26/11/20071

CDMA: An Introduction

EY0619douros06@aueb.gr

2Motivation

z Why do we need CDMA?z Which are its basic principles?z What do we earn by using it?

3Outline

z Introduction z CDMA Basics z CDMA Deeper z CDMA Problemsz CDMA Benefitsz Conclusions

4Why Multiple Access?

z Goal: Multiple use of a shared medium.

z Multiplex channels in three dimensions:

Time (t)

Frequency (f)

Code (c)

5Frequency Division Multiple Access (FDMA)

z Cocktail Party Analogy: People create teams and discuss. There is a distance among them.

z (-) Requires guard band between channels

z (-) Waste of bandwidth if traffic is distributed unevenly

z Example: broadcast radio

6Time Division Multiple Access (TDMA)

z Cocktail Party Analogy: People have access to the same room but each of them waits for his turn to speak.

z (-) Precise synchronization necessary

7Time and Frequency Division Multiple Access

z (-) Precise coordination required

z Example: GSM

8Code Division Multiple Access (CDMA)

z Cocktail Party Analogy: All people are in the same room together. They can all be talking the same time!

z Example: UMTS

9Spread Spectrum

z PN: Pseudo-Noise code sequence spread/ despread the signal.

z Modulation:

FSK Frequency hopped (FH) multiple access)

PSK Direct sequence (DS) multiple access)

D mD

10

FHMA

z Bandwidth divides in non overlapping bands.z Signal shifts from band to band in predefined

intervals.z Receiver is synchronized with the transmitterz (+) less interferencez Use: Bluetooth

11

CDMA Basics (1)

z Each station is assigned a unique m-bit code (chip sequence) z To send bit 1, station sends chip sequence.z To send bit 0, station sends the complement.z Example: 1 MHz band with 100 stations. z FDMA

Each station a 10kHz band

Rate:10 kbps (Assume that you can send 1bit/Hz)z CDMA

Each station uses the whole 1MHz band106 cps.

If 10 kbps

12

CDMA Basics (2)

z Let or

z Compare any pair of these sequences-vectors

z Multiply any pair of these sequences-vectors

z Two chips S,T are orthogonal IFFz 0 0S T S T

= =0S T =

1

1 0m

i ii

S T S Tm =

= =2 2

1 1 1

1 1 1 ( 1) 1m m m

i i ii i i

S S S S Sm m m= = =

= = = = _ _1 1

1 1 1( 1) ( ) 1m m

iii i

S S S S mm m m= =

= = = =

13

CDMA Basics (3)

z Let A, B, C, D transmit correspondingly bit 1,0,1,_.

z Assume that:

All stations are perfectly synchronous.

All codes are pair wise orthogonal (arent they?).

If two or more stations transmit simultaneously, the bipolar signals add up linearly.

z Receiver understands z How can the receiver understand what bit station C send?

_

( 1 1 3 3 1 1 1 1)S A B C= + + = + + + +

14

CDMA Basics (4)

z Lets compute the normalized inner product SC

z Right! z By accident??

z Remember: All codes are pair wise orthogonal!

1 ( 1 +1 -3 +3 +1 -1 -1 +1) (-1 +1 -1 +1 +1 +1 -1 -1)=8

1 1= (1 1 3 3 1 1 1 1) 8 18 8

S C =

+ + + + + = =

( ) 0 0 1 1S C A B C C A C B C C C = + + = + + = + + =

15

CDMA Basics (5)

z Reverse wayz Think that each chip sequence arrives separatelyz Receiver separately computes each inner product

z It keeps only the non-orthogonal pair, i.e. the right bit

0 (1)

0 (2)1 (3)

0 0 1 1

A C

B CC CS

= = == + + =

16

CDMA Deeper (1)

z More advanced analysisz Sender:

z Receiver:

( ) cos(2 ( ))( ) {0, }( ) { 1, 1}( ) cos(2 ( )) ( )

d c

c

s t A f t tt

c ts t A f t t c t

= + + += +

( ) ( ) cos(2 ( )) ( ) ( )cos(2 ( )) ( )

c

c d

s t c t A f t t c t c tA f t t s t

= + =

= + =

17

CDMA Deeper (2)

z With orthogonal codes, we can safely decode the coding signals.

z Noise?z R=R+N, N: m-digit noise vector and N=(a aa)z Decode z No problem if chipping codes are balanced (same )

R' S=(R+N) S=S S +(orthogonal codes) S +N S= 0 ?1+ +

R' S=(R+N) S=S S +(orthogonal codes) S +N S==1+0+(a a a a)(+1+1-1-1)=1+0+0=1

18

CDMA Deeper (3)

z How many codes can we construct with m chips?z m (why?)z If m=2k, Walsh-Hadamard codes can be

constructed recursively!z The set of codes of length 1 is z For each code we have two codesz Code Tree:z

0 { }C = < + >kc C< >

_

k+1{ >

0

1

2

{ }{ , }{ , - - , - - , - - }

CCC

= < + >= < + + > < + >= < + + + + > < + + > < + + > < + + >

19

CDMA Deeper (4)

z Correlation: Determines similarity between two sets of data.

Possible valuesz 1 sequences are similarz 0 no relationship between them. z -1 one is the mirror of the other

z Cross correlation: Compare two sequences from different sources

z Auto correlation: Compare a sequence with itself after a time-interval

z Walsh Codes: No cross correlation Low auto correlationz PN sequences: Low cross correlation Low auto Correlation

20

CDMA Deeper (5)

z We cannot have more than m orthogonal codes.z Let m + k stations and m chips z Idea: Use PN Sequences.

zz ?: the sum of the k random variables that are either 1 or -1.z But PN Sequences = low cross correlation. ? should be 0. z Experimental evaluation: For k=m=128, decoding is correct

more than 80%.

( random codes) S+(m-1 orhogonal codes?

) =1+ +0R S S S k S = +

21

CDMA Problems (1)

z All stations are received with the same power level

z In reality users may be received with very different powers!z Near-far Problemz Solutions:

Empirical rule: Each MS transmits with the reverse power that it receives from the BS

Power Control!z Open Loopz Fast Closed Loop

22

CDMA Problems (2)

z Bad Properties of Walsh Codesz Perfect Synchronization of all

users required.z Impossiblez is nothing! Use a long

enough known chip sequence.

z ButIn a multipath channel, delayed copies may be received, which are not orthogonal any longer.

z Self-Interference.

23

CDMA Problems (3)

z So farz (-)tight synchronizationz (-)self-interference z (-)Near-far problemz (-)Higher complexity of sender/ receiverz z How did Qualcomm convince people to use

this stuff??

24

CDMA Benefits (1)

z Unlike FDMA and TDMA, CDMA does not rely on orthogonal frequency and time slots!

25

CDMA Benefits (2)

z In TDMA and FDMA systems

Nothing to send time/frequency slot is wasted

Dynamic allocation is very difficult

z In CDMA systems

Nothing to send less interference

Transmit ~half times doubles the capacity

26

CDMA Benefits (3)

z FDMA-TDMA use sectors to decrease the reuse distance

z CDMA use sectors to increase capacity (triple it)!

27

CDMA Benefits (4)

z Why handoff?z Types

Hard

Soft

28

CDMA Benefits (5)

z Break-Before-Makez Each MS

communicates with only one BS each time

z (+)Reduced dropped calls

Hard Handoff

29

CDMA Benefits (6)

z Each MS communicates with more than one BS each time

z Use Signal Strength to decide where to connect.

z Make-Before-Breakz (+++) no dropped calls

Soft Handoff

30

CDMA Benefits (7)

z Capacityz TDMA-FDMA: bandwidth limitedz CDMA: interference limitedz CDMAs capacity is bigger.z How?z Long Story

31

Conclusions

z Back to the startz Why do we need CDMA?

Introduction

z Which are its basic principles?

CDMA Basics

CDMA Deeper

z What do we earn by using it?

CDMA Problems

CDMA Benefits

32

!

CDMA: An IntroductionMotivationOutline Why Multiple Access?Frequency Division Multiple Access (FDMA)Time Division Multiple Access (TDMA)Time and Frequency Division Multiple AccessCode Division Multiple Access (CDMA)Spread SpectrumFHMACDMA Basics (1)CDMA Basics (2)CDMA Basics (3)CDMA Basics (4)CDMA Basics (5)CDMA Deeper (1)CDMA Deeper (2)CDMA Deeper (3)CDMA Deeper (4)CDMA Deeper (5)CDMA Problems (1)CDMA Problems (2)CDMA Problems (3)CDMA Benefits (1)CDMA Benefits (2)CDMA Benefits (3)CDMA Benefits (4)CDMA Benefits (5)CDMA Benefits (6)CDMA Benefits (7)Conclusions!