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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKU p. 1 Part 6. 3G Mobile Communication Systems WCDMA and cdma2000

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 1

Part 6. 3G Mobile Communication Systems

―WCDMA and cdma2000

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 2

Introduction― Objectives to develop 3G

Achieving significantly higher transmission speed capability, encompassing

circuit- and packet-switched networks as well as support of multimedia services.

Higher spectral efficiency and overall cost improvement by utilizing advanced

technologies.

Maximizing the commonality by radio interfaces for multiple operating

environments.

Compatibility of services within IMT-2000 and fixed networks.

2G: voice

3G: voice, image, video

Data Networks

2G: low rate 2G: low rate

3G: high rate3G: high rate

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 3

Introduction― Key Properties Emphasized in 3G

Improved performance over 2G, including:

– Improved capacity;

– Improved coverage, enabling migration from a 2G deployment.

A high degree of service flexibility, including:

– Support of a wide range of services with maximum bit rates above 2 Mb/s and the

possibility for multiple parallel services on one connection;

– A fast and efficient packet-access scheme.

A high degree of operator flexibility, including:

– Support of asynchronous inter-base-station operation;

– Efficient support of different deployment scenarios, including hierarchical cellstructure and hot-spot scenarios;

– Support of evolutionary technologies such as adaptive antenna arrays and multi-user

detection.

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 4

Introduction― Differences Between 2G and 3G Systems

Flexible offer of mobile multimedia services

– Voice/fax/data

– Wideband data services (high speed Internet/high quality images)

Slow bit pipe provided by 2G

Faster bit pipe by 3G

<64kbps

(25-64kHz)Voice

Low rate data

2Mbps

(5MHz)Internet

Voice

ImagesMulti-media

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 5

Introduction― Spectrum allocation of 3G (1)

1992, ITU, World Administrative Radio Conference

– the frequencies around 2GHz were available for use by 3G mobile systems

– called International Mobile Telephony 2000 (IMT-2000)

– defined several different air interfaces based on CDMA or TDMA– target: a single common global IMT-2000 air interface for 3G

Target: a single common global IMT-2000 air interface for 3G

– Europe and Asia: same air interface WCDMA, frequencies around 2GHz– North America: spectrum around 2GHz has been auctioned for 2G and no new

spectrum is available for IMT-2000, 3G must be implemented within the

existing bands by replacing part of the spectrum with 2G

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 6

Introduction― Spectrum allocation of 3G (2)

WRC-2000 IMT-2000 Frequencies source:

http://www.umtsworld.com/ 

technology/frequencies.htm

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 7

The nature of communications has been changing …

– People to People→ People to Things→ Things to Things

Family of ITU standards consisting of two main systems

– Direct Spread Option (Wideband CDMA) with chip rate of 3.84

Mcps and BW of 5 MHz.

– Multi-Carrier Option (Cdma2000).

Key 3G Requirements:

– High Speed Packet Data: 144 kbps -- Vehicular; 384 kbps --Pedestrian, 2 Mbps -- Indoor

– Global Roaming

Introduction― 3G Standards

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 8

Introduction― Standardization Efforts (1)

SDO working for radio interfaces standardization

source: Willie W. Lu,"Broadband wireless mobile"

Universal Wireless Consortium (UWC)

Standard

Development

Organization

Partnership

Project

Radio

Interfaces

Japan

China

North America

Korea

Japan

Europe

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 9

Introduction― Standardization Efforts (2)

3GPP (3G Partnership Project)– Spearheaded by ETSI (European Telecommunication Standards Institute)

– Memberships as in December 1998: ARIB (Japan), ETSI (Europe), T1 (USA), TTA

(Korea) and TTC (Japan); May 1999: CWTS (China)

– Aim: to prepare, approve, and maintain globally applicable technical specificationsand technical reports for a 3G mobile system (called Universal Mobile

Telecommunication System UMTS) based on the evolved GSM core network and

Universal Terrestrial Radio Access (UTRA) (UTRA TDD+FDD=> WCDMA)

3GPP2– Spearheaded by ANSI (American National Standards Institute)

– Memberships as in January 1999: ARIB, TIA (USA), TTA and TTC.

– Aim: to cooperate in the preparation of globally applicable technical specifications

for a 3G mobile system based on the evolved ANSI/TIA/EIA-41 core networks andcdma2000.

OHG (Operators’ Harmonization Group)

– To prevent a multiple standard problem.

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 10

Introduction― Standardization Efforts (3)

Radio interfaces defined for IMT-2000

source: Willie W. Lu,

"Broadband wireless mobile"

IMT-Direct Spread

IMT-Multi Carrier

IMT-Time Code

IMT-Single Carrier

IMT-Frequency Time

IMT Radio

Technologies

Access

Technologies

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11ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 11

Introduction─ IMT2000 Capability (1)

Indoor

2Mbps

Indoor

2Mbps Pedestrian

384kbps

Pedestrian

384kbps

Vehicular

144kbps

Vehicular144kbps

IMT2000

Network 

Planned to deploy in May 2001

Frequency band:2GHz band

Information rates: up to 2Mbps

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 12

Introduction― IMT2000 Capacity (2)

Variable bit rates to offer bandwidth on demand

Multiplexing of services with different quality requirements on a single

connection, e.g., speech video and packet data

Delay requirements from delay-sensitive real-time traffic to flexible best-effortpacket data

Quality requirements from 10% frame error rate to 10-6 bit error rate

Coexistence of second and third generation systems and inter-system handovers

for coverage enhancements and load balancing Support of asymmetric uplink and downlink traffic, e.g., web browsing causes

more loading to downlink than to uplink 

High spectrum efficiency

Coexistence of FDD and TDD modes

source: H. Holma and A. Toskala,

"WCDMA for UMTS"

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 13

Introduction― Commercial 3G Services (1)

Start with crazy spectrum auctions in Europe

– Huge success of 2G

– Telecommunication companies in Europe spent more than 120 billion$ on

3G licenses

– Great Britain: 34 billion$

– Germany: 46 billion$

– Vodafone: 9.4 billion$ for one license in Great Britain

“We spent €10 billion

too much”

Sir Peter Bonfield, CEO, BT

Sunday Times, London,

18th February 2001

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 14

Introduction― Commercial 3G Services (2)

Voice

E-m ai   l  i   n  g

 W

 e  b  b r  o w

 s i   n  g

TransactionsBankingReservations for flights

and accommodations Stock trading, etc

Daily informationWeatherNews Stock prices, etc.

Data baseRestaurant guideTown pageDictionaryTrain transfer info.Cooking recipes, etc.

EntertainmentKaraoke

Network gameMovie listingsFortune-telling etc.

A successful example of 3G– The world first 3G network was launched by NTT DoCoMo, Japan, in 2001

– Big success of its 3G services “i-mode”: internet services are added to voice

communications

– Creation of mobile multimedia era

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 15

Introduction― Commercial 3G Services (3)

Jan. 2004

Hutchison

Dec. 2004

Smartone

H.K. CSL

Jun. 2005

Sunday

Jul. 2006

3G

subscribers:

1million

3G in Hong Kong

– Mainland China: no 3G services

– Hong Kong: only WCDMA is employed

Jun. 2008

3G

subscribers:

2.38million

all mobile

subscribers:

10.98million

Oct. 2001

Spectrum

Auction

four 3G

licenses; valid

for 15 years;each with a

spectrum of 

2x14.8MHz

+1x5MHz

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 16

Introduction― Commercial 3G Services (4)

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 17

Introduction― Commercial 3G Services (5)

CDMA20001x

WCDMA

CDMA20001xEV-DO

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 18

Summary: What Is 3G?

Why necessary?

– Explosive expansion of markets

– Mobile multimedia communications

– Global standard terminals

– Big business chances

– Lower cost due to mass markets

Which services?

– Unknown, but services indicated by the success of “i-mode”

– Point-to-point, point-multi points, broadcasting services

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 19

WCDMA

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 20

Introduction (1)

Wideband CDMA– a predominant wireless access technology for the 3G systems

– designed to offer wideband services

wireless internet services: download information from the Web, video transmission,...

– data rate: indoor: 2Mbps, pedestrian: 384kbps, vehicular: 144kbps

– wide bandwidth (5MHz) is needed for high data rate

physical limitations and impairments on radio

channels presents a fundamental technical challenge

to reliable high data rate communications

Two Modes: FDD and TDD

– Frequency division duplex: optimized for wide-

area coverage, i.e., public macro and micro cells

– Time division duplex: optimized for public micro

and pico cells and unlicensed cordless applications

uplink 

downlink 

BS

BS

MS

MS

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 21

Introduction (2)

Freq.Uplink Downlink  

190MHz

5MHz 5MHzFDD: paired

spectrum; ideal

for symmetric

services (voice);

inefficient forasymmetric

services (e.g. mp3

downloading)

Freq.Uplink 

Downlink 

5MHz

TDD: no need for

paired spectrum;

flexible, efficientfor asymmetric

services

TimeUplink Downlink  

TimeUplink 

Downlink 

Downlink Downlink  

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 22

Introduction (3)

Main features of WCDMA Asynchronous inter-base-station operation

– no requirement on any external system such as GPS

– new challenges like cell acquisition and soft handoff 

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 23

Introduction (4)

Main features of WCDMA Variable rate transmission

– to provide multimedia services

– multi-code transmission is employed in downlink to achieve higher bit rates

Adaptive antenna array– null out interference and maximize the signal to interference ratio

– particularly useful for multimedia communications

a small number of high rate users give

significant interference to low rate users.

Without adaptive antenna array, the link 

capacity would be significantly reduced.

– dedicated pilot symbols in both up- and

down-link facilitate user-unique antenna

patterns

Turbo coding

– large coding gain

Desired

user

with

low rate

services with high

rate

serviceslike online

game

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 24

System Architecture (1)

source:

http://www.mobileguru.co.uk/Mo

bile_Technology_globe.html

New protocols for WCDMA

UMTS R99 Architecture

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 25

System Architecture (2)

UTRA Terminologies UE: User Equipment

– interfaces the user and the radio interface

– consists of Mobile Equipment (ME) and UMTS Subscriber Identity Module (USIM)

UTRAN: UMTS Terrestrial Radio Access Network 

– handles all radio related functionality

– consists of Node B (Base Station) and Radio Network Controller (RNC)

Core Network 

– evolved GSM core network 

– switching and touting calls and data connection to external networks

– consists of Home Location Register (HLR), Mobile Services Switching Center

(MSC), Visitor Location Register (VLR), Gateway MSC, Service GPRS Support

Node (SGSN), Gateway GPRS Support Node (GGSN)

External Network 

– consists of Circuit Switching (CS) network and Packet Switching (PS) network 

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 26

System Architecture (3)

Note: the

functionality

of each pair is

not necessary

the same

Compare GSM and UMTS Terminologies

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 27

Radio Interface - Channel Concepts

Three separate channel concepts in UTRA: logical channel, transport channel andphysical channel

Logical channels define what type of data is transferred

Transport channels define how and with which type of characteristics the data is

transferred by the physical layer Physical channels define the exact physical characteristics of the radio channel

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 28

Radio Interface - Transport Channels (1)

Transport Channels: Data generated at higher layers is carried over the air withtransport channels, which are mapped in the physical layer to different physical

channels

HigherLayers

Physical

Layer

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 29

Radio Interface - Transport Channels (2)

CCTrCh (Coded Composite Transport Channel): a technology in the UMTSphysical layer, is the connection between Transport Channel and Physical Channel

which results a data stream from encoding and multiplexing of one or several

transport channels

One physical control channel + one or more physical data channel => one CCTrCh

Two types of Transport Channels

– dedicated channel (DCH): identified by a certain code on a certain frequency,reserved for a single user only; carries all the information intended for the given user

from layers above the physical layer, including data for the actual services and

higher layer control information

Features: fast power control, fast data rate change on a frame-by-frame basis,support adaptive antenna, support soft handover (illustrated in later sections)

– common channel: a resource divided between all or a group of users in a cell

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 30

Radio Interface - Transport Channels (3)

Six types of Common Transport Channels– Broadcast Channel (BCH): downlink, transmit network information, e.g., available

random access codes and access slots, important for register

– Forward Access Channel (FACH): downlink, carry control information or packet

data– Paging Channel (PCH): downlink, carry data relevant to the paging process when the

network wants to initiate communication with the terminal

– Random Access Channel (RACH): uplink, carry control information from the

terminal, e.g., requests to set up a connection, or packet data

– Uplink Common Packet Channel (CPCH): uplink, carry packet-based user data

– Downlink Shared Channel (DSCH): downlink, carry dedicated user data and/or

control information, shared by several users, associated with a downlink DCH

Basic network operation needs BCH, RACH, FACH and PCH; DSCH and CPCH isoptional

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 31

Radio Interface - Transport Channels (4)

Mapping of Transport Channels onto the physical channels

Transport Channels Physical Channels

DCH

BCH

FACH

DSCH

RACH

PCH

CPCH

Dedicated Physical Data Channel (DPDCH)

Dedicated Physical Control Channel (DPCCH)

Primary Common Control Physical Channel (PCCPCH)Secondary Common Control Physical Channel (SCCPCH)

Physical Random Access Channel (PRACH)

Physical Downlink Shared Channel (PDSCH)Physical Common Packet Channel (PCPCH)

Synchronization Channel (SCH)

Common Pilot Channel (CPICH)

Acquisition Indication Channel (AICH)

Paging Indication Channel (PICH)

CPCH Status Indication Channel (CSICH)

Collision Detection/ Channel Assignment Indicator

Channel (CD/CA-ICH)

Not directly visible to

higher layers, carry onlyinformation relevant to

physical layer procedures

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 32

Physical Layer (FDD)

Multiple access method: DS-CDMA System bandwidth 5M

– allocated spectrum: 1920-1980MHz and 2110-2170MHz

– chip rate: 3.84Mcps

Radio frame structure

– 10ms/frame, 15slots, 2560chips/slot

Slot #0 Slot #1 Slot #i Slot #14

One radio frame: Tf =10ms

Tslot=2560 chips

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 33

Uplink - Introduction

Spreading factors: 4- 256

modulation scheme: BPSK

Two type of uplink dedicated physical channels

– uplink dedicated physical data channel (uplink DPDCH)carry the DCH transport channel

can be zero, one, or several DPDCH on each radio link 

– uplink dedicated physical control (or pilot) channel (uplink DPCCH)

carry control information: known pilot bits to support channel estimation forcoherent detection, transmit power control (TPC) commands, feedback information

(FBI), and an optional transport-format combination indicator (TFCI)

one and only one uplink DPCCH on each radio link 

– DPDCH and DPCCH are I/Q code multiplexed within each radio frame Variable data rate: change the spreading factor on DPDCH on a frame-by-frame

basis

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 34

Uplink - Frame Structure

Source: Jiangzhou Wang, BroadbandWireless Communications, 3G, 4G

and Wireless LAN

Frame structure for uplink DPDCH/DPCCH

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 35

Uplink - Spreading

Spreading for uplink DPCCH and DPDCHs

Source: Jiangzhou Wang,Broadband Wireless

Communications, 3G, 4G and

Wireless LAN

Complex Scrambling

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 36

Uplink - Design Criteria (1)

Two terminal oriented design criteria– maximize the terminal amplifier efficiency

– minimize the audible interference from the terminal transmission

Uplink DPDCH and DPCCH: Why I/Q code multiplexed (Dual channel QPSKmodulation)?

– Time multiplexed: audible interference due to discontinuous transmission

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 37

Uplink - Design Criteria (2)

uplink DPDCH and DPCCH: Why I/Q code multiplexed? (Con't)– Pure code multiplexed: multicode transmission, increases transmitted signal

envelope variations => Higher PAPR (Peak-to-Average Power Ratio)

– I/Q code multiplexed: DPCCH is maintained on a separate continuous channel, no

pulse transmission, minimize audible interference

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 38

Uplink - Design Criteria (3)

uplink DPDCH and DPCCH: Why complex scrambled?– power levels of the DPDCH and DPCCH are typically different; lead to extreme

cases to BPSK-type transmission if transmitting the branches independently

– the I and Q branches are mixed using complex scrambling

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 39

Uplink Multiplexing

CRC attachment

Transport block 

concatenation/Code

block segmentation

Channel coding

Radio frame equalization

First Interleaving

(20, 40, or 80ms)

Radio frame segmentation Rate Matching

Transport Channel

Multiplexing

Other Transport

ChannelsPhysical channel

segmentation

Second interleaving

(10ms)

Physical channel mapping

DPDCH #1 DPDCH #2 DPDCH #N

Source: Harri Homa andAntti Toskala, WCDMA

for UMTS

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 40

Downlink (1)

Spreading factors: 4-512 modulation scheme: QPSK

One type of downlink dedicated physical channel

– downlink dedicated physical channel (downlink DPCH)

– dedicated data (downlink DPDCH) and control information (downlink DPCCH)(pilot bits, TPC, TFCI) are transmitted on DPCH in time multiplex mode

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 41

Downlink (2)

Common downlink pilot channels (CPICH)

– fixed rate, SF=256, 30kbps

– carry predefined symbol/bit sequence

– Primary Common Pilot Channel (P-CPICH): a phase reference for the downlink 

channels

– Secondly Common Pilot Channel (S-CPICH): a phase reference for a secondary

CCPCH carrying downlink access channels only and /or a downlink DPCH

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 42

Downlink (3)

downlink DPDCH and DPCCH: Why time-multiplexed?

– Time multiplexed: the common channels have continuous transmission, no audible

interference

– I/Q code multiplexed: downlink multicode transmission: no need for optimization of 

PAPR as with single code (pair) transmission

– Code multiplexed: reserving a code for DPCCH results in worse code resource

utilization

D li k (4)

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ELEC6040, Mobile Radio Communications, Dept. of E.E.E., HKUp. 43

Downlink (4)

downlink spreading: one scrambling code (one code tree) per sector in the base

station

– Variable data rate: rate matching operation or discontinuous transmission

– Why cannot the spreading factor on DPDCH vary on a frame-by-frame basis?

downlink scrambling: long codes

– number of scrambling codes: limited to 512 codes, otherwise the cell search

procedure would become too excessive

scramble

code #0

scramble

code #1scramble

code #0

scramblecode #1

scramble

code #2scramble

code #3

scramble

code #4

scramble

code #5scramble

code #6

scramble

code #7

scramble

code #8

D li k M lti l i

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Downlink Multiplexing

CRC attachment

Transport block 

concatenation/Code

block segmentation

Channel coding

Rate matching

Insertion of DTX indication

(with fixed bit positions only)

First Interleaving

(20,40 or 80ms)Radio frame

segmentation

Transport Channel

Multiplexing

Other Transport

Channels

Physical channel segmentation

Second interleaving

(10ms)

Physical channel mapping

DPDCH #1 DPDCH #2 DPDCH #N

Insertion of DTX indication

(with flexible positions only)

Source: Harri Homa andAntti Toskala, WCDMA

for UMTS

S bli C d (1)

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Scrambling Codes (1)

Scrambling in WCDMA is used on top of spreading– does not change the signal bandwidth and symbol rate

– to separate terminals or base stations from each other; use pseudo-noise (PN) codes

Spreading in WCDMA

– increase signal bandwidth– to separate channels from each other (channelisation); use orthogonal codes

(channelisation codes)

S bli C d (2)

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Two types of scrambling codes: long and short scrambling codes

Scrambling Codes (2)

Scrambling Codes (3)

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Uplink physical channels: complex-valued scrambling code, either long or short

– Long scrambling codes: used if the base station uses a Rake receiver

– Short scrambling codes: used if the base station uses advanced multiuser detectors or

interference cancellation receivers

Scrambling Codes (3)

long scrambling

code, shift #1

long scrambling

code, shift #0

long

scrambling

code #1

long

scrambling

code #0

long: BS has a Rake

receiver

short: BS uses multiuser

detection

GPS

IS-95 or CDMA2000WCDMA

Scrambling Codes (4)

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Signal detection at BS

Scrambling Codes (4)

Slot #0

Time

Slot #15Slot #1

long scrambling code: one frame: 10ms, 38400 chips

Slot #0 Slot #15Slot #1

Time

Slot #0 Slot #15Slot #1

Time

Received signal at BS

Terminal #0

(Scrambling code #0)

Terminal #1

(Scrambling code #1)

Terminal #2(Scrambling code #2)

Scrambling Codes (5)

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Descrambling using

scrambling code #0

Descrambling usingscrambling code #1

Descrambling using

scrambling code #2

Signal detection

for user #0

Signal detectionfor user #1

Signal detection

for user #2

Receivedsignal at BS

Recovered data

symbols for user #0

Recovered datasymbols for user #1

Recovered data

symbols for user #2

Interference

Regenerator for user #0

Delay

Descrambling using

scrambling code #0

Signal detection

for user #0

Recovered data

symbols for user #0

Multiuser detectors or interference cancellation receivers

Scrambling Codes (5)

Advantage of short scrambling codes: reduce of processing delay

Channelisation Codes (1)

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Channelisation Codes (1)

Transmissions from a single source are separated by channelisation codes

– downlink connection within one sector

– dedicated channels in the uplink from one terminal

WCDMA uses Orthogonal Variable Spreading Factor (OVSF) codes

OVSF allows the spreading factor to be changed and orthogonality between

different spreading codes of different lengths to be maintained

c1,1=(1)

c2,1=(1,1)

c2,2=(1,-1)

c4,1=(1,1,1,1)

c4,2=(1,1,-1,-1)

c4,3=(1,-1,1,-1)

c4,4

=(1,-1,-1,1)

c

(c,c)

(c,-c)