wcdma_lectures

1

11.4.2002 1

Lecture 4: Physical layer• Key parameters of WCDMA

• Transport channels ó Physical channels• Sperading & modulation

• User Data transmission• Signalling

• Physical layer procedures

11.4.2002 2

Key parameterd of WCDMA

QPSKModulation

10 msFrame length

Variable spreading factor and multicode

Multirate consept

Multiple services with different QoS-requirements can be multiplexed into one connection.

Service multiplexing

Coherent detection, RAKE receiver

Detection

3.84 McpsChip rate

DS-CDMAMultiple access method

FDDDuplexing method

Asynchronous operationBase station synchronisation

11.4.2002 3

Spectrum

Uplink Downlink

DownlinkUplink

Uplink Downlink

11.4.2002 4

Spectrum• Normal carrier spacing is 5 MHz, but it can be adjusted

with 200 kHz raster within operators band.

• Adjacent Channel Leakage Ratio (ACLR): Uplink: 33 dB and 43 dB, Downlink: 45 dB and 50 dB

3.84 Mhz

5 Mhz

n200 kHz

P

Nf 1Nf + 2Nf +

1ACKR 2ACKR

2

11.4.2002 5

Spreading• Spreading is done using two different codes

– Channelisation code: Separates transmissions from single source from each other

– Scrambling code: Separates different sources from each other

Spreading code= Channelisation code x Scrambling Code

– Spreading factor: W /R

Channelisationcode

Scramblingcode

DataBit rate, R

Chip rate,W

11.4.2002 6

Spreading• Spreading codes

– Short code: Spreading code spans only one symbol

Interference is cyclostationaryShort codes are used for simplifying the use of advanced receiver technologies such as multiuser detection.

– Long code: Spreading code spans several symbols

Aim to randomize interference.

Code is repeated

11.4.2002 7

Scrambling• Channelisation code: Separates transmissions from

single source from each other.

• There is need to plan the code usage in downlink (~ frequency planning in TDMA systems).

11.4.2002 8

Scrambling• Consider a bipolar sequence

• Cross correlation

• Welch bound: For any set of M sequences of length n

• Gold sequences:

{ }1,1ib ∈ −

( ) ( )1

( ) 2 1 2 1 , 0 1n

i i ji

j b b j nφ +=

= − − ≤ ≤ −∑

( ) ( )1

max1j

Mj

n Mφ

−≥

−

( )1

2

22

1 2 odd max

1 2 even

M

j M

Mj

M

φ

+

+

+=

+

3

11.4.2002 9

Scrambling• Gold codes

11.4.2002 10

Channelisation• Channelisation codes

– Transmissions from a single source are separated by channelisation codes.

– Orhogonal Variable Spreading Factor (OVSF) technique: Walsh codes

– Codes are dynamically managed by RNC, no preplanning is required

{1}

{1,1}

{1,-1}

{1,1,1,1}

{1,1,-1,-1}

{1,-1,1,-1}

{1,-1,-1,1}

1 10

1 1

, 1k kk

k k

H HH H

H H− −

− −

= = −

11.4.2002 11

Channelisation & Scrambling

Does not affect bandwidthIncreases transmission bandwidth

Spreading

Long: Gold codeShort: Extended S(2) code family

Orthogonal Variable Spreading Factor

Code family

Uplink: 224

Downlink: 512Number of codes under one scrambling code = sperading factor

Numberof codes

Uplink: - long 10 ms => 38400 chips- short 66.7 µs => 256 chipsDownlink: 38400 chips

Uplink: 4-256 chips Downlink: 4-512 chips

Code length

Uplink: Separation of sectors and cells.Downlink: Separation of UEs

Uplink : Separation DPDCH and DPCCHDownlink: Separation of downlink connections to different UEs within one cell

Usage

Scrambling codeChannelisation code

11.4.2002 12

Downlink ModulationOffset QPSK (OQPSK)

DPDCHDPCCH Channelisation code

Scrambling codeMUX

Serialto

Parallel∑

cos ctω

sin c tω

I

Q

P(f)

P(f)

P(f) is square root raised cosine filterwith β=0.22

D

Delay of ½ chip lenght

4

11.4.2002 13

Downlink Modulation• Symbol transitions:

– Because of the delay in Q -branch only real or imaginary part can change at a time => Changes in the phase are limited to 90°

Im

Re

1+i

1-i

-1+i

-1-i

Im

Re

1+i

1-i

-1+i

-1-i

QPSK OQPSK

11.4.2002 14

Uplink ModulationHybrid PSK (HPSK)

Channelizaion code

i

∑

Complex scrambling code

Re{}

Im{}

∑

cos ctω

sin c tω

P(f)

P(f)DPCCH

DPDCH

11.4.2002 15

Channelisation & Scrambling• Why is uplink and downlink are different?

– In downlink data and control information is multiplexed together. If there is no data to transmit only the power control bits are sent: Power is controlled at 1.5kHz rate. A waveform like this will cause audible distortions on the frequency band used for voice transfer in the phone. => In uplink, data and control information cannot be multiplexed together.

1.5 ms

P

11.4.2002 16

Complex Scrambling

I iQ I jQ I iQ I I Q Q i I Q Q I

A A i i

chip chip s s chip s chip s chip s chip s

chip s chip s

+ = + + = − + +

= +

c hb g c h c hc hexp φ φ

2

Im

Re

Im

Re

2

I iQs s+

5

11.4.2002 17

Complex Scrambling

I iQ I jQ I iQ I I Q Q i I Q Q I

A A i i

chip chip s s chip s chip s chip s chip s

chip s chip s

+ = + + = − + +

= +

c hb g c h c hc hexp φ φ

Im

Re

Im

Re

I iQs s+

Different power inI and Q branches The same power in both

branches! 11.4.2002 18

Complex Scrambling

• The channelisation code is chosen so that the consecutive bits are always +1,+1 or +1 -1 pairs. =>The number of available codes is decreased.

• Let us code a pair of bits using {+1,+1} code in I -branch and {+1 -1} code in Q -branch (This is called Walsh rotator)=>90° phase shift between two consecutive symbols =>

Better peak-to-average power ratio than if 0 ° or 180 °

2

Im

Re

Im

Re

22. symbol

1. symbol

11.4.2002 19

Complex Scrambling• In order to separate the UEs from each other we still

need to add the PN-sequence to the modulated signal:

I iQ PN I jQ I k iQ PN kchip chip s s+ = + + =1 2 1c hb g( ) , ,2

http://www.planetee.com/planetee/servlet/DisplayDocument?ArticleID=394

11.4.2002 20

Raised Cosine Filter

Idal bandpass filter can not be realized in practice -Raised cosine filter is a very good approximation for the ideal filter.

102

1 1 1( ) 1 cos2 2 2 2

102

T fT

T TP f f fT T T

fT

β

π β β ββ

β

− ≤ <

− − + = + − ≤ ≤

+ >

2 2

cos( ) sinc

1 4

tt Tp t

tTT

πβ

β

=

−

6

11.4.2002 21

-2 -1.5 -1 -0.5 0 0.5 1 1.5 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

f

H(f

)

Raised Cosine Filter

β=1, 0.5, 0.25, 0

11.4.2002 22-5 -4 -3 -2 -1 0 1 2 3 4 5-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

t

h(t)

Raised Cosine FilterThe greater β , the faster the impulse response dies off and the the the shorter FIR filter we need to realize it.

( )( )1

0

( )

( )0, 1

K

ll

l

l

y k t a u k l t

a h l ta l K

−

=

∆ = − ∆

= ∆≈ > −

∑

11.4.2002 230 1 2 3 4 5 6 7 8 9 10

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2β=0.22

t

Zero Crossing• Large phase transition implies amplitude peak

180° phase shift

Amplitude peak

I-branch

11.4.2002 24

0 1 2 3 4 5 6 7 8 9 100

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

tS

igna

l pow

er

β=0.22

Zero Crossing• Rapid change in power

7

11.4.2002 25

Zero Crossinghttp://www.planetee.com/planetee/servlet/DisplayDocument?ArticleID=394

11.4.2002 26

Nonlinear Power Amplifier• The peak-to-average power ratio should be small in

order stay in the linear region

• Operation in the nonlinear region– consumes more power if nonlinearity is compensated

– shapes the spectrum if nonlinearity is not compensated

Linear region

Bias

outP

inP

11.4.2002 27

HPSK Signal Constillation

http://literature.agilent.com/litweb/pdf/5968-8438E. pdf

11.4.2002 28

Transport ChannelsUser plane

– Dedicated channels• DCH, Dedicated Channel

is intended to carry dedicated user data and corresponding control information.

– Common channels• DSCH, Downlink Shared Channel

is intended to carry dedicated user data and corresponding control information, but unlike DCH it can be shared by many users in time.

• RACH, Random Acces Channelis utilized to carry control information or small packets in the uplink direction. New connection is initialized using RACH.

• CPCH, Uplink Common Packet Channelis extension of RACH to carry packet data in the uplink direction.

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11.4.2002 29

Transport Channels• Control plane

– Common channels • BCH, Broadcast Channel

System and cell information broadcasted to all users in the coverage area. E.g. what spreading codes are availabele to RACH

• PCH, Paging ChannelIf UE is not active, its location on the MSV/VLR or SGSN level is known only in RNC level. In order to determine its location, it must be paged from all the cells controlled by the particular RNC.

• FACH, Forward Access ChannelControl information to terminals known to locate in a given cell. Can also be used for transmitting small data packets.

11.4.2002 30

Physical Channels• Control plane

– PCCPCH, Primary Common Control Physical Channel– SCCPCH, Secondary -”-– SCH, Synchronisation Channel– AICH, Acquisition Indication Channel– PICH, Paging Indication Channel– DPCCH, Dedicated Physical Control Channel– CSICH, CPCH Status Indication Channel– AP-AICH, Access Preamble Acquisition Channel – CD/CA-ICH, Collision Detection/Channel Assignment

Indicator Channel

11.4.2002 31

Physical Channels• User plane

– Dedicated channels• DPDCH, Dedicated Physical Data Channel• PDSCH, Physical Downlink Shared Channel

– Packet Channels • PRACH, Physical Random Access Channel• PCPCH, Physical Common Packet Channel

11.4.2002 32

Transport Channels ó Physical Channels

• The physical layer is required to support variable bit rate transport channels to offer bandwidth-on-demand services, and to multiplex several services to one physical data channel.

• Each transport channel is accompanied by the Transport Format Indicator (TFI)

• Physical layer combines the TFI information of the different multiplexed transport channels to Transport Format Combination Indicator (TFCI) which is transmitted in physical control channel.

• One physical control channel and the associated physical control channel form a single Coded Composite Transport Channel (CCTrCh). Even if a connection uses more than one CCTrCh channels only one physical control channel is transmitted over the radio interface.

• TFCI is decoded in the receiver to find out which transport channels were active in the given frame.

• In downlink, there is an option to use Blind Transport Format Detection (BTFD). In that case, TFCI don’t have to be transmitted.

9

11.4.2002 33


Link layerPhysical layer

TFI TFI

TFCIcoding

Transport block

Multiplexing & coding

Physical control channel

Transport channel 1

644474448 Transport channel 2

644474448

Transport block Transport block

Layer 1controlinformation

CCTrCh

1444442444443Physical control channel

Transmitter

11.4.2002 34


Link layerPhysical layer

TFI TFI

TFCIdecoding

Transport block& Error indication

Decoding & Demultiplexing

Physical control channel

Transport channel 1

644474448 Transport channel 2

644474448

Layer 1controlinformation

CCTrCh

1444442444443Physical control channel



Receiver

11.4.2002 35


BCCH PCCPCH Primary Common Control Physical ChannelFACH SCCPCH Secondary -”-PCHRACH PRACH Physical Random Access ChannelDCH DPDCH Dedicated Physical Data Channel

DPCCH Dedicated Physical Control ChannelCPCH PCPCH Physical Common Packet Channel

SCH Synchronisation ChannelAICH Acquisition Indication ChannelPICH Paging Indication ChannelCSICH CPCH Status Indication ChannelCD/CA-ICH Collision Detection/Channel Assignment

Indicator Channel

11.4.2002 36

Uplink Dedicated Channel• DPDC

– Spreading factor can vary from frame to frame

• DPCC– Spreading factor 256– TFCI Transport format

combination indicator tells which rate was used in given frame. Error in TFCI will cause the whole frame to be destroyed.

– FBI Feedback Information (0 to 2 bits) phase difference information if two transmitting antennas are used.

– TPC Transmission Power Control bit (with repetition coding)

DPDC Data

DPCC PILOT TFCI FBI TPC

DCH 0 1 2 3 … 14

1 frame =10 ms

1 slot =2/3 ms=2560 chips

10

11.4.2002 37

Uplink DPDCH Data Rates• Maximum user data

rate assumes ½ rate coding

• One user can utilize up to 6 code channels Max data rate is 6 x 960 kbit/s = 5740 kbit/s => 2.3 Mbit/s user data rate

4809604

2404808

12024016

6012032

306064

1530128

7.515256

Maximum user data rate (kbit/s)

Channel bit rate (kbit/s)

DPDCH Spreading factor

11.4.2002 38

Tasks of Uplink Receiver• DPCCH is received and despreaded decoded in a slot by

slot manner while the DPDCH is first buffered and then decoded together with other frames that were jointly coded with it (interleaved).

• For every slot– A channel estimate (amplitude and phase) and SIR

estimate are made based on the received pilot bits.– Based on SIR determine downlink power control

command and send it– Decode the TPC bit and adjust downlink

transmission power accordingly• For every scond or fourth slot

– Decode FBI bits over two or four slots and adjust antenna phase and/or amplitude accordingly dependinf on transmission diversity mode

11.4.2002 39

Tasks of Uplink Receiver• For every 10 ms frame

– Decode TCFI and obtain the bit rate and channel decoding parameters for DPDCH

• For Transmission Time Interval (TTI), i.e. how often data must be delivered to higher layer protocol (10 – 80 ms), decode DPDCH

11.4.2002 40

Tasks of Downlink Receiver• The same as in uplink except

– In downlink, the dedicated channel bit rate is constant (except the bit rate of Downlink Shared Channel DSCH which can vary)

– FBI bits are not used– There is a Common Pilot Channel (CPICH) available

which can be used to increase the accuracy of channel and SIR estimates.

– If transmission diversity option is used receiver must estimate the channel state for the two different pilot patterns provided by the antennas

11

11.4.2002 41

Uplink Multiplexing

Rate matching

Transport channel

multiplexing

Physical channel

segmentation

2. Interleaving

Physicalchannel mapping

DPDCHsCRC

attachment

Transport blockconcatenation/Code block segmentation

Channel coding

Radio frameequalisation

Rate matching

1. Interleaving

Radio framesegmentation

11.4.2002 42

Uplink Multiplexing1. CRC attachment is used to add error detection information to

the transport blocks (0,8,12,16 or 24 bits)2. Transport blocks are either concatenated together or

segmented to different coding blocks3. The channel encoding is applied to the coding blocks.4. The task of radio frame equalisation is to divide the data

block evenly between 10 ms frames by adding padding bits5. Inter-frame interleaving performs interleaving over 20, 40 or

80 ms depending on TTI.6. Rate Matching matches the number of bits to be transmitted

with the number of bits available in the frame either by using repetition (preferred) code puncturing (only to avoid multi-code transmissions)

7. The different transport channels are multiplexed together by the transport channel multiplexing operation.

8. Intra-frame interleaving is done independently for each physical (code) channel (block interleaver, permutation of columns)

11.4.2002 43

Transmission Time Interval• TTI defines the maximum interleaving time

• All frames that are interleaved together should have the same rate

TTI start time

TTI = 10 ms

TTI = 20 ms

TTI = 40 ms

TTI = 80 ms

Datarate

11.4.2002 44

Downlink Dedicated Channel• Guided transport channel:

Position of CRC bits depend on the transport format combination. By calculating checksums the receiver can find out which TFC was used. This method is called Blind Transport Format Detection (BTFD).

• BTFD can only be used with relatively low rate channels (typically voice channels). In high rate case, TFCI is transmitted.

• DTX indication bits can be used in downlink to mark transmission pauses.

P

Data TPC TFCI Data PILOT

DCH 0 1 2 3 … 14

1 frame =10 ms

1 slot =2/3 ms=2560 chips

DT

X

t

12

11.4.2002 45

Downlink Multiplexing

CRCattachment

Transport blockconcatenation/Code block segmentation

Channel coding

Rate matching

Radio framesegmentation

Transport channel

multiplexing

Physical channel

segmentation

2. Interleaving

Physicalchannel mapping

1. Interleaving

Insertation of DTX indication

DPDCHs

Insertation of DTX indication

11.4.2002 46

Downlink DPDCH rates• User data rate of 2.3 Mbps can be achieved with 3 codes

1872

912

432

210

90

42-51

12-24

3-6

DPDCH channel rate (kbit/s)

1-315512

93619204

4569608

21548016

10524032

4512064

20-2460128

6-1230256

Maximum user data rate (kbit/s)

Channel bit rate (kbit/s)

Spreading factor

11.4.2002 47

DSCH, Downlink Shared Channel• Reserving codes for connections that have high peak

rate but only low activity cycle wastes resources (codes can run out) => Share one code between several users.

• Several users with different data rates can be multiplexed into one DSCH. Maximum spreading factor is 256 (512 is not available for DSCH).

• Both fixed and flexiple frame structures are defined. I.e. those that do not need TFCI and those who need it.

• Power control of one particular UE is maintained even if there is no data to send to it.

• Corresponding physical channel: Physical DSCH (PDSCH)

11.4.2002 48

Packet access in uplink• Random Access Channel (RACH)

– Signaling: Initial access of UE to the network, location update, connection establishment requests,...

– Packet access: 10 to 20 ms long packets with spreading factor of 256: up to 16 kbit/s

– Slotted ALOHA principle with power ramping• High access probability• Fast acquisition indication• Low interference

– Fast power control and macro diversity combining (soft handover) cannot be used.

• Common Packet Channel (CPCH)– As RACH, but can transmit longer packets – utilizes collsion detection– Fast power control is used during the message

transmission

13

11.4.2002 49

RACH Procedure• UE decodes BCH to find out the available RACH sub-channels

and theis scrambling codes and signatures.• It selects randomly one of the available sub-channels and

signatures.• The downlink power is measured and the initial RACH power

level is set with a proper margin due to open loop inaccuracy• UE transmits 1 ms long preamble with the selected signature

• Node-B replies by repeating the preamble using Acquisition Indication Channel (AICH)

• UE decodes AICH message to see whether the node-B has detected the preamble.– If AICH is not detected, the preamble is resend with 1dB

higher transmit power. – If AICH is detected, a 10 or 20 ms long message part is

transmitted with the same power as the last preamble.

11.4.2002 50

RACH Procedure

0 1 2 3 14

20 ms (two frames)

11.4.2002 51

CPCH Procedure• As in RACH case, except UE can check CPCH Status Indication

Channel (CSICH) if there exists a free channel (code and signature). If no sub-channels are free, transmission is not attempted.

• After getting response from node-b (CPCH API) CPCH CD preamble is send to detect possible collision. Node B echoes back the preamble using Collision Detection Indication Channel (CD/CAICH). It also sends Channel Assignment message that points a free channel to UE for actual packet transmission.

CPCH

CPCHCD/CAICH

CPCH AP-AICH

Long messagePreamble

CPCH API

CPCH CD

CPCH CAICPCH CD

11.4.2002 52

Packet access in downlink• Forward Access Channel

– Corresponds to RACH in uplink. I.e. for transmitting control signaling and small user data packets.

– Does not support fast power control, but slow power control based on received frame quality feedback can be applied if the packet is long.

– Macro diversity combining is not supported.– FACH frame can contain PILOT symbols if downlink

beamforming is utilized– FACH can be decoded by all the users within the cell. In-

band signaling is needed to add receiver address information to it.

– The data rate of FACH should be small to minimize interference.

– FACH is usually multiplexed with the paging channel to the same Secondary Common Physical Channel (S-CCPCH)

14

11.4.2002 53

Paging • User equipments are divided into groups• Paging Indication (PI) message per paging group are

periodically transmitted in the PICH channel when some UE in the group is paged.

• UE has to listen for the PI messages in those intervals defined its paging group.

• If PI reception indicates that someone in the group is paged, then all the members of the group have to decode the next PCH frame from the Secondary Common Control Physical Channel (S-CCPCH).

• The less frequently PI is sent, the less often must UE awake from the sleep mode to listen to the channel, but also the longer is the delay in connection establishment.

PIPICHS-CCPCH Paging message

7680 chips

11.4.2002 54

Paging

• PICH frame structure:

N is the paging indicator repetition ratio (17,36,72 or 144)• How often a terminal needs to listen to PICH channel is

parameterised and the exact moment is determined by System Frame Number (SFN).

10 ms frame

288/N bits

288 bits

PI 12 idle bits

11.4.2002 55

CPICH, Common Pilot Channel• Unmodulated code channel with spreading factor 256 which is

scrambled with the cell-specific primary scrambling code.• Provides a known reference signal to aid channel estimation.

(Amplitude and phase information for the Rake receiver and SIR estimator)

• There are two kinds of pilot signals– Primary: Cell/sector specific primary scrambling code to be

used for the whole cell/sector – Secondary: A secondary scrambling code with or without a

channelisation code of length 256 to be used in a narrow beam (Adaptive antennas/Beam steering) e.g. hot spot areas.

• Primary CPICH channel power defines the handover regions.I.e. cell boundaries. By adjusting the CPICH channel powers of two neighbouring base stations, the traffic load can be balanced between them.

11.4.2002 56

SCH, Synchronisation Channel• Primary synchronisation channel

– is utilized to find the slot timing used in one particular cell so that the control information broadcasted in that cell could be heard.

– it uses 256-chip spreading sequence identical in every cell

• Secondary synchronisation– is utilized to find the frame synchronisation and the

code group utilized by the cell (Codes are grouped into 64 different code groups)

0 1

10 ms

256 chips

2560 chips

14...SCH

15

11.4.2002 57

CCPCH, Common Control Physical Channel

• Primary CCPCH is the physical channel carrying the Broad Cast Channel (BCH). – Delivers system parameters needed by all the

terminals in the cell (e.g. codes to be used with RACH). Hence, it needs to be decoded by all the terminals served by the cell.

– P-CCPCH channel alternates with the SCH channel– Available bit rate for control information is only 27

kbit/s

• Secondary CCPCH Carries FACH and PCH which can either share the same physical channel or to both have their own channels.

2304 chips

2560 chips

...P-CCPCH 0 1 1 4

10 ms

11.4.2002 58

Cell Search• Step 1: Correlate against the common 256-chip primary

synchronisation code. Maximum correlation peak gives the slot boundary. [P -SCH]

• Step 2: Detect scrambling code group by cross-correlation of the received signal with all 64 permitted secondary synchronisation code sequences at the timing instants found in step 1; this also establishes frame synchronisation (as each sequence has unique cyclic shifts). [S-SCH]

• Step 3: identify the primary scrambling code by cross -correlation with the received signal with all scrambling codes belonging to the group found in step 2 [CPICH]

• Detect primary common control physical channel (carrying the broadcast channel) and read system information

11.4.2002 59

Cell Search

11.4.2002 60

Convolutional Coding• Encoder structutre for convolutional coding

DMessageSequence m

D Dk shift registers

n modulo 2sums

Coded message X

Code rate R=k/n

Parallel-to-serialconversion

16

11.4.2002 61

State diagram• Example

State diagram

00

01 10

11

0/00

1/11

1/000/10

1/11

0/000/01

1/01

First bit

Second bitm c

11.4.2002 62

1/11

00

10

01

11

00

11

00

11

01

00

00

11

01

00

0011

01

10

00

01 10

11

0/00

1/11

1/000/10

1/11

0/000/01

1/01

Trellis diagram

00

11

01

00

0011

01

10

11.4.2002 63

Maximum likelihood decoding• Consider two paths through trellis that start from the 00

state and and returns to it after three state transitions (branches): – Information sequences 000 and 101

– Transmittef (coded) sequences 00 00 00 and 11 01 11

00

10

01

11

00

11

00

11

01

00

00

11

01

00

0011

01

10

00

11

01

00

0011

01

10

Consider the transmittedsequence.Let us denote the mthbit in the jth branch by

, 1,2,3; 1,2jmc j m= =

and the correspondingdemodulator (correlator)output by jmr

Path 0

Path 1

Brach 1 Branch 2 Branch 311.4.2002 64

Maximum likelihood decoding• Transmitted coded message

– Correlator output (single user, no multipath)

– Probability density function conditioned on code corresponding to path i

Concolutionalencoder

MemorylessChannel Decoder

jmcjmr

( )2 1jm c jm jmr E c z= − +

jmc

jmz denotes a gaussian noise process

( ) ( )( )2( )

( )2 11

exp22

ijm c jmi

jm jm

r E cp r c

σπσ

− − = −

17

11.4.2002 65

Maximum likelihood decoding• The probability density conditioned on path i coded

sequence is given by

• Taking the logarithm and ignoring the common terms gives us correlation metric

• The message corresponding to the larges metric is the most likely message to have been sent.

( )( )( )2

( )

( )2 11

exp22

ijm c jmi

j m

r E cp r c

σπ σ

− − = −

∏∏

( )( )

( ) ( )2 1i

jm

i ijm jm

j m

CM r c

µ

= −∑∑ 14243

11.4.2002 66

Maximum likelihood decoding• Now returning to our example...• Assume that the information sequence was 101, then

the transmitted sequence was 11 01 11• Assume that due to the noise the received sequence

was

• Correlation metric of path 00 00 00

• Correlation metric of path 11 01 11

• There are no other paths that could return to 00 state in three steps. Since , we make the right decision that 101 was the coded message.

• Without coding one of the bits would have been detected erroneously.

{ }0.1, 0.3, 0.2, 0.1,0.1,0.2r = − − −

(0) 0.1 0.3 0.2 0.1 0.1 0.2 0CM = − + + + − − =

(1) 0.1 0.3 0.2 0.1 0.1 0.2 0.2CM = − + − + + =

(1) (0)CM CM>

11.4.2002 67

Maximum likelihood decoding• Decoding long sequences: Viterbi algorithm

00

10

01

11

00

11

00

11

01

00

00

11

01

00

0011

0110

00

11

01

00

0011

0110

3 3(0) (1) (0) (1)

1 1 1 1

3n n

jm jm jm jmj m j m j m j m

nµ µ µ µ= = = =

< ⇒ < ∀ ≥∑∑ ∑∑ ∑∑ ∑∑We dont have to care about the path 0 anymore⇒

11.4.2002 68

Turbo coding• Encoder

18

11.4.2002 69

Turbo coding• Decoder (Standard does not specify decoder)

11.4.2002 70

Performance Turbo-DecoderQuantization for UMTS.

H. Michel and N. Wehn. In IEEE Communications Letters, pages 55-57, February 2001

11.4.2002 71

Channel coding

XXXXCPCH

XXXXFACH

XXXXDSCH

XXXXDCH

XXRACH

XPCH

XBCH

1/3 rate1/3 rate 1/2 rate

Turbo coding

Convolutional coding

No coding

Transport channel

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