSS is ex pressible in only three different seq uenc es, each of which repre sents the base station (referred to
as eNodeB) se ctors’ ID. This presents two main drawbacks : (1) the received signal is highly affected by interference
from neighbor ing eNodeBs with the same PSS sequences and (2) the user equipment (UE) can only simultaneously
track a maximum of three eNodeBs, which is not desirable in an environment with more than three eNodeBs .
Another reference sequence is the SSS, which represents the cell group identifier. Second, the SSS is expressible in
only 168 different sequences; therefore, it does not have the aforementioned drawbacks of the PSS. The transmission
bandwidth of the SSS is less than 1 MHz, leading to low TOA accuracy in a multipa th environment. However,
it can prov ide computationally low-cost and relatively precise pseudorange information using conventional delay-
locked loops (DLLs). The third re ference sequence is the CRS, which is mainly transmitted to estimate the channel
between the eNodeB and the UE. Therefore, it is scattered in both frequency and time and is transmitted from
all transmitting antennas. The CRS is known to provide hig he r accura cy in estimating the TOA due to its higher
transmission bandwidth [24].
This paper’s objective is to study the achievable po sitioning precision with SSS versus CRS signals. To this end,
the architectures of an SSS-based and a CRS-based SDRs are presented. Then, an extended Kalman filter (EKF)
framework for navigating with LTE signals using the presented SDRs is given. Finally, experimental analysis for
a ground vehicle-mounted receiver is presented for the (1) precisio n of the pseudoranges obtained from each of the
SDRs and (2) the accuracy of the navigation solution obtained from the EKF framework.
The remainder of this paper is organize d as follows. Section II provides an overview of the LTE frame structure and
reference signals and discusses the signal acquisition pr ocess. Section III discusses the a rchitecture of the SSS-based
LTE SDR. Section IV provides an architecture for a CRS-based LTE SDR. Section V presents an EKF framework
for navigating using LTE signals and provides ex perimental results showing (1) the pseudoranges obtained fro m each
of the proposed SDRs and (2) a ground vehic le navigating via real LTE signals using the SDRs and EKF framework
proposed in this pap e r. Concluding remarks are given in Sectio n VI.
II. LTE FRAME AND SIGNALS
In this section, the structur e of the LTE signals is outlined. Then, two types of signals that can be exploited fo r
navigation purposes are discussed, namely (1) synchronization signals (i.e., PSS and SSS) and (2) the CRS. Finally,
a method for acquiring a coarse estimate of the TOA of the LTE signal that exploits synchronization signals is
discussed.
A. LTE Frame Structure
In the LTE downlink transmission protoco l, the transmitted data is enc oded using orthogonal fre quency division
multiplexing (OFDM). In OFDM, the transmitted symbols are mapped to multiple carrie r frequencies called subcar-
riers. Fig. 1 represents the block diagram of the OFDM encoding scheme for digital transmission. The serial data
symbols are first parallelize d in gro ups of length of N
r
, where N
r
represents the number of subcarriers tha t carry
data. Then, each group is zero-padded to length N
c
, and the inverse fast fourie r transfor m (IFFT) of the result is
taken. To provide a guard band in the frequency-domain, N
c
is set to be greater than N
r
. Finally, to protect the
data from multipath effect, the last L
CP
elements of the obtained symbols are repeated at the beginning of the data,
which is called cy clic prefix (CP). The transmitted symbols at the receiver can be obtained by reverting all these
steps.
The obtained OFDM signa ls are arranged into multiple blocks, which are called frames. In an LTE system, the
structure of the frame is dependent on the transmission type, which can be frequency division duplexing (FDD) or
time division duplexing (TDD). Due to the superior performance of FDD over TDD [25], most network providers
use FDD for LTE transmission. Therefore, this pap er considers FDD frames only, and an FDD frame will be simply
denoted frame.
Serial
to
parallel
S
N
c
, . . . , S
1
. . .
IFFT
S
1
S
N
c
Cyclic
prefix
. . .
s
1
s
N
c
OFDM signal
Parallel
to
serial
s
N
c
−L
CP
+1
s
N
c
. . .
Fig. 1. OFDM transmission block diagram.
A frame is compose d of 10 ms of data, which is divided into 20 slots with a duration of 0.5 ms each – equivalent to 10
subframes with a duration of 1 ms each. A slot can be decompose d into multiple resource grids (RGs), and each RG
has numerous resource blocks (RBs). A RB is divided into smaller elements, namely resource elements (REs), which
are the smallest building blocks of an LTE frame. The frequency and time indices of an RE are called subcarrier and
symbol, respectively. The structure of the LTE frame is illustrated in Fig. 2 [26].
grid
Resource
block
Resource element
0
1 Slot = 0.5 ms
1 Frame = 10 ms
1 Subframe = 1 ms
1 2 3
. . .
16 17 18 19
. . .
. . .
Resource
. . .
. . .
Slot
. . .
. . .
. . .
. . .
. . .
. . .
. . .
Fig. 2. LTE frame structure.
The number of subcarriers in an LT E frame, N
c
, and the number of used subcarriers, N
r
, are assigned by the network
provider and can only take the values that are tabulated in Table I. The subcarrier spacing is typically ∆f = 15 KHz.
Hence, the occupied bandwidth can be c alculated using W = N
r
× ∆f, w hich is less than the assigned bandwidth
shown in Table I to provide a guar d band for LTE transmission.
TABLE I
LTE system bandwidths and number of subcarriers.
Bandwidth
(MHz)
Total number
of subcarriers
Number of
subcarriers used
1.4 128 72
3 256 180
5 512 300
10 1024 600
15 1536 900
20 2048 1200
When a UE rece ives an LTE signal, it must reconstruct the LTE frame to be able to extract the information
transmitted in the signal. This is achieved by first identifying the frame start time. Then, knowing the frame timing,
the receiver can remove the CPs and take the fast four ie r transform (FFT) of each N
c
symbols. The duration o f the
normal CP is 5.21 µs for the first symbol of each slot and 4 .69 µs for the rest of the sy mbols [26]. To deter mine the
frame timing, PSS and SSS must b e acquired, which will be discussed in the next subsection.
B. Synchronization Signals
To provide the symbol timing, the PSS is tr ansmitted on the last symbol of slot 0 and repeated on slot 10. The
PSS is a length-62 Zadoff-Chu sequence which is located in 62 middle subcarriers of the bandwidth excluding the
DC subcarrier. The PSS can be one of only three possible sequences, each of which maps to an integer value
N
(2)
ID
∈ {0, 1, 2}, re presenting the sector number of the eNodeB. To detect the PSS, the UE ex ploits the orthogonality
of the Zadoff-Chu sequences and correlates the received signal with all the possible choices of the PSS, as given by
Corr(r, s
P SS
)
m
=
N−1
X
n=0
r(n)s
∗
P SS
(n + m)
N
= r(m) ⊛
N
s
∗
P SS
(−m)
N
, (1)
where r(n) is the received signal, s
P SS
(n) is the receive r-generated time-do main PSS sequence, N is the frame
length, (·)
∗
is the complex-conjugate operator, (·)
N
is the circular shift ope rator, and ⊛
N
is the circular convolution
operator. By taking the FFT then IFFT o f (1), the correlation can be r ewritten as
Corr(r, s
P SS
)
m
= IFFT{R(k)S
∗
P SS
(k)}, (2)
where R(k) , FFT{r(n)} , and S
P SS
(k) , FFT{s
P SS
(n)}.
The SSS is an orthogonal length-62 se quence, which is transmitted in either slot 0 or 10, in the symbol preceding the
PSS, and on the same subcarriers as the PSS. The SSS is obtained by concatenating two maximal-length sequences
scrambled by a third orthogonal sequence generated ba sed on N
(2)
ID
. There ar e 168 possible sequences for the SSS that
are mapped to an integer number N
(1)
ID
∈ {0, . . . , 167}, called the cell group identifier. The FFT-based corr elation
in (2) is also exploited to detect the SSS signal. Fig. 3 shows the PSS and SSS cor relation results with re al LTE
signals.
Time [s]
PSS correlation
SSS correlation
Fig. 3. PSS and SSS correlation results with real LTE signals.
Once the PSS and SSS are detected, the UE can estimate the frame start time,
ˆ
t
s
, and the eNode B’s ce ll ID using
N
cell
ID
= 3N
(1)
ID
+ N
(2)
ID
.
C. CRS
The CRS is a pseudo-random sequence, which is uniquely defined by the eNodeB’s cell ID. It is spread across
the entire bandwidth and is transmitted mainly to estimate the channel frequency response. The CRS subcarrier
allocation depends on the cell ID, a nd it is designed to keep the interference with CRSs from other eNodeBs to a
minimum. The transmitted OFDM symbol containing the CRS at the k-th subcarrier, Y (k), c an be expressed as
Y (k) =
(
S(k), if k ∈ A
CRS
,
D(k), otherwise,
(3)
where S(k) is the eNodeB’s CRS sequence, D(k) is other data signals, A
CRS
is the set of s ubca rriers carrying C RS
signal.
III. SSS-BASED RECEIVER
In Section II, acquiring a coarse estimate of frame timing using the PSS and SSS signals was discussed. After
acquisition, the UE tr acks the frame timing to estimate the TOA. The SSS is one possible sequence that a UE
can exploit to track the frame timing [23]. In this section, the structure of this SSS-based tracking algorithm is
discussed. Fig. 4 represents the block diagram of an SSS-based tracking loop [23]. This structure is composed of
a frequency-locked loo p (FLL)-assisted phase -locked loop (PLL) and a carrier-aided de lay-locked loop (DLL). Each
component is discussed next in detail.
Correlator
S
p
k
S
e
k
S
l
k
SSS
generator
1
ω
c
Phase
discrim.
Code phase
data
Baseband
ˆ
t
s
Frequency
discrim.
z
−1
Loop
filter
Loop
filter
Loop
filter
1
1−z
−1
NCO
discrim.
Tracking
v
PLL,k
v
DLL,k
v
FLL,k
2π
ˆ
f
D
k
Fig. 4. SSS-based signal tracking block diagram.
A. FLL-Assisted PLL
The FLL-assisted PLL consists of a phase discriminator, a phase loop filter, a frequency discr iminator, a frequency
loop filter, and a numerically-controlled oscillator (NCO). Since there is no data modulated on the SSS, an atan2
phase disc riminator, which remains linear over the full input error range of ±π, could be used without the risk of
introducing phase ambiguities. A third-order PLL was used to track the carrier phase, with a loop filter transfer
function given by
F
PLL
(s) = 2.4ω
n,p
+
1.1ω
2
n,p
s
+
ω
3
n,p
s
2
, (4)
where ω
n,p
is the undamped natural freq ue nc y of the phase loop, which can be related to the PLL noise-equivalent
bandwidth B
n,PLL
by B
n,PLL
= 0.784 5ω
n,p
[27, 28]. The output of the phase loop filter is the rate of change of the
carrier phase error 2π
ˆ
f
D
k
, expressed in rad/ s, where
ˆ
f
D
k
is the Doppler frequency. The phase loop filter transfer
function in (4) is discretized and realized in state-space. The nois e-equivalent bandwidth B
n,PLL
is chosen to range
between 4 and 8 Hz. The PLL is assisted by a second-order FLL with an atan2 discriminator for the frequency a s
well. The frequency error at time step k is expressed as
e
f
k
=
atan2
Q
p
k
I
p
k−1
− I
p
k
Q
p
k−1
, I
p
k
I
p
k−1
+ Q
p
k
Q
p
k−1
T
sub
,
where S
p
k
= I
p
k
+ jQ
p
k
is the prompt correlatio n at time-step k and T
sub
= 0.0 1 s is the subaccumulation period,
which is chosen to b e one frame length. The tra nsfer function of the freque nc y loop filter is given by
F
FLL
(s) = 1.414ω
n,f
+
ω
2
n,f
s
, (5)
where ω
n,f
is the undamped natural freq ue ncy of the frequency loop, which can be related to the FLL noise-equivale nt
bandwidth B
n,FLL
by B
n,FLL
= 0 .53ω
n,f
[27]. The output of the freque ncy loop filter is the rate of change of the
angular frequency 2π
ˆ
˙
f
D
k
, expre ssed in rad/s
2
. It is ther e fore integrated a nd added to the output of the phase loop
filter. The fre quency loop filter transfer function in (5) is dis c retized and realized in state-space. The noise-equivalent
bandwidth B
n,FLL
is chosen to range between 1 and 4 Hz.
B. Carrier-Aided DLL
Two types of discr iminators for the DLL are considered: (1) coherent and (2) noncoherent [29]. The carrier-aided
DLL employs these discriminators to compute the SSS code phase error using the prompt, early, and late correlatio ns,
denoted by S
p
, S
e
, and S
l
, respectively. The early and late correlations are calculated by correlating the received
signal with an early and a delayed version of the prompt SSS sequence, respectively. The time shift between S
e
and
S
l
is defined by an early -minus-late time t
eml
, ex pressed in chips. The chip interval T
c
for the SSS can be expressed as
T
c
=
1
W
SSS
, where W
SSS
is the bandwidth of the synchronization signal. Since the SSS occupies only 62 subcarriers,
W
SSS
is calculated to be W
SSS
= 62 × 15 = 930 KHz, hence T
c
≈ 1.0752µs.
The DLL loop filter is a simple gain K, with a noise-equivalent bandwidth B
n,DLL
=
K
4
≡ 0 .5 Hz. The output of
the DLL loop filter v
DLL
is the rate of change o f the SSS code phase, expressed in s/s. Assuming low-side mixing,
the code start time is updated according to
ˆ
t
s
k+1
=
ˆ
t
s
k
− (v
DLL,k
+
ˆ
f
D
k
/f
c
) · T
sub
.
Finally, the frame start time estimate is used to reconstruct the transmitted LTE frame.
IV. CRS-BASED RECEIVER
After obta ining the TOA using the SSS-ba sed receiver, the UE could improve the TOA estimate using the CRS
signal. For this purpose, the signal must be first converted to the frame structure. Then, the UE must estimate the
channel frequency response
ˆ
H(k) from
ˆ
H (k) = S
∗
(k)R(k)
= H(k)
S
(u
′
)
(k)
2
+ V (k),
where k ∈ A
CRS
and V (k) is additive white Gaussian noise . Knowing that
S
(u
′
)
(k)
2
= 1, the estima te of the
channel frequency response is simplified to
ˆ
H(k) = H (k) + V (k). (6)
By applying a Hamming window w(k) whose length is equal to the channel frequency response and ta king a 2K
point IFFT from (6), the channel impulse respons e can be expressed as
ˆ
h(n) =
1
2K
K−1
X
κ=0
ˆ
H (κ)w(κ)e
j2πnκ
2K
.
where K is the length of the channel. The symbol timing error is the time shift at which the first peak of the channel
impulse response occurs. Fig. 5 represents the block diagram of e xtracting the TOA from the CRS.
Cell ID
CRS
Channel
Timing Information Extraction
τ
estimation
MedianLTE
Frame Filter
Fig. 5. Timing information extraction block diagram.
The estimated TOA obtained by the CRS is exploited as a feedback to cor rect the SSS-based results. Section V will
demonstrate the efficacy of this feedback in multipath environments.
V. EXPERIMENTAL RESULTS
In this section, a navigation framework that employs the SDRs proposed in this paper and an EKF is described.
Next, experimental results demonstra ting a gr ound vehicle navigating using real LTE signals are presented.
A. Navigation Framework
Sections III and IV discussed how a TOA estimate can be extracted from LTE signals. By multiplying the obtained
TOA estimate with the s peed of light, c, a pse udorange measurement can be formed. This measurement can be
parameterize d by the receiver and eNodeB states. The sta te of the vehicle-mounted receiver is given by
x
r
=
h
r
T
r
,
˙
r
T
r
, cδt
r
, c
˙
δt
r
i
T
,
where r
r
= [x
r
, y
r
, z
r
]
T
is the receiver’s three-dimensional (3-D) position vector, δt
r
is the receiver’s clock bias, and
˙
δt
r
is the receiver’s clock drift. The s tate of the i-th eNodeB is given by
x
s
i
=
h
r
T
s
i
, cδt
s
i
, c
˙
δt
s
i
i
T
,
where r
s
i
= [x
s
i
, y
s
i
, z
s
i
]
T
is the i-th eNodeB’s 3-D position vector, δt
s
i
is the eNodeB’s clock bias, and
˙
δt
s
i
is the
eNodeB’s clock drift. The pseudorange betwe e n the rece iver a nd i-th eNodeB can be expressed as
ρ
i
= kr
r
− r
s
i
k
2
+ c · [δt
r
− δt
s
i
] + v
i
,
where v
i
is the measurement noise, which is modeled as a zero-mean Gaussian random variable with variance σ
2
i
.
The receiver’s clock bias and drift are assumed to evolve according to the following dis c rete-time (DT) dynamics
x
clk
r
(n + 1) = F
clk
x
clk
r
(n) + w
clk
r
(n),
where
x
clk
r
,
cδt
r
c
˙
δt
r
, F
clk
=
1 T
0 1
, w
clk
r
=
w
δt
r
w
˙
δt
r
,
where T ≡ T
sub
is the sampling time and w
clk
r
is the process noise, which is modeled as a DT zero-mean white
sequence with covar iance Q
clk
r
with
Q
clk
r
=
"
S
˜w
δt
r
T+S
˜w
˙
δt
r
T
3
3
S
˜w
˙
δt
r
T
2
2
S
˜w
˙
δt
r
T
2
2
S
˜w
˙
δt
r
T
#
.
The terms S
˜w
δt
r
and S
˜w
˙
δt
r
are the clock bias and drift proces s noise power spectra, respectively, which can be related
to the power-law coefficients, {h
α
}
2
α=−2
, which have been shown through laboratory experiments to characterize the
power spectral density of the fractiona l frequency de viation of an oscillator from nominal frequenc y according to
S
˜w
δt
r
≈
h
0
2
and S
˜w
˙
δt
r
≈ 2π
2
h
−2
[30].
The i-th eNodeBs’ clock states evolve according to the same dynamic model as the receiver’s clock state, except
that the process noise is replaced with w
clk
s
i
,
h
w
δt
s
i
, w
˙
δt
s
i
i
T
, w hich is modeled as a DT zero-mean process with
covariance Q
clk
s
i
[31].
One of the main challenges in navigation with LTE signals is the unavailability of the eNodeBs’ positions and clock
states. It ha s been previously shown that the SOP position can be mapped with a high degree of accuracy whether
collaboratively or non-co llab oratively [31–33]. In what follows, the eNodeBs’ pos itions are assumed to be known, and
an EKF will be utilized to estimate the vehicle’s position r
r
and ve locity
˙
r
r
states simultaneously with the difference
between the receiver and each eNodeB s’ clock bias and drift states. The difference between the receiver’s clock state
vector and the i-th eNodeB’s clock state vector ∆x
clk
i
, x
clk
r
− x
clk
s
i
evolves according to
∆x
clk
i
(n + 1) = F
clk
∆x
clk
i
(n) + w
clk
i
(n),
where w
clk
i
,
w
clk
r
− w
clk
s
i
is a DT zero-mean white sequence with covariance Q
clk
i
, where Q
clk
i
, Q
clk
r
+Q
clk
s
i
.
The receiver is assumed to move in a two-dimensional (2-D) plane with known height, i.e., z(n) = z
0
and ˙z(n) = 0,
where z
0
is a known constant. Moreover, the r eceiver’s 2- D position is assumed to evolve according to a veloc ity
random walk, with the continuous-time (CT) dynamics given by
¨x
r
(t) = ˜w
x
, ¨y
r
(t) = ˜w
y
, (7)
where ˜w
x
and ˜w
y
are zero-mean white noise pr ocesses w ith powe r spectral densities ˜q
x
and ˜q
y
, respectively. The
receiver’s DT dynamics are hence given by
x
pv
(n + 1) = F
pv
x
pv
(n) + w
pv
(n),
where
x
pv
,
x
r
y
r
˙x
r
˙y
r
, F
pv
=
1 0 T 0
0 1 0 T
0 0 1 0
0 0 0 1
,
and w
pv
is a DT zero-mean white sequence with covariance Q
pv
, where
Q
pv
=
˜q
x
T
3
3
0 ˜q
x
T
2
2
0
0 ˜q
y
T
3
3
0 ˜q
y
T
2
2
˜q
x
T
2
2
0 ˜q
x
T 0
0 ˜q
y
T
2
2
0 ˜q
y
T
.
The augmented state vector which will be estimated by the EKF is defined as x ,
x
T
pv
, ∆x
T
clk
1
, . . . , ∆x
T
clk
M
T
. This
vector has the dynamics
x(n + 1) = Fx(n) + w(n),
where F , diag [F
pv
, F
clk
, . . . , F
clk
] and w is a DT zero-mean white sequence with covariance Q , diag [Q
pv
, Q
clk
]
and
Q
clk
=
Q
clk
r
+ Q
clk
s
1
Q
clk
r
. . . Q
clk
r
Q
clk
r
Q
clk
r
+ Q
clk
s
2
. . . Q
clk
r
.
.
.
.
.
.
.
.
.
.
.
.
Q
clk
r
Q
clk
r
. . . Q
clk
r
+ Q
clk
s
M
.
B. Results
To evaluate the performance of the SSS- and CRS-based LTE SDRs, a field test was conducted with real LTE signals
in a suburban environment. For this purpose, a mobile ground receiver was equipped with three antennas to acquire
and track: (1) GPS signals a nd (2) LTE signals in two different bands from nearby eNodeBs. The LTE antennas
were consumer-grade 800/1 900 MHz cellular omnidirectional antennas a nd the GP S antenna was a surveyor-grade
Leica antenna. The LTE signals were simultaneously down-mixed and synchronously sampled via a dual-channel
universal software radio p e ripheral (USRP) driven by a GPS-disciplined oscillator (GPSDO). The GPS signals were
collected on a separate single-channel USRP a lso driven by a GPSDO. It is worth mentioning that the GPSDO is
only used to discipline the clock on the USRP, which is not very stable without a GPSDO. The LTE receiver was
tuned to the carrier frequencies of 1955 and 2145 MHz, which are allocated to the U.S. LTE providers AT&T and
T-Mobile, respectively, and the tra nsmission bandwidth was measured to be 20 MHz. Samples o f the received signals
were stored for off-line post-processing. The GPS signal was pro cessed by a Generalized Radionavigation Interfusion
Device (GRID) SDR [34] and the LTE signals were pro cessed by the proposed SSS- and CRS-based LTE SDRs. Fig.
6 shows the experimental hardware and software setup.
Over the course of the experiment, the vehicle-mounted receiver traversed a total trajectory of 2 Km while listening
to 2 eNodeBs simultaneously. The position states of the eNode Bs were mapped prior to the experiment. The first
part of the experiment was to evaluate the quality of the pseudoranges obtained by the SSS- and the CRS-based
SDRs. To this end, the change in the pseudorange b etween the receiver and eNodeB 1 and 2 was calculated using
the SSS- and CRS-ba sed SDRs. The result is plotted for each eNodeB in Fig. 7 and Fig. 9 , respectively. The change
in true range calculated from the GPS solution is also shown in thes e figures. The pseudorange error obtained from
the SSS-based SDR had a standard deviation of 32.72 m for eNodeB 1 and 3 7.49 m for eNodeB 2. The pseudorange
error obta ine d from the CRS-based SDR had a s tandard deviation of 5.14 m for eNodeB 1 and 6.01 m for eNodeB
GRID GPS SDR
MATLAB
Estimator
LTE SDR
Storage
USRP
RIO
USRP
NI-2930
GPS
Antenna
LTE
Antennas
Fig. 6. Experimental setup. The LTE antennas were connected to a dual-channel National Instrument (NI) USRP RIO and the GPS
antenna was connected to an NI-2930 USRP. T he USRPs were driven by two independent GPSDOs.
2. Fig. 8 and Fig. 10 show the pseudorange error and its cumulative distribution function (CDF) obtained by the
SSS- and CRS-based SDRs for eNo de B 1 and e NodeB 2, respectively.
On one hand, Fig. 7 and Fig. 9 show that the ma in cause of error in the pseudorange obtained by tracking the SSS
signal is due to multipath. The estimated CIR at t = 13.0 4 s for eNodeB 1 and t = 8 .89 s for eNodeB 2 (Fig. 7 and
Fig. 9, respectively) show several peaks resulting from multipath. These peaks are the main so urce of pseudor ange
error at t = 13.04 s for eNodeB 1 a nd t = 8.89 s for eNodeB 2, which are around 330 m and 130 m, res pectively.
On the other hand, Fig. 7 and Fig. 9 show that the CRS-based receiver has a significantly lower pseudorange error
compared to the SSS-based receiver in multipath environments.
It is worth mentioning that in some environments with severe multipath, the line-of-sight (LOS) sig nal may have
a significantly lower amplitude compared to the multipath signals. In this case, the CIR peak-detection threshold
must be dynamically tuned in the receiver in order to detect the LOS peak. The pseudorang es shown in Fig. 7 and
Fig. 9 are obtained by tuning the receiver threshold in post-processing. Fig. 11 (a) shows the pseudorange obtained
without dynamically adjusting the p eak-detection thre shold and Fig. 11(b) depicts the in-phase and quadrature
components of the pr ompt correlation during tracking. An instance of having a LOS peak that is significantly lower
than multipath peaks is shown in the estimated CIR at t = 40.5 s in Fig. 9. It can be seen from this estimated CIR
that the LOS peak is at approximately -40 m, whereas the highes t peak of the estimated C IR, which corresponds to
a multipath signal, is at approximately 400 m. Consequently, an error of approximately 440 m due to multipa th will
be introduced into the pseudorange, as shown in 11(a). Moreover, Fig. 11(b) shows that the receiver loses track of
the signal at t = 40.5 s.
The second part of the experiment was to navigate using LTE signals exclusively and via the EKF framework discussed
in the previous subsection. For this purpos e, the receiver’s position and velocity a long with the difference of clock
biases between the re ceiver a nd each eNodeB as well as the difference of c lock drifts were estimated dynamically. To
make the problem observable, it is assumed that the re ceiver had a ccess to GPS befor e navigating with LTE signals;
hence, the receiver had full knowledge of its initial state [4].
The environment layout as well as the true and estimated receiver trajectories are shown in Fig. 12. The root
mean squared error (RMSE) betwee n the GPS and SSS-based navigation solutions along the traversed trajectory
was ca lculated to be 50.46 m with a standard deviatio n of 41.07 m and a maximum error of 419.66 m. The RMSE
between the GPS and CRS-based navigation solutions was calculated to be 9.32 m with a standard deviation of 4.36
m and a maximum error of 33.47 m. Theses results are summariz ed in Table II.
TABLE II
Experimental results [in meters] comparing navigation solutions obtained from SSS-based and CRS-based SDRs.
LTE
Receiver
RMSE
Standard
deviation
Maximum
error
SSS 50.46 41.07 419.66
CRS 9.32 4.36 33.47
Channel taps (m)
-1000 -800 -600 -400 -200 0 200 400 600 800 1000
CIR amplitude
0
1000
2000
3000
4000
Time (s)
0 20 40 60 80 100 120 140 160 180 200
Pseudorange (m)
-100
0
100
200
300
400
500
600
GPS
SSS
CRS
t=13.04 (s)
Fig. 7. Estimated change in pseudorange and estimated CIR at t = 13.04 s for eNodeB 1. The change in the pseudorange was calculated
using: (1) SSS pseudoranges, (2) CRS pseudoranges, and (3) true ranges obtained using GPS.
Time [s]
Distance Error [m]
Experimental CDF
(b)
(a)
Error [m]
CRS-based receiver
SSS-based receiver
CRS-based receiver
SSS-based receiver
Fig. 8. (a) Error of the change in pseudorange between (1) GPS and SSS and (2) GPS and CRS. (b) CDF of the error i n (a).
It is worth mentioning that there is a slight mismatch between the true vehicle’s dyna mical model and the assumed
model in (7). The rec eiver was moving on a road, mostly in straight segments. The velocity ra ndom walk model
used by the EKF does no t take into consideration the trajectory constra ints. Therefore, the EKF might allow the
vehicle’s position and velo c ity e stimates to move freely. This model misma tch will cause the estimation error to
become larger. In order to minimize the misma tch between the true a nd assumed model, multiple models for the
vehicle’s dynamics may be used to accommodate the different behaviors of the vehicle in differ e nt segments of the
Time (s)
0 20 40 60 80 100 120 140 160 180 200
Pseudorange (m)
-400
-200
0
200
GPS
SSS
CRS
Channel taps (m)
-1000 -500 0 500 1000
CIR amplitude
0
5000
10000
15000
Channel taps (m)
-1000 -500 0 500 1000
CIR amplitude
0
5000
10000
15000
t=8.9 (s)
t=40.5 (s)
LOS peak
Fig. 9. Estimated change in pseudorange and estimated CIR at t = 8.89 s and t = 40.5 s for eNodeB 2. The change i n the pseudorange
was calculated using: (1) SSS pseudoranges, (2) CRS pseudoranges, and (3) true ranges obtained using GPS.
Time [s]
Distance Error [m]
Experimental CDF
(b)
(a)
Error [m]
CRS-based receiver
SSS-based receiver
CRS-based receiver
SSS-based receiver
Fig. 10. (a) Error of the change in pseudorange between (1) GPS and SSS and (2) GPS and CRS. (b) CDF of the error in (a).
trajectory. Alternatively, an inertial measurement unit (IMU), which is available in many practical applications, can
be used to propagate the state of the vehicle. This will also aid in alleviating multipath-induced e rrors [14].
0 5 10 15 20 25 30 35 40 45 50
Time (s)
-1000
-800
-600
-400
-200
0
Pseudorange (m)
Loss of track
Fig. 11. Tracking results for eNodeB 2: (a) pseudorange obtained without dynamically tuning the peak-detection threshold and (b)
in-phase and quadrature components of the prompt correlation during tracking. Fig. (b) shows that the receiver loses track when the
threshold is not tuned to detect the LOS signal in severe multipath environments.
GPS
SSS
CRS
eNodeB 1
eNodeB 2
720 m
930 m
Fig. 12. Vehicle-mounted receiver’s GPS tr ajectory and trajectories estimated with LTE SSS and CRS signals. Also shown are the LTE
eNodeBs’ locations.
VI. CONCLUSION
This paper presented two SDR architectures for positioning with LTE sig nals. The first architecture relies on tracking
the SSS, which has a bandwidth of a round 1 MHz. The second architecture exploits the CRS, which has a bandwidth
of up to 20 MHz. In the latter, the CIR is first estimated using the CRS, and a TOA estimate is obtained by detec ting
the first peak of the estimated CIR. The precision of the pseudorange measurement obtained from each receiver is
evaluated using real LTE signals. Experimental results showing a ground vehicle equipped with the proposed LTE
SDRs navigating using real LTE signals in an EK F framework were pr ovided. The results show an RMSE of 50.46
m for the SSS-based SDR and an RMSE of 9.32 m for the CRS-based SDR ove r a 2 Km trajectory.
ACKNOWLEDGMENT
This work was supported in part by the Office of Naval Research (ONR) under Grant N00014-16-1-23 05.
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