93755181 lte-hoping

Channel Tracking versus Frequency
Hopping for Uplink LTE
KEN ERIKSSON
Master’s Degree Project
Stockholm, Sweden March 2007
XR-EE-KT 2007:003

Ericsson Internal
TECHNICAL REPORT 1 (34)
Prepared (also subject responsible if other) No.
LN/EAB/PDB/B Ken Eriksson
Approved Checked Date Rev Reference
2007-03-09 A
Channel tracking versus frequency hopping for uplink
LTE
Abstract
The aim of this work is to compare several algorithms in a receiver for uplink
LTE (Long Term Evolution). In this receiver, the radio propagation channel is
estimated using pilot SC-FDMA symbols. For a continuous transmission on a
constant frequency interval, these channel estimates can be interpolated over
time. The interpolation is done over several pilot symbols thus making it
possible to use previous pilot sequences transmitted from one terminal in
estimating the new data from the same terminal. This paper only investigates
algorithms used for estimating the channel for data sequences. The
investigated algorithms are different regression and interpolation methods,
and also an MMSE (Minimum Mean Square Error) method. Here the
performance between frequency hopping and an interpolation algorithm is
compared. With frequency hopping this interpolation is not possible. Instead a
frequency diversity gain is expected when the transmitter regularly changes
frequency interval. The LTE environment is simulated with a simulator written
in Matlab.
This is a report for a master thesis done at Ericsson Lindholmen.

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Contents
1 Background .........................................................................................3
1.1 Uplink and Transmitter structure .........................................................3
1.2 Downlink..............................................................................................4
1.3 OFDM..................................................................................................4
1.4 Sub-Carrier..........................................................................................4
1.5 MIMO...................................................................................................4
1.6 Sub-Frame ..........................................................................................5
1.6.1 Data SC-FDMA symbol .......................................................................5
1.6.2 Pilot SC-FDMA symbol........................................................................5
1.6.3 Cyclic Prefix.........................................................................................5
1.7 Channel model ....................................................................................6
1.7.1 Frequency Selective Channel Fading .................................................7
1.7.2 Time Varying Channel Fading .............................................................7
1.8 Inter Symbol Interference ....................................................................7
1.9 Inter Carrier Interference .....................................................................7
1.10 Receiver structure ...............................................................................7
1.11 Channel tracking .................................................................................9
1.12 Frequency Hopping .............................................................................9
2 Problem Description ..........................................................................11
2.1 Channel tracking versus Frequency hopping ....................................11
3 Procedure..........................................................................................12
3.1 Estimating channel at pilot SC-FDMA symbol...................................12
3.2 Estimating channel at data SC-FDMA symbol...................................12
3.2.1 Interpolation.......................................................................................13
3.2.2 Regression ........................................................................................14
4 Simulation results ..............................................................................20
4.1 Typical Urban 15 km/h.......................................................................21
4.2 Typical Urban 50 km/h.......................................................................23
4.3 Typical Urban 300 km/h.....................................................................26
4.4 Case3 10 km/h ..................................................................................27
4.5 AWGN ...............................................................................................28
4.6 Channel estimation with added delay..Error! Bookmark not defined.
5 Future Work.......................................................................................31
5.1 Time-variant channel estimates...........Error! Bookmark not defined.
5.2 Estimating the optimal SNR for the MMSE channel estimator ..........31
5.3 Velocity estimator for MMSE channel estimator................................31
6 Summary ...........................................................................................32
7 Notation .............................................................................................33
8 References ........................................................................................34

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1 Background
LTE is the next step in the ongoing development of today’s 3G standard
WCDMA to retain its competitiveness in the future. Each spectrum of 20 MHz
will have downlink capacity of approximately 100 Mbps, and uplink capacity of
approximately 50 Mbps. Technologies used in LTE includes OFDM
(Orthogonal Frequency Division Multiplexing) and MIMO (Multiple Input
Multiple Output). The carrier spacing is 15 kHz and a maximum of 1200 sub-
carriers can be used for a spectrum of 20 MHz.
1.1 Uplink and Transmitter structure
The communication technique used for uplink is SC-FDMA (Single Carrier
Frequency Division Multiple Access) and is based on DFT-spread OFDM. It is
similar to OFDMA (see section 1.2), which is the technique used on the
downlink, but has a lower PAPR (Peak-to-Average Power Ratio) thus making
it more suitable for uplink where mobile communication devices can transmit
information with a better power efficiency and less complex amplifiers. An
example of a transmitter for uplink is given in Figure 1.
Map
ping
Filte
ring
IDFT
DFT CP
inse
rtion
Modula
tion
Information
bits
Symbols Frequency
Domain
samples
Time
Domain
samples
Turbo
Codin
g
Localized
or
distributed
Raw/mode
m
bits
CRC
gener
ator
Check
sum
added
Figure 1. Transmitter structure for uplink LTE
When the information bits enter the transmitter it will first get a CRC
generated sequence attached. These attached bits will be used at the
receiver for verification to see if the information bits have changed during the
transmission. Turbo coding will then be used to increase the redundancy of
the information. After turbo coding, those bits will be coded into symbols by
one of the supported modulation formats: QPSK, 16QAM, or 64QAM.
The symbols will go through a DFT to transform them into frequency domain
samples. These samples will then be mapped to a number of sub-carriers,
which depends on the spectrum allocation (See section 1.4). This can be
done by two different methods, localized mode or distributed mode. The two
methods differ in how they handle the mapping of sub-carriers. Localized
mode will place all sub-carriers from the same user next to each other on an
allocated frequency spectrum. Distributed mode will spread the sub-carriers
and interlace them with sub-carriers from other users making use of a larger
frequency spectrum thus creating frequency diversity. The spectral efficiency
is the same in both methods.

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The frequency domain samples will be converted back into time domain
samples through an IFFT, and the cyclic prefix (See section 1.6.3) will be
inserted before the signal exits the transmitter.
1.2 Downlink
OFDMA is used on the downlink. This is a multi-carrier technique very similar
to the one used on the uplink but with a higher PAPR. The possible
modulations on downlink are QPSK, 16QAM, and 64QAM. The Downlink will
not be further discussed in this paper.
1.3 OFDM
OFDM (Orthogonal Frequency Division Multiplexing) based technique will be
used in both uplink and downlink. This technique maps the signal to a number
of sub-carriers with carrier spacing of 15 kHz. Each sub-carrier will be
orthogonal to each other hence avoiding ICI, See Figure 2
Frequency [Hz]
Figure 2. Frequency response for five orthogonal sub-carriers
1.4 Sub-Carrier
A sub-carrier is a narrow band carrier for use in OFDM based
communications. Sub-carriers will be spread over the entire frequency band
allocated to the user creating a spectrum of up to 1200 narrow band and
orthogonal carriers. By being narrow band the fading that each sub-carrier
experience can be approximated as a flat fading channel.
1.5 MIMO

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MIMO (Multiple Input Multiple Output) is a term used for multiple antenna
communication systems. Several independent signals can be transmitted,
leading to an increased spectral efficiency by exploiting spatial diversity. To
achieve this antennas have to be physically separated. Another way is to
separate the antennas through polarization. There are several ways to use
the multiple antennas depending on the area of priority, for example
redundancy or data rate.
1.6 Sub-Frame
A sub-frame is defined as a packet containing 6 data SC-FDMA symbols (see
section 1.6.1), 2 pilot SC-FDMA symbols (see section 1.6.2), and 8 cyclic
prefixes (see section 1.6.3), See Figure 3. This is subject to change since the
standardization of LTE is still under work.
0.5 ms
Long Block
Short Block
Cyclic Prefix
Figure 3. Sub-frame structure for uplink LTE (subject to change)
1.6.1 Data SC-FDMA symbol
A data SC-FDMA symbol, also called long block, contains unknown data for
the receiver, sent from the transmitter. It has the size of 2048 samples over
66.7 microseconds for a 20 MHz spectrum allocation. The data SC-FDMA
symbol contains relevant information transmitted over the radio channel, be it
speech or some other data.
1.6.2 Pilot SC-FDMA symbol
Pilot SC-FDMA symbol, also called short block, have half the length of long
blocks, 1024 samples over 33.3 microseconds for a 20 MHz spectrum
allocation. The information contained in a pilot SC-FDMA symbol is known by
the receiver, and by using these blocks the channel coefficients can be
estimated as described in section 3.1.
1.6.3 Cyclic Prefix

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A cyclic prefix is a repeat of the last part of an OFDM symbol attached to the
beginning. The purpose of the Cyclic Prefix is to act as a guard interval,
making it redundant to ISI (Inter Symbol Interference, See 1.8), and to convert
a linear convolution of the channel impulse response to a circular one.
OFDM symbol
CP
Figure 4. Cyclic prefix attached to the front of an OFDM symbol
1.7 Channel model
Multipath is a phenomenon that occurs when the signal sent from the
transmitter gets reflected by ambient objects. This causes the signal to reach
the receiver by two or more paths separated by a delay. The delayed signals
will cause ISI (Inter Symbol Interference, see section 1.8).
TX RX
Figure 5. Channel model for multipath signal
Multipath propagation will be modelled as
( ) ( ) ( ) ( ) (n
v
t
n
s
h
t
n
s
h
t
n
s
h
n
y L
L + )
−
+
+
−
+
−
= K
2
2
1
1
where y(n) is the received signal, hk is the channel coefficient, s(n-tk) is a
delayed version of transmitted signal s(n) due to reflection, and v(n) is
additive noise, caused by natural sources and interference from other
transmitters.

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1.7.1 Frequency Selective Channel Fading
A radio channel will almost never have a flat frequency response. The
interference caused by multipath will create dips in certain frequencies due to
destructive interference. For narrowband signals this could possibly cause all
information to be lost if the dip occurs at the transmission frequency. For LTE
this is partially overcome by spreading the signals to a large number of sub-
carriers, thus if a dip will appear on the transmission frequency not all of the
sub-carriers will be affected and only some information will be lost.
1.7.2 Time Varying Channel Fading
When the transmitter is standing still the channel will be time invariant, which
means the channel will not change over time. But when the transmitter is in
motion the channel will start to vary over time due to the change in the
propagation path of the reflected signals and results in a time varying
channel. This can cause a destructive interference resulting in a dip in the
channel response at certain times, creating a negative gain on the signals that
arrive during that time.
1.8 Inter Symbol Interference
ISI is the name for the interference that occurs when two OFDM symbols
overlap each other. This is caused by the superposition of delayed signals
due to reflection from surrounding objects, also called multipath interference
For OFDM based communication systems, this problem is overcome by
spreading the signal to multiple sub-carriers and letting each of them have an
OFDM symbol period that is higher than the delay spread by letting the cyclic
prefix act as a guard interval, extending the period of the OFDM symbol, and
thus letting the delay spread signal settle before the next symbol.
1.9 Inter Carrier Interference
ICI occurs when a frequency is interfered by nearby frequencies. For OFDM
modulated signals, this can be avoided by having the surrounding sub-
carriers being orthogonal to each other resulting in zero cross-talk as long as
no frequency error exists. In cases where frequency error exists, which
causes a small shift on the carrier frequency, the orthogonality will not be
maintained and results in ICI.
1.10 Receiver structure
A structure of a receiver for data SC-FDMA symbol in an uplink LTE system is
illustrated in Figure 6.

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Figure 6. Receiver structure for uplink LTE
The Cyclic prefixes will first be removed when the signal enters the receiver
followed by a DFT to turn the time domain samples into frequency domain
samples.
For each pilot SC-FDMA symbol a channel estimate is achieved as described
in [3]. Channel compensation (equalization) and antenna combination are
done within the equalizer. Channel estimation for data SC-FDMA symbols are
described in section 3.2.
The sub-carriers corresponding to one transmitter in SC-FDMA are all
dependent and the equalization will be more computationally complex for
uplink where one equalizer is used for all sub-carriers simultaneously, in
contrast to downlink where the sub-carriers are independent and therefore
every sub-carrier will be assigned one equalizer each, see
Figure 7. Equalizer for uplink and downlink
Because a SC-FDMA symbol has its modulated symbols contained in the time
domain, an IFFT is needed before the turbo decoder. This is also the major
difference compared to OFDMA, which is used on the downlink since OFDMA
has its modulated symbols contained in the frequency domain, and therefore
the receiver does not need an IFFT.
The modulated symbols, QPSK, 16QAM, or 64QAM, will be demodulated into
soft bits. A soft bit is when the symbols are demodulated into decimal values
CRC
chec
k
Turb
o
deco
ding
Soft
bit
gene
rator
IDFT
Equaliz
er
DFT
CP
remov
al
DFT
CP
remov
al
Pilot
chann
el
DFT Equalizer
SC-FDMA
DFT
Equalizer
Equalizer
Equalizer
Equalizer
Equalizer
OFDMA

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ranging from -1 to 1 depending on the certainty of the bit value where a
negative value corresponds to a transmitted “1 bit” and a positive value
corresponds to “0 bit”. A hard bit is when the symbols are demodulated into
either 0 or 1 without respect to the certainty of the symbol actually being
correct. The turbo decoder will then use the soft bits as input.
1.11 Channel tracking
An interpolation is done by using channel estimates from previous pilot SC-
FDMA symbol. The advantage with this method is that more information about
the channel will be available due to the increase in the number of received
pilot SC-FDMA symbols. This interpolation is possible if the same frequency
interval is used over several sub-frames, see Figure 8. The algorithms used
for interpolation will be discussed in section 3.2.1, and for regression in
section 3.2.2.
Sub-frame #1 Sub-frame #2 Sub-frame #3
1.5 ms
Sub-frame to estimate
Previous sub-frames
f
t
Figure 8. Channel tracking over a time interval of three sub-frames
1.12 Frequency Hopping
Frequency Hopping uses a pseudorandom code, known by both transmitter
and receiver, to map which sub-carrier frequency the signal will change to.
Since frequency hopping changes the sub-carrier frequency it also avoids
staying on a bad fading channel for a long time thus improving performance,
in terms of less bit errors, when the channel is frequency selective. However,
the frequency hopping is done before each sub-frame and therefore this
method will only have two available pilot sequences which should give a less
accurate estimation of the channel compared to the interpolating method.

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Sub-frame #1
Sub-frame #2
Sub-frame #3
Sub-frame to estimate
Previous sub-frames
f
t
0.5 ms
Figure 9. Frequency hopping over a time interval of three sub-frames

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2 Problem Description
The goal of this paper is to compare the performance between frequency-
hopping and an algorithm that interpolates pilot SC-FDMA symbols over
several sub-frames. The comparison will be done in terms of BER and BLER.
2.1 Channel tracking versus Frequency hopping
Channel tracking and frequency hopping will both have their own optimal
conditions. Frequency hopping emulates a fast varying channel by changing
the sub-carrier frequencies. This makes it redundant to frequency selective
channel fading.
On the other hand, if the same sub-carriers are used over several sub-frames,
the advantage will come from the possibility of collecting previous pilot SC-
FDMA symbols to use them in estimating the channel in future sub-frames.
More pilot SC-FDMA symbols should equal a better estimate of the channel.
Comparing these two methods gives a hypothesis that frequency hopping will
be the preferred choice for very slow time-varying channels since it has the
capability of emulating a fast time varying channel by making a frequency
hop. If the interpolation method would experience the same channel, it could
get stuck in a bad channel, and since the channel varies slowly this could go
on for a significant amount of time.
For very fast time-varying channels both methods should come out about
equal because such channel would give almost the same effect as frequency
hopping resulting in both methods experiencing a change in channel for every
sub-frame or faster.
The interpolative method of using previous pilot SC-FDMA symbols should be
the better choice when a channel shows small variations over two or three
sub-frames. This kind of variation would make best use of previous pilot SC-
FDMA symbols.
For channels with small variations in frequency, frequency hopping will not get
any diversity gain because the possibility of hopping to a frequency with better
gain will be zero since the spectrum is almost flat. For this type of channel the
channel tracking method is better suited where the possibility of using channel
coefficients from very far back in time will give an advantage due to the
channel being almost time-invariant.

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3 Procedure
The procedure for estimating the channel of data SC-FDMA symbols starts by
first estimating the channel of pilot SC-FDMA symbols, and from that
information estimating the channel coefficients for the unknown data. The
algorithm used for estimating the channels for the pilot sequences is the same
for all simulations, but the algorithm used in estimating the data SC-FDMA
symbols will differ.
The channel estimation simulated for both frequency hopping and multiple
sub-frame interpolating algorithms. The frequency hopping will be simulated
by generating a new random start phase for the channel before every new
sub-frame.
3.1 Estimating channel at pilot SC-FDMA symbol
The channel is estimated at each short block with an LS algorithm, see [3].
3.2 Estimating channel at data SC-FDMA symbol
The data SC-FDMA symbols will be estimated through a number of block
based algorithms. The algorithms use previous sub-frames to gain access to
a larger number of pilot SC-FDMA symbols. There is no limit on how many
previous sub-frames that can be used but only the last sub-frame’s data SC-
FDMA symbol will be estimated. In other words, previous and current pilot
SC-FDMA symbols are used for estimating the channel at the data SC-FDMA
symbols for the last incoming sub-frame. This is done either by regression or
interpolation in time-domain, as described in section 3.2.1 and 3.2.2.
The algorithms discussed in the preceding sections will be described for
interpolation of only one channel tap. In multipath channels, one interpolation
has to be done for every reflection of the original signal. Here n is the index
used for time in a time varying channel.
h(n)
hSB(n1)
hSB(n2)
hSB(n3)
hSB(n4)
hLB(n)
1 ms
n
Figure 10. Time domain interpolation of one channel tap

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The channel over a data SC-FDMA symbol will be approximated as time-
invariant with one channel tap for each received reflection of the original
signal sent by the transmitter. This is done for every data SC-FDMA symbol.
These taps will then be Fourier transformed to create a frequency response of
the channel to be used in the equalization of data SC-FDMA symbols, see
section 1.10.
3.2.1 Interpolation
Interpolation is a method that constructs a function from a discrete number of
known data points, and the function that is created has to pass exactly
through those points. The channel at the last data SC-FDMA symbol will be
estimated through extrapolation.
3.2.1.1 Linear interpolation
Linear interpolation will create a segmented curve where two samples are
connected by a straight line. A segment is made up of a linear curve:
( )
( ) ( )
( )
1
1
1
1
)
( −
−
−
−
+
−
−
−
= k
k
k
k
k
SB
k
SB
n
h
n
n
n
n
n
h
n
h
n
h
The number of segments will be n-1 where n is the number samples. Channel
estimation based on linear interpolation will only use three of the four
available pilot symbols, this due to only the samples on each side of the point
to be estimated will have any influence on the outcome, and should only give
a very slight increase over non-interpolating methods. The channel at last
data SC-FDMA symbol will be extrapolated from the last segment.
Figure 11. Example of linear interpolation
n
h(n)
3.2.1.2 Polynomial interpolation
Polynomial interpolation will draw a single polynomial function through all of
the points in space. The polynomial must be in the order of n-1 where n is the

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]
number of points. The function is calculated to minimize the error in least
square sense.
Figure 12. Example of polynomial interpolation
n
h(n)
3.2.2 Regression
Regression is a statistical model to estimate the relationship between several
random variables. Here a function is created by minimizing the error in least
square sense.
3.2.2.1 Linear regression
Linear regression computes a linear curve with best fit for several points in
space. In the case of only two points the linear regression will be equal to
linear interpolation. In cases with more than two points a line that minimizes
the error in least square sense will be computed.
A linear curve is given by
b
mx
y +
= (1)
To find the curve of best fit in vertical least square sense for several points in
space, the sum of the squares is calculated for all points.
( ) [
∑
=
+
−
=
n
i
i
i b
mx
y
b
m
R
1
2
)
(
, (2)
The minimum can be found by calculating the derivative and equalling it to
zero.
( )
[ ]
∑
=
=
+
−
−
=
∂
∂ n
i
i
i
i x
mx
b
y
m
R
1
0
2 (3)
( )
[
∑
=
=
+
−
−
=
∂
∂ n
i
i
i mx
b
y
b
R
1
0
2 ] (4)
These equations can be rewritten as

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∑
∑
∑ =
=
=
+
n
i
i
n
i
i y
x
m
nb
1
1
2
(5)
∑ ∑
= =
=
=
+
n
i
n
i
i
i
n
i
i
i y
x
x
m
x
b
1 1
1
2
(6)
Rewriting these two into matrix form and solving for m and b gives the line of
best fit
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
=
⎥
⎦
⎤
⎢
⎣
⎡
∑
∑
∑
∑
∑
=
=
−
=
=
=
n
i
i
i
n
i
i
n
i
i
n
i
i
n
i
i
y
x
y
x
x
x
n
m
b
1
1
1
1
2
1
1
(7)
n
h(n)
Figure 13. Example of linear regression
3.2.2.2 Polynomial regression
A polynomial regression creates a polynomial function that minimizes the
error in least square sense. If the polynomial is of order n-1 where n is the
number of samples, the curve will be the same as a polynomial interpolation.
n
h(n)
Figure 14. Example of polynomial regression
3.2.2.3 MMSE estimation
A Minimum Mean Square Error method minimizes the residual error by using
the fading properties of electromagnetic waves. A commonly used model of

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how the channel taps are fading is to model the autocorrelation function of a
channel tap as a Bessel function of zero order and first kind, which can also
be derived from Maxwell’s equations.
The channel estimate for one pilot SC-FDMA symbol is modelled as
( ) ( ) ( )
k
k
k
SB n
v
n
h
n
h +
=
ˆ m
k ,
,
3
,
2
,
1 K
= (1)
Where h(nk) is the true channel at time instant nk, with k as the index for the
pilot SC-FDMA symbol, and v(nk) is white Gaussian noise.
The autocorrelation of the above equation gives
( )
( )
{ } ( ) ( )
( )
{ } ( )
( )
{ } ( )
( )
{ 2
2
2
2
ˆ
k
k
k
k
k
SB n
v
E
n
h
E
n
v
n
h
E
n
h
E +
=
+
= } (2)
where
( )
( )
{ } 2
2
h
k
n
h
E σ
= and ( )
( )
{ } 2
2
v
k
n
v
E σ
= (3)
where is the signal power, and is the noise power.
2
h
σ 2
V
σ
The channel coefficients for the data SC-FDMA symbols are determined by
interpolation of channel coefficients from pilot SC-FDMA symbols. See Figure
15.
n
h(n)
ĥSB(n1)
ĥSB(n2)
ĥSB(nm-1)
ĥSB(nm)
ĥLB(n)
Figure 15. Interpolation of channel coefficients from pilot SC-FDMA symbols
This is modeled as
( ) ( ) ( ) ( ) ( ) ( ) ( m
SB
m
SB
SB
LB n
h
n
a
n
h
n
a
n
h
n
a
n
h ˆ
ˆ
ˆ
ˆ
2
2
1
1 +
+
+
= K ) (4)
where ak(n) are the MMSE coefficients to be calculated.
These MMSE coefficients are determined by minimizing the mean square
error of the residual error function e(n)
( ) ( ) ( ) SB
h
n
A
n
h
n
e −
= (5)

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where the MMSE coefficient vector, A(n), and the channel coefficient vector,
hSB(nSB), are defined as
( ) ( ) ( ) ( )
[ n
a
n
a
n
a
n
A m
L
2
1
= ] (6)
( ) ( ) ( )
[ T
m
SB
SB
SB
SB n
h
n
h
n
h
h ˆ
ˆ
ˆ
2
1 L
= ] (7)
The mean square error is
( )
{ } ( ) ( )
( )
{ }
( ) ( )
( ) ( ) ( )
( )
{ }
∗
−
−
=
−
=
=
SB
SB
SB
h
n
A
n
h
h
n
A
n
h
E
h
n
A
n
h
E
n
e
E
J
2
2
(8)
The * denotes transponate and conjugate.
Finding the minimum with respect to A is done by calculating the first
derivative of the mean square error and setting it equal to zero.
( ) ( )
( )
{ 0
2 =
−
= ∗
SB
SB h
h
n
A
n
h
E
dA
dJ
} (9)
Rewriting this gives
( )
{ } ( ) { } 0
=
− ∗
∗
SB
SB
SB h
h
E
n
A
h
n
h
E (10)
resulting in the MMSE coefficients
( ) { } ( )
{ }
∗
−
∗
= SB
SB
SB h
n
h
E
h
h
E
n
A
1
(11)
Rewriting the right hand side of equation (8) into matrix form gives
{ }
( ) ( )
{ } ( ) ( )
{ } ( ) ( )
{ }
( ) ( )
{ } ( ) ( )
{ }
( ) ( )
{ } ( ) ( )
{ }⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
∗
∗
∗
∗
∗
∗
∗
∗
m
SB
m
SB
SB
m
SB
SB
SB
SB
SB
m
SB
SB
SB
SB
SB
SB
SB
SB
n
h
n
h
E
n
h
n
h
E
n
h
n
h
E
n
h
n
h
E
n
h
n
h
E
n
h
n
h
E
n
h
n
h
E
h
h
E
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
1
2
2
1
2
1
2
1
1
1
L
L
M
O
M
M
L
(12)
( )
{ }
( ) ( )
{ }
( ) ( )
{ }
( ) ( )
{ }⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
=
∗
∗
∗
∗
m
SB
SB
SB
SB
n
h
n
h
E
n
h
n
h
E
n
h
n
h
E
h
n
h
E
ˆ
ˆ
ˆ
2
1
M
(13)

Ericsson Internal
2007-03-09 A
where every element in the matrices can be calculated using the Bessel
function of zero order and first kind
( ) ( ) ( )
{ } ( )
l
J
l
n
h
n
h
E
l
r D
h
h ω
σ 0
2
=
−
= ∗
(14)
( ) ( ) ( )
{ } ( ) ( )
l
l
r
l
n
h
n
h
E
l
r V
h
SB
SB δ
σ 2
ˆ
ˆ +
=
−
= ∗
(15)
Where ( )
l
δ is the Dirac delta function, is the signal power, is the
noise power, the Bessel function of zero order and first kind is given
by
2
h
σ 2
V
σ
( l
J D )
ω
0 , and with angular Doppler frequency given by D
ω :
( ) ( )
( )
∑
∞
=
⎟
⎠
⎞
⎜
⎝
⎛
+
Γ
−
=
0
2
0
2
1
!
1
p
p
D
p
D
l
p
p
l
J
ω
ω (16)
s
D
cf
fv
π
ω
2
= (17)
Where f is the transmission frequency e.g. 2.5 GHz, v is the velocity of the
transmitter, c is the speed of light, fs is the sampling frequency. This sampling
frequency will be 30.72 MHz for spectrum allocation of 20 MHz.
This definition of correlation holds for all processes that fade according to a
Rayleigh function.
The matrices in equation (9) and (10) can then be rewritten using equations
(9) and (10) resulting in
( ) ( ) ( )
( ) ( ) (
( ) ( ) ( ) ⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
−
−
−
−
=
0
0
0
2
1
2
1
2
1
2
1
r
n
n
r
n
n
r
n
n
r
r
n
n
r
n
n
r
n
n
r
r
R
m
m
m
m
K
M
O
M
L
)
(18)
(19)
( )
( )
( )⎥
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎢
⎣
⎡
−
−
−
=
∗
∗
∗
m
h
h
h
n
n
r
n
n
r
n
n
r
b
M
2
1
And rewriting equation (11) in compact matrix form becomes
(20)
( ) b
R
n
A 1
−
=
The coefficients resulting from this equation will be the MMSE coefficients for
interpolation of a Rayleigh fading channel.

Ericsson Internal
2007-03-09 A
3.3 Channel estimation with delay
Adding a delay to get access to one future pilot SC-FDMA symbol should give
a better estimate of the channel. The procedure is illustrated in Error!
Reference source not found.. A future pilot SC-FDMA symbol is made
available by using a delay. By this method no extrapolation is needed and
should result in a better channel estimate at the last data SC-FDMA symbol
and should also improve the channel estimates over all other data SC-FDMA
symbols due to more information about the channel being available.
Sub-Frame to estimate
t
f
Short block
Figure 16. Estimation with delay to get access to one future pilot SC-FDMA symbol

Ericsson Internal
2007-03-09 A
4 Simulation results
Performance of uplink LTE is given in this section, in terms of BLER (block
error rate). Here the following parameter settings are used:
• 20 MHz bandwidth
• Carrier frequency 2.5 GHz
• Localized carrier allocation
• Bandwidth (BW) allocation fraction of current user: 4
/
1
• No frequency hopping within a sub-frame.
• Interpolation is done between sub-frames when previous sub-frame is
available.
• A hop in frequency will be done after every fiftieth sub-frame even in
non-frequency hopping algorithms.
• One transmit antenna
• Two receiver antennas
• Channel model:
o Typical Urban 15 km/h
o AWGN (One tap static)
o Case 3 10 km/h
• Algorithms:
o Linear Regression
o Linear Interpolation
o Polynomial Regression
o Polynomial Interpolation
o MMSE

Ericsson Internal
2007-03-09 A
• The velocity used in the estimation of Doppler frequency for the
MMSE algorithm is always set equal to the true velocity of the
channel.
4.1 Typical Urban 15 km/h
Figure 17. Performance in a TU15 channel
Simulations are done for different algorithms in a TU15 (Typical Urban 15
km/h) channel, see Figure 17. From the simulation results it can be seen that
linear regression is the algorithm with overall best performance.

Ericsson Internal
2007-03-09 A
Figure 18. Performance for linear regression with different number of pilot SC-FDMA
symbols in a TU15 channel
Comparing the performance between different numbers of available pilots for
the linear regression algorithms (See Figure 18) gives an idea of the optimal
number of pilot SC-FDMA symbols to use.
Figure 19. Close-up of Figure 18

Ericsson Internal
2007-03-09 A
From the results in Figure 19 it can be concluded that the best performance in
a slowly varying typical urban channel comes from the linear regression with
six pilot SC-FDMA symbols, with very close results from the algorithms with
four and eight pilot SC-FDMA symbols. For channels with faster variations the
algorithm with four pilot SC-FDMA symbols should probably be the best
choice.
The performance for different algorithms in a TU50 (Typical Urban 50 km/h)
channel is illustrated in Figure 20. Linear regression gives the best overall
performance, but is beaten by the frequency hopping at around 11 dB.

Ericsson Internal
2007-03-09 A
The MMSE channel estimator has third best performance, behind Linear
regression and Frequency hopping, see Figure 21. Also the Linear
interpolation with two pilot SC-FDMA symbols and no frequency hopping
outperforms the linear interpolation with four pilot SC-FDMA symbols which is
not what was expected.
Figure 22. MMSE estimator with different values for estimated SNR

Ericsson Internal
2007-03-09 A
The MMSE algorithm needs an estimate of the SNR in order to calculate the
MMSE coefficients. Figure 22 shows simulation results with the MMSE
algorithm simulated with a number of different SNR values used in calculating
the MMSE coefficients.
The best performance in a TU50 channel comes from the algorithm with SNR
set to 7 dB, see Figure 23. Also it seems that it is better to overestimate the
SNR rather than underestimating it.

Ericsson Internal
2007-03-09 A
For a very fast varying channel the linear regression cannot keep up with the
rest of the algorithms, see Figure 24. MMSE “knows” the velocity since the
velocity used for calculating the Doppler frequency is equal to the true
velocity, in this case 300 km/h, and is therefore not affected. This leads to
MMSE as being the algorithm with best performance, followed by frequency
hopping.

Ericsson Internal
2007-03-09 A
4.4 Case3 10 km/h
Figure 25 Performance in a Case3 channel
Linear regression and MMSE have the best overall performance for a slow
varying case3 channel, see Figure 25. Both algorithms has performance very
close to each other.

Ericsson Internal
2007-03-09 A
As it can be seen in the close-up of the case3 performance graph (see Figure
26), the two top performers are very close to each other.
4.5 AWGN
Figure 27. Performance in an AWGN channel
The results from the AWGN simulation did not come out quite as expected,
see Figure 27. It was expected that most of the simulations would result in
very similar performance graphs, but the results are telling that frequency
hopping is performing slightly better than the rest of the algorithms. The
MMSE performance is far off due to the SNR not being correctly estimated.
4.6 Typical Urban 50 km/h with delay
Performance of several algorithms with an added delay is compared in a
TU50 channel as described in Section 3.3. The algorithms investigated are:
Linear regression, Linear interpolation, and MMSE estimator.

Ericsson Internal
2007-03-09 A
Figure 28. Performance of linear regressions with different conditions in a TU50
channel
In Figure 28 the performance for different linear regressions is compared. The
performance of the Linear regression with added delay and the Linear
regression with four pilot SC-FDMA symbols are extremely close, however the
algorithm using the extra pilot SC-FDMA symbol seems to perform slightly
better.
Figure 29. Performance of linear interpolations with different conditions

Ericsson Internal
2007-03-09 A
Figure 29 shows the performance of two linear interpolation algorithms where
one of them uses a delay to get access to one extra pilot SC-FDMA symbol.
There is a slight improvement in performance can be observed by adding the
delay. Compared to Linear regression, Linear interpolation seems to win more
from using the extra pilot SC-FDMA symbol.
Figure 30. Performance for MMSE with different conditions
The results from the MMSE simulations in Figure 30 did not come out as
expected. An increase in performance was expected by using a delay to get
access to a future pilot SC-FDMA symbol, but that did not happen. All three
algorithms gives very similar performance, but the algorithm using the delay
seems to fall behind the rest slightly.

Ericsson Internal
2007-03-09 A
5 Future Work
Extending the scope of this project can result in other areas of work to
consider. Work that could be investigated in the future is as follows.
5.1 Estimating the optimal SNR for the MMSE channel estimator
The communication channel will change as the transmitter/receiver moves
and this will change the SNR. Signal-to-Noise-Ratio is needed in calculating
the channel coefficients for the MMSE estimator. An adaptive channel
estimator could be created to adapt itself to the different SNR conditions. Also
it could be of interest to understand how often this estimation has to be done.
5.2 Velocity estimator for MMSE channel estimator
In order to calculate the Doppler frequency the velocity of the transmitter has
to be known. During the simulations made in this report, the velocity was
always set to the true velocity of the transmitter, but in reality the velocity of
the transmitter has to be estimated.

Ericsson Internal
2007-03-09 A
6 Summary
The overall best performance comes from MMSE estimator. It showed good
performance in all but one simulation, and that was probably due to the SNR
being way off. Linear regression has good potential at slow varying channels
but shows its weakness when the variations get faster. Frequency hopping
showed solid results in most of the simulations.
• Channel tracking with MMSE estimator is the best choice
• Frequency hopping is still a good choice considering it is less complex
than the MMSE estimator
• Linear regression was surprisingly good in slow varying channels
• Adding a delay did not give any noteworthy increase in performance

Ericsson Internal
2007-03-09 A
7 Notation
3G – Third Generation
3GPP – Third Generation partnership Project
AWGN – Additive White Gaussian Noise
BER – Bit Error Rate
BLER – Block Error Rate
BPSK – Binary Phase-Shift Keying
CP – Cyclic Prefix
CRC – Cyclic Redundancy Check
DFT – Discrete Fourier Transform
FFT – Fast Fourier Transform
GHz – Giga Hertz
ICI – Inter Carrier Interference
IDFT – Inverse Discrete Fourier Transform
IFFT – Inverse Fast Fourier Transform
ISI – Inter Symbol Interference
kHz – kilo Hertz
LB – Long Block
LS – Least Square
LTE – Long Term Evolution
Mbps – Mega bit per second
MHz – Mega Hertz
MIMO – Multiple Input Multiple Output
MMSE – Minimum Mean Square Error
OFDM – Orthogonal Frequency Division Multiplexing
OFDMA – Orthogonal Frequency Division Multiple Access
PAPR – Peak-to-Average Power Ratio
QAM – Quadrature Amplitude Modulation
QPSK – Quadrature Phase-Shift Keying
SB – Short Block
SC-FDMA – Single Carrier Frequency Division Multiple Access
SNR – Signal to Noise Ratio
TU – Typical Urban
WCDMA – Wideband Code Division Multiple Access

Ericsson Internal
2007-03-09 A
8 References
[1] 3GPP TS 36.211, “Physical Channels and Modulation” Technical Specification
Group Radio Access Network, V0.2.2 (2006-12), Release 8.
http://www.3gpp.org/ftp/Specs/archive/36_series/
[2] Simon Haykin, “Adaptive Filter Theory”, Third Edition
[3] Henrik Sahlin, “Introduction and overview of LTE Uplink Baseband Algorithms”,
Ericsson internal technical report
[4] 3GPP TR 25.814, “Physical layer aspects for evolved Universal Terrestrial Radio
Access (UTRA)” Technical Specification Group Radio Access Network, V7.0.0
(2006-06), Release 7
[5] Ove Edfors, Magnus Sandell, Jan-Jaap van de Beek, Daniel Landström, Frank
Sjöberg, “An introduction to orthogonal frequency-division multiplexing”, September
1996

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