lte hoping

7/31/2019 Lte Hoping

1/35

Channel Tracking versus Frequency

Hopping for Uplink LTE

KEN ERIKSSON

Masters Degree Project

Stockholm, Sweden March 2007

XR-EE-KT 2007:003


2/35

Ericsson Internal

TECHNICAL REPORT 1 (34)Prepared (also subject responsible if other) No.

LN/EAB/PDB/B Ken ErikssonApproved Checked Date Rev Reference

2007-03-09 A

Channel tracking versus frequency hopping for uplinkLTE

Abstract

The aim of this work is to compare several algorithms in a receiver for uplinkLTE (Long Term Evolution). In this receiver, the radio propagation channel isestimated using pilot SC-FDMA symbols. For a continuous transmission on aconstant frequency interval, these channel estimates can be interpolated overtime. The interpolation is done over several pilot symbols thus making itpossible to use previous pilot sequences transmitted from one terminal inestimating the new data from the same terminal. This paper only investigatesalgorithms used for estimating the channel for data sequences. Theinvestigated algorithms are different regression and interpolation methods,and also an MMSE (Minimum Mean Square Error) method. Here theperformance between frequency hopping and an interpolation algorithm iscompared. With frequency hopping this interpolation is not possible. Instead a

frequency diversity gain is expected when the transmitter regularly changesfrequency interval. The LTE environment is simulated with a simulator writtenin Matlab.

This is a report for a master thesis done at Ericsson Lindholmen.


3/35

Ericsson Internal



2007-03-09 A

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 ..........315.3 Velocity estimator for MMSE channel estimator ................................31 6 Summary...........................................................................................32 7 Notation .............................................................................................33 8 References........................................................................................34


4/35

Ericsson Internal



2007-03-09 A

1 Background

LTE is the next step in the ongoing development of todays 3G standardWCDMA to retain its competitiveness in the future. Each spectrum of 20 MHzwill have downlink capacity of approximately 100 Mbps, and uplink capacity ofapproximately 50 Mbps. Technologies used in LTE includes OFDM(Orthogonal Frequency Division Multiplexing) and MIMO (Multiple InputMultiple 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 CarrierFrequency Division Multiple Access) and is based on DFT-spread OFDM. It issimilar to OFDMA (see section 1.2), which is the technique used on thedownlink, but has a lower PAPR (Peak-to-Average Power Ratio) thus makingit more suitable for uplink where mobile communication devices can transmitinformation with a better power efficiency and less complex amplifiers. Anexample of a transmitter for uplink is given in Figure 1.

Mapping

Filtering

IDFTDFT CPinsertion

Modulation

Informationbits

Symbols FrequencyDomainsamples

TimeDomainsamples

TurboCoding

Localizedor

distributed

Raw/modembits

CRCgenerator

Checksumadded

Figure 1. Transmitter structure for uplink LTE

When the information bits enter the transmitter it will first get a CRCgenerated sequence attached. These attached bits will be used at thereceiver for verification to see if the information bits have changed during the

transmission. Turbo coding will then be used to increase the redundancy ofthe information. After turbo coding, those bits will be coded into symbols byone of the supported modulation formats: QPSK, 16QAM, or 64QAM.

The symbols will go through a DFT to transform them into frequency domainsamples. These samples will then be mapped to a number of sub-carriers,which depends on the spectrum allocation (See section 1.4). This can bedone by two different methods, localized mode or distributed mode. The twomethods differ in how they handle the mapping of sub-carriers. Localizedmode will place all sub-carriers from the same user next to each other on anallocated frequency spectrum. Distributed mode will spread the sub-carriersand interlace them with sub-carriers from other users making use of a largerfrequency spectrum thus creating frequency diversity. The spectral efficiencyis the same in both methods.


5/35

Ericsson Internal



2007-03-09 A

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 beinserted before the signal exits the transmitter.

1.2 Downlink

OFDMA is used on the downlink. This is a multi-carrier technique very similarto the one used on the uplink but with a higher PAPR. The possiblemodulations on downlink are QPSK, 16QAM, and 64QAM. The Downlink willnot be further discussed in this paper.

1.3 OFDM

OFDM (Orthogonal Frequency Division Multiplexing) based technique will beused in both uplink and downlink. This technique maps the signal to a numberof sub-carriers with carrier spacing of 15 kHz. Each sub-carrier will beorthogonal 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 basedcommunications. Sub-carriers will be spread over the entire frequency bandallocated to the user creating a spectrum of up to 1200 narrow band andorthogonal carriers. By being narrow band the fading that each sub-carrierexperience can be approximated as a flat fading channel.

1.5 MIMO


6/35

Ericsson Internal



2007-03-09 A

MIMO (Multiple Input Multiple Output) is a term used for multiple antennacommunication systems. Several independent signals can be transmitted,

leading to an increased spectral efficiency by exploiting spatial diversity. Toachieve this antennas have to be physically separated. Another way is toseparate the antennas through polarization. There are several ways to usethe multiple antennas depending on the area of priority, for exampleredundancy or data rate.

1.6 Sub-Frame

A sub-frame is defined as a packet containing 6 data SC-FDMA symbols (seesection 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 thestandardization 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 forthe receiver, sent from the transmitter. It has the size of 2048 samples over66.7 microseconds for a 20 MHz spectrum allocation. The data SC-FDMAsymbol contains relevant information transmitted over the radio channel, be itspeech or some other data.

1.6.2 Pilot SC-FDMA symbol

Pilot SC-FDMA symbol, also called short block, have half the length of longblocks, 1024 samples over 33.3 microseconds for a 20 MHz spectrumallocation. The information contained in a pilot SC-FDMA symbol is known bythe receiver, and by using these blocks the channel coefficients can beestimated as described in section 3.1.

1.6.3 Cyclic Prefix


7/35

Ericsson Internal



2007-03-09 A

A cyclic prefix is a repeat of the last part of an OFDM symbol attached to thebeginning. 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 converta linear convolution of the channel impulse response to a circular one.

OFDM symbolCP

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 thetransmitter gets reflected by ambient objects. This causes the signal to reachthe receiver by two or more paths separated by a delay. The delayed signalswill cause ISI (Inter Symbol Interference, see section 1.8).

TX RX

Figure 5. Channel model for multipath signal

Multipath propagation will be modelled as

( ) ( ) ( ) ( ) (nvtnshtnshtnshny LL + )+++= K2211

where y(n) is the received signal, hk is the channel coefficient, s(n-tk) is adelayed version of transmitted signal s(n) due to reflection, and v(n) isadditive noise, caused by natural sources and interference from othertransmitters.


8/35

Ericsson Internal



2007-03-09 A

1.7.1 Frequency Selective Channel Fading

A radio channel will almost never have a flat frequency response. Theinterference caused by multipath will create dips in certain frequencies due todestructive interference. For narrowband signals this could possibly cause allinformation to be lost if the dip occurs at the transmission frequency. For LTEthis 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 thesub-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, whichmeans the channel will not change over time. But when the transmitter is inmotion the channel will start to vary over time due to the change in thepropagation path of the reflected signals and results in a time varyingchannel. This can cause a destructive interference resulting in a dip in thechannel response at certain times, creating a negative gain on the signals thatarrive 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 signalsdue to reflection from surrounding objects, also called multipath interferenceFor OFDM based communication systems, this problem is overcome byspreading the signal to multiple sub-carriers and letting each of them have anOFDM symbol period that is higher than the delay spread by letting the cyclicprefix act as a guard interval, extending the period of the OFDM symbol, andthus 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 OFDMmodulated signals, this can be avoided by having the surrounding sub-carriers being orthogonal to each other resulting in zero cross-talk as long asno frequency error exists. In cases where frequency error exists, whichcauses a small shift on the carrier frequency, the orthogonality will not bemaintained 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.


9/35

Ericsson Internal



2007-03-09 A

Figure 6. Receiver structure for uplink LTE

The Cyclic prefixes will first be removed when the signal enters the receiverfollowed 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 describedin [3]. Channel compensation (equalization) and antenna combination aredone within the equalizer. Channel estimation for data SC-FDMA symbols aredescribed in section 3.2.

The sub-carriers corresponding to one transmitter in SC-FDMA are alldependent and the equalization will be more computationally complex foruplink where one equalizer is used for all sub-carriers simultaneously, incontrast to downlink where the sub-carriers are independent and thereforeevery 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 timedomain, an IFFT is needed before the turbo decoder. This is also the majordifference compared to OFDMA, which is used on the downlink since OFDMAhas its modulated symbols contained in the frequency domain, and thereforethe receiver does not need an IFFT.

The modulated symbols, QPSK, 16QAM, or 64QAM, will be demodulated intosoft bits. A soft bit is when the symbols are demodulated into decimal values

CRCcheck

Turbo

decoding

Softbit

generator

IDFTEqualiz

er

DFTCPremoval

DFTCPremoval

Pilotchannel

DFT EqualizerSC-FDMA

DFT

E ualizerE ualizer

E ualizer

E ualizer

E ualizer

OFDMA


10/35

Ericsson Internal



2007-03-09 A

ranging from -1 to 1 depending on the certainty of the bit value where anegative value corresponds to a transmitted 1 bit and a positive value

corresponds to 0 bit. A hard bit is when the symbols are demodulated intoeither 0 or 1 without respect to the certainty of the symbol actually beingcorrect. 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 aboutthe channel will be available due to the increase in the number of receivedpilot SC-FDMA symbols. This interpolation is possible if the same frequency

interval is used over several sub-frames, see Figure 8. The algorithms usedfor interpolation will be discussed in section 3.2.1, and for regression insection 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 transmitterand receiver, to map which sub-carrier frequency the signal will change to.Since frequency hopping changes the sub-carrier frequency it also avoidsstaying 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 thismethod will only have two available pilot sequences which should give a lessaccurate estimation of the channel compared to the interpolating method.


11/35

Ericsson Internal



2007-03-09 A

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


12/35

Ericsson Internal



2007-03-09 A

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 overseveral 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 optimalconditions. Frequency hopping emulates a fast varying channel by changing

the sub-carrier frequencies. This makes it redundant to frequency selectivechannel 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 willbe the preferred choice for very slow time-varying channels since it has thecapability of emulating a fast time varying channel by making a frequencyhop. If the interpolation method would experience the same channel, it couldget 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 aboutequal because such channel would give almost the same effect as frequencyhopping resulting in both methods experiencing a change in channel for everysub-frame or faster.The interpolative method of using previous pilot SC-FDMA symbols should bethe better choice when a channel shows small variations over two or threesub-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 getany diversity gain because the possibility of hopping to a frequency with bettergain will be zero since the spectrum is almost flat. For this type of channel thechannel tracking method is better suited where the possibility of using channelcoefficients from very far back in time will give an advantage due to thechannel being almost time-invariant.


13/35

Ericsson Internal



2007-03-09 A

3 Procedure

The procedure for estimating the channel of data SC-FDMA symbols starts byfirst estimating the channel of pilot SC-FDMA symbols, and from thatinformation estimating the channel coefficients for the unknown data. Thealgorithm used for estimating the channels for the pilot sequences is the samefor all simulations, but the algorithm used in estimating the data SC-FDMAsymbols will differ.

The channel estimation simulated for both frequency hopping and multiplesub-frame interpolating algorithms. The frequency hopping will be simulatedby generating a new random start phase for the channel before every newsub-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 toa larger number of pilot SC-FDMA symbols. There is no limit on how manyprevious sub-frames that can be used but only the last sub-frames data SC-FDMA symbol will be estimated. In other words, previous and current pilotSC-FDMA symbols are used for estimating the channel at the data SC-FDMAsymbols for the last incoming sub-frame. This is done either by regression orinterpolation in time-domain, as described in section 3.2.1 and 3.2.2.

The algorithms discussed in the preceding sections will be described forinterpolation of only one channel tap. In multipath channels, one interpolationhas to be done for every reflection of the original signal. Here n is the indexused 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


14/35

Ericsson Internal



2007-03-09 A

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 ofthe channel to be used in the equalization of data SC-FDMA symbols, seesection 1.10.

3.2.1 Interpolation

Interpolation is a method that constructs a function from a discrete number ofknown 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 beestimated through extrapolation.

3.2.1.1 Linear interpolation

Linear interpolation will create a segmented curve where two samples areconnected by a straight line. A segment is made up of a linear curve:

( )( ) ( )

( )111

1 )(

+

= kk

kk

kSBkSB nhnnnn

nhnhnh

The number of segments will be n-1 where n is the number samples. Channelestimation based on linear interpolation will only use three of the fouravailable pilot symbols, this due to only the samples on each side of the pointto be estimated will have any influence on the outcome, and should only givea very slight increase over non-interpolating methods. The channel at lastdata 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


15/35

Ericsson Internal



2007-03-09 A

]

number of points. The function is calculated to minimize the error in leastsquare sense.

Figure 12. Example of polynomial interpolation

n

h(n)

3.2.2 Regression

Regression is a statistical model to estimate the relationship between severalrandom variables. Here a function is created by minimizing the error in leastsquare sense.

3.2.2.1 Linear regression

Linear regression computes a linear curve with best fit for several points inspace. In the case of only two points the linear regression will be equal tolinear interpolation. In cases with more than two points a line that minimizesthe error in least square sense will be computed.

A linear curve is given by

bmxy += (1)

To find the curve of best fit in vertical least square sense for several points inspace, the sum of the squares is calculated for all points.

( ) [=

+=n

i

ii bmxybmR1

2)(, (2)

The minimum can be found by calculating the derivative and equalling it tozero.

( )[ ]=

=+=

n

i

iii xmxbym

R

1

02 (3)

( )[=

=+=

n

i

ii mxbyb

R

1

02 ] (4)

These equations can be rewritten as


16/35

Ericsson Internal



2007-03-09 A

==

=+n

i

i

n

i

i yxmnb11

2 (5)

= ==

=+n

i

n

i

ii

n

i

ii yxxmxb1 11

2 (6)

Rewriting these two into matrix form and solving for m and b gives the line ofbest fit

=

=

=

==

=n

i

ii

n

i

i

n

i

i

n

i

i

n

i

i

yx

y

xx

xn

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 theerror in least square sense. If the polynomial is of order n-1 where n is thenumber 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 usingthe fading properties of electromagnetic waves. A commonly used model of


17/35

Ericsson Internal



2007-03-09 A

how the channel taps are fading is to model the autocorrelation function of achannel tap as a Bessel function of zero order and first kind, which can also

be derived from Maxwells equations.

The channel estimate for one pilot SC-FDMA symbol is modelled as

( ) ( ) ( )kkkSBnvnhnh += mk ,,3,2,1 K= (1)

Where h(nk) is the true channel at time instant nk, with k as the index for thepilot SC-FDMA symbol, and v(nk) is white Gaussian noise.

The autocorrelation of the above equation gives

( )( ) ( ) ( )( ){ } ( )( ){ } ( )( ){2222

kkkkkSB nvEnhEnvnhEnhE +=+= } (2)

where

( )( ) 22 hknhE = and ( )( )22

vknvE = (3)

where is the signal power, and is the noise power.2h2

V

The channel coefficients for the data SC-FDMA symbols are determined byinterpolation of channel coefficients from pilot SC-FDMA symbols. See Figure

15.

n

h(n)

SB(n1)

SB(n2)

SB(nm-1)SB(nm)LB(n)

Figure 15. Interpolation of channel coefficients from pilot SC-FDMA symbols

This is modeled as

( ) ( ) ( ) ( ) ( ) ( ) ( mSBmSBSBLB nhnanhnanhnanh 2211 +++= K ) (4)

where ak(n) are the MMSE coefficients to be calculated.

These MMSE coefficients are determined by minimizing the mean squareerror of the residual error function e(n)

( ) ( ) ( ) SBhnAnhne = (5)


18/35

Ericsson Internal



2007-03-09 A

where the MMSE coefficient vector, A(n), and the channel coefficient vector,hSB(nSB), are defined as

( ) ( ) ( ) ( )[ nanananA mL21= ] (6)

( ) ( ) ( )[ TmSBSBSBSB nhnhnhh 21 L= ] (7)

The mean square error is

( ){ } ( ) ( )( )

( ) ( )( ) ( ) ( )( ){ }===

SBSB

SB

hnAnhhnAnhE

hnAnhEneEJ2

2

(8)

The * denotes transponate and conjugate.

Finding the minimum with respect to A is done by calculating the firstderivative of the mean square error and setting it equal to zero.

( ) ( )( ){ 02 == SBSB hhnAnhEdA

dJ } (9)

Rewriting this gives

( ){ } ( ) { } 0=SBSBSB hhEnAhnhE (10)

resulting in the MMSE coefficients

( ) { } ( ){ }= SBSBSB hnhEhhEnA1

(11)

Rewriting the right hand side of equation (8) into matrix form gives

{ }

( ) ( ){ } ( ) ( ){ } ( ) ( ){ }( ) ( ){ } ( ) ( ){ }

( ) ( ){ } ( ) ( ){ }

=

mSBmSBSBmSB

SBSBSBSB

mSBSBSBSBSBSB

SBSB

nhnhEnhnhE

nhnhEnhnhE

nhnhEnhnhEnhnhE

hhE

1

2212

12111

LL

MOM

M

L

(12)

( ){ }

( ) ( ){ }( ) ( ){ }

( ) ( ){ }

=

mSB

SB

SB

SB

nhnhE

nhnhE

nhnhE

hnhE

2

1

M (13)


19/35

Ericsson Internal



2007-03-09 A

where every element in the matrices can be calculated using the Besselfunction of zero order and first kind

( ) ( ) ( ){ } ( )lJlnhnhElr Dhh 02== (14)

( ) ( ) ( ){ } ( ) ( )llrlnhnhElr VhSBSB 2 +== (15)

Where ( )l is theDirac delta function, is the signal power, is thenoise power, the Bessel function of zero order and first kind is given

by

2

h2

V

( lJ D )0 , and with angular Doppler frequency given by D :

( ) ( )( )

=

+

=

0

2

021!

1p

p

D

p

D lpp

lJ

(16)

s

Dcf

fv

2= (17)

Where fis the transmission frequency e.g. 2.5 GHz, vis the velocity of thetransmitter, cis the speed of light, fs is the sampling frequency. This samplingfrequency 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

21

212

121

rnnrnnr

nnrrnnr

nnrnnrr

R

mm

m

m

K

MOM

L

) (18)

(19)

( )( )

( )

=

mh

h

h

nnr

nnrnnr

bM

2

1

And rewriting equation (11) in compact matrix form becomes

(20)( ) bRnA 1=The coefficients resulting from this equation will be the MMSE coefficients for

interpolation of a Rayleigh fading channel.


20/35

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 givea better estimate of the channel. The procedure is illustrated in Error!Reference source not found.. A future pilot SC-FDMA symbol is madeavailable by using a delay. By this method no extrapolation is needed andshould result in a better channel estimate at the last data SC-FDMA symboland should also improve the channel estimates over all other data SC-FDMAsymbols 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


21/35

Ericsson Internal



2007-03-09 A

4 Simulation results

Performance of uplink LTE is given in this section, in terms of BLER (blockerror 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 isavailable.

A hop in frequency will be done after every fiftieth sub-frame even innon-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


22/35

Ericsson Internal



2007-03-09 A

The velocity used in the estimation of Doppler frequency for theMMSE 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 15km/h) channel, see Figure 17. From the simulation results it can be seen thatlinear regression is the algorithm with overall best performance.


23/35

Ericsson Internal



2007-03-09 A

Figure 18. Performance for linear regression with different number of pilot SC-FDMAsymbols 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 optimalnumber of pilot SC-FDMA symbols to use.

Figure 19. Close-up of Figure 18


24/35

Ericsson Internal



2007-03-09 A

From the results in Figure 19 it can be concluded that the best performance ina slowly varying typical urban channel comes from the linear regression with

six pilot SC-FDMA symbols, with very close results from the algorithms withfour and eight pilot SC-FDMA symbols. For channels with faster variations thealgorithm with four pilot SC-FDMA symbols should probably be the bestchoice.



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.


25/35

Ericsson Internal



2007-03-09 A


The MMSE channel estimator has third best performance, behind Linearregression and Frequency hopping, see Figure 21. Also the Linearinterpolation with two pilot SC-FDMA symbols and no frequency hoppingoutperforms the linear interpolation with four pilot SC-FDMA symbols which isnot what was expected.

Figure 22. MMSE estimator with different values for estimated SNR


26/35

Ericsson Internal



2007-03-09 A

The MMSE algorithm needs an estimate of the SNR in order to calculate theMMSE coefficients. Figure 22 shows simulation results with the MMSE

algorithm simulated with a number of different SNR values used in calculatingthe MMSE coefficients.


The best performance in a TU50 channel comes from the algorithm with SNRset to 7 dB, see Figure 23. Also it seems that it is better to overestimate theSNR rather than underestimating it.


27/35

Ericsson Internal



2007-03-09 A



For a very fast varying channel the linear regression cannot keep up with therest of the algorithms, see Figure 24. MMSE knows the velocity since thevelocity used for calculating the Doppler frequency is equal to the truevelocity, in this case 300 km/h, and is therefore not affected. This leads toMMSE as being the algorithm with best performance, followed by frequencyhopping.


28/35

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 slowvarying case3 channel, see Figure 25. Both algorithms has performance veryclose to each other.


29/35

Ericsson Internal



2007-03-09 A


As it can be seen in the close-up of the case3 performance graph (see Figure26), 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 invery similar performance graphs, but the results are telling that frequencyhopping is performing slightly better than the rest of the algorithms. TheMMSE 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 aTU50 channel as described in Section 3.3. The algorithms investigated are:Linear regression, Linear interpolation, and MMSE estimator.


30/35

Ericsson Internal



2007-03-09 A

Figure 28. Performance of linear regressions with different conditions in a TU50channel

In Figure 28 the performance for different linear regressions is compared. Theperformance of the Linear regression with added delay and the Linearregression with four pilot SC-FDMA symbols are extremely close, however thealgorithm using the extra pilot SC-FDMA symbol seems to perform slightlybetter.

Figure 29. Performance of linear interpolations with different conditions


31/35

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 thedelay. Compared to Linear regression, Linear interpolation seems to win morefrom 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 asexpected. An increase in performance was expected by using a delay to getaccess to a future pilot SC-FDMA symbol, but that did not happen. All threealgorithms gives very similar performance, but the algorithm using the delayseems to fall behind the rest slightly.


32/35

Ericsson Internal



2007-03-09 A

5 Future Work

Extending the scope of this project can result in other areas of work toconsider. 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 movesand this will change the SNR. Signal-to-Noise-Ratio is needed in calculatingthe channel coefficients for the MMSE estimator. An adaptive channelestimator 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 hasto be known. During the simulations made in this report, the velocity wasalways set to the true velocity of the transmitter, but in reality the velocity ofthe transmitter has to be estimated.


33/35

Ericsson Internal



2007-03-09 A

6 Summary

The overall best performance comes from MMSE estimator. It showed goodperformance in all but one simulation, and that was probably due to the SNRbeing way off. Linear regression has good potential at slow varying channelsbut shows its weakness when the variations get faster. Frequency hoppingshowed 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 complexthan the MMSE estimator

Linear regression was surprisingly good in slow varying channels

Adding a delay did not give any noteworthy increase in performance


34/35

Ericsson Internal



2007-03-09 A

7 Notation

3G Third Generation3GPP Third Generation partnership ProjectAWGN Additive White Gaussian NoiseBER Bit Error RateBLER Block Error RateBPSK Binary Phase-Shift KeyingCP Cyclic PrefixCRC Cyclic Redundancy CheckDFT Discrete Fourier TransformFFT Fast Fourier Transform

GHz Giga HertzICI Inter Carrier InterferenceIDFT Inverse Discrete Fourier TransformIFFT Inverse Fast Fourier TransformISI Inter Symbol InterferencekHz kilo HertzLB Long BlockLS Least SquareLTE Long Term EvolutionMbps Mega bit per secondMHz Mega Hertz

MIMO Multiple Input Multiple OutputMMSE Minimum Mean Square ErrorOFDM Orthogonal Frequency Division MultiplexingOFDMA Orthogonal Frequency Division Multiple AccessPAPR Peak-to-Average Power RatioQAM Quadrature Amplitude ModulationQPSK Quadrature Phase-Shift KeyingSB Short BlockSC-FDMA Single Carrier Frequency Division Multiple AccessSNR Signal to Noise RatioTU Typical UrbanWCDMA Wideband Code Division Multiple Access


35/35

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 RadioAccess (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 Landstrm, FrankSjberg, An introduction to orthogonal frequency-division multiplexing, September1996
http://www.3gpp.org/ftp/Specs/archive/36_series/http://www.3gpp.org/ftp/Specs/archive/36_series/

lte hoping

Documents