CDMA Cellular System

transcript

8/8/2019 CDMA Cellular System

1/13

EE5401 Cellular Mobile Communications

Institute for Infocomm Research 128 National University of Singapore

CDMA Cellular System

Earlier lecture on cellular system mainly for

FDMA/TDMA systems, i.e., reuse factor > 1.

- We determine the cochannel cell interference based on

the desired SIR for a given modulation technique.

- Path loss model come into picture when determining the

received signal power and the interference powers from

from co-channel cell. User in the same cell does not

interfere the referenced user because they use different

time slots or frequencies to transmit.

- For example, if only first tier and no sectorization,

==

6

1i

ni

n

D

R

SIR

- Conversely, if a minimum SIR is given, the cluster size

Ncan be determined. The total number of available

voice channels then split among these cells within a

cluster, and this is the total number of handover/newly

generated calls that each cell can handle.

- We demostrated the use of Erlang B table for newlygenerated traffic. A more complete scenerio is to

include the handover traffic.

- Resource management newly generated vs handover

traffic (dropped call probabilities), maintaining GoS

(blocking probability) and qaulity-of-service QoS (such

as, packet loss probabilities, delay constraints etc)



CDMA systems are different in terms of

- Reuse factor is 1.

- The capacity of CDMA systems is interference limited,

whilst it is bandwidth limited in FDMA and TDMA.

Hence, any reduction in the interference will cause an

increase in the capacity. Alternatively, this means that

if the number of users decreases, the link performance

will be improvedfor the same transmit power.

(a) Asynchronous short code

(bit asynchronous but chip synchronous)

Alternative way of representing the evaluation process

1231[]3113111[

1111[]1111111[2

13313113111

]1111111[]111-1111[3

]1111111[]1111111[2

]1111111[]1111111[1

+++++++

+++++

++++++

++++++

+++++++++++++++

Despread

Rx

Tx

7+ will decode as bit +1


2/13



(b) Synchronous short code

Alternative way of representing the evaluation process



In the downlink, BS is capable of synchronizing the

transmission of all the users signals, such that the symbol

durations are aligned with each other. Such a scenario is

known as symbol (bit) synchronous transmission.

Designing for perfectly orthogonal code in this case is

simple since the use of short code is sufficient. However,

there will still be interference from users in neighboring

cell BSs. Further, the presence of multiple paths could

distort the orthogonality.

Short code cannot be used in uplink since orthogonality

cannot be achieved when transmission is asynchronous

(no coordination in the transmission of users signals).

Long codes such as PN sequences perform much better

but perfect orthogonality cannot achieve for such codes.

Example to show why short code cannot be used in

symbol asynchronous transmission.

Consider two orthogonal Walsh codes

]1111[ and ]1111[

Data transmit is A=[1 1 ... ] B=[-1 1 1...]

If bit synchronous transmission,

=

02

20

02

20

11

11

1

1

1

1

1

1

1

1


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At the receiver,

=

44

44

02

20

02

20

1111

1111

If transmission is bit asynchronous but chip

synchronous, offset by a chip period for user B

1

1 1 1 1 1 1 1 1

1 1 1 1 1 1 1 1 1

2 2 2 0 0 0 0 0

1 1 1 1 1 1 1 1

( ) 6 0)N

A

B

Tx

A

+ + + +

+ + + + + + +

+ + + +

At the receiver, an error may occur due to loss in

orthogonality of the short code.

Multipath interference is always present in both the

forward and reverse link. Multipath interference is due

to the different arrival times of the same signal via the

different paths at the receiver (also known as self-interference). This is analogous to the signals

transmitted from other users and generates interference.

Hence, multipath interference is normally analyzed in

the same way as MAI.



Consider Walsh codes ]1111[

Data transmit is [1 1 ... ]

At the receiver, due to multipath (assume no phase

change and only power split in 9:1)

++

++++

++++

++++

3.67.3

0.18.00.18.00.18.00.19.0

1.01.01.01.01.01.01.01.0

9.09.09.09.09.09.09.09.0

Multipath reduces the received SNR if conventional

single user detector is used.

A chip ofprevious

bit

Channel

Multiple0.9

0.1


4/13


5/13



- Now examine only thek

W term defined in (1). Since all

the a s take only 1 or 1 equally, kW only takes on

discrete values. Performing some manupulation to the

expression of kW , and using the following results:

[ ]2

1

0

c

T

c

k

Td

TE

c

==

[ ]3

12

0

22 c

T

c

k

Td

T

Ec

==

It can be proved that 1

[ ]3

22 GWE k = , or

6

22 GPT kc

Ik=

- Here the expectation is taken over all values of kk , and b (bits).

-1

Reference for the proof can be found in Textbook,Appendix C and Smart antennas for Wireless

Communications by Joseph C Liberti and T.S

Rappaport, pp.305).

- Now go back to the MAI component when detecting the

information of user 0.

=

=

=

=

=

=

=

=

==

1

1

1

1

21

1

21

1

21

1

21

1

222

][][

])[(][

K

k

K

llk

K

kk

K

kk

K

k

k

K

k

k

IIEIEIE

IEIEEE

Assume that the terms kI are independent, i.e.,

0][][][ == jkjk IEIEIIE , this leads to



=

===

1

1

21

1

22

6][

K

kkc

K

kk PGTIE

- The desired detected signal has mean given by

bTbP

s 0,00

02

=

- Can show that in general

Variance of interference =

= +

1

10

2

42

K

kbkc

TNPa

GT

- where a is constant determine by

a =3 (chip and phase asynchronous) previous derived

a =1 (chip and phase synchronous)

a =2 (chip synchronous and phase asynchronous)

adopted

a =1.5 (phase synchronous and chip asynchronous)

- For adopted case, i.e. chip synchronous and phase

asynchronous

Variance of interference =

=

+1

1

0

2

44

K

k

bk

c TNPGT

The bit error rate is therefore given by

+=

+

=

=

=

WNP

GPQ

TNP

GT

TP

QPK

kk

bK

kk

c

b

e

0

1

1

0

01

1

2

20

2

44

2


6/13



where BWTTGcb

// == andbb

RTB == /1 is the

(unspread) signal bandwidth, bR is the data rate, Wis

the spread signal bandwidth.

- If the number of usersKis large, then thermal noise is

negligibly small.

)2(2

0

1

1

0 GQ

WNP

PGQP

K

kk

e =

+

=

where

WNP

PK

pkk

k

p

p

01

+=

=

is defined as the signal-to-

interference plus noise ratio (SINR) for userp.

- For BPSK, another way of viewing this is to define

WN

PG

WNP

PGG

N

E

IK

kk

p

I

b 0

0

1

1

0 =+

==

=

Ib NE / is defined at the output of matched filter whilst

SIR at the front end of the receiver.

(Note: in AWGN, 0/ NEb is defined as SNR and BER isgiven by )2( SNRQ , but here we just called it Ib NE / to

distinguish from SIR or SINR defined in CDMA system)

+=

=

1

10

K

kkI PWNWN



Power Control

Unless otherwise stated, we will assume that

- Single user detector is used. Power control is necessary

to avoid near far problem each mobile must achieve

the required SNR to achieve its pre-specified

performance (normally specified as minimum BER).

- Omni-directional antennas are used in both mobiles andBS. This affects how the amount of interference imposed

on a referenced user.

- Thermal noise is less significant if number of MSs is large.

Power control is needed

- CDMA allows all MSs to access the common bandwidth

without setting time slots or frequency bands.

- Power control is to maintain the required link QoS by

adapting to MS movements and also the statistical

variations in radio propagation paths. This helps to

mitigating interference to increase the system capacity.

- Without power control and simply let all MSs transmit

at same power, their signals will arrive at BS with

vastly different power levels near-far effect.- When an user transmits at excessive power level, its

performance gets improve but will degrade the

performance of other MSs. Others will try to increase

their transmit power to restore their link reliability, and

hence results in unhealthy competition among all MSs

are not properly co-ordinated.


7/13



- In the uplink, power control is to minimize power

consumption and prolong the battery operating time.

An example : centralized power control algorithm

- Requires the knowledge of all the radio link gains.

- If feasible solution exists, it gives the optimal solution

for the power control problem. This solution can become

a performance measurement criterion.- We consider a cellular system with N BSs and M MSs.

The transmitted power of MS k is denoted byk

P and theM dimensional vector P is the transmitted power

vector to be determined.

- We consider the ith MS (referenced) communicates with

BS nearest to it. The BS is then also labeled as i. The

link gain between the i th BS and the j th MS is denoted

by ijg . Then iig corresponds to the desired radio links,whereas ijg corresponds to the unwanted interference

links.

- The link gain ijg depends on the path loss model,

lognormal fading and fast fading component.

- Assuming that MS i knows which BS it is connected to

(an example is by connecting each MS to the nearest

BS). Its channel gain to that BS is defined as iig . If MS2 also connects to BS i, then we have 222 ggi = , 211 ggi = ,

jij gg 2= ,

(i.e., in the example, the BS has two identities, 2 and i)

Note: sometimesgis used to represent path loss, but sometimes is used as voltage gain. In

the following, we use it as voltage gain.



BS

User i

User 1

1ig

2ig

User j

ijg

User 2iig

MS

- The CIR of mobile i at its base station is given by2

2

0

1

,i ii

i M

j ij

jj i

P g

P g N W

=

=+

Mi 1

or can be rewritten as

WNPA

PM

ijj

jij

ii

01

+=

=

, Mi 1 ,

where

2

;

0;

ij ii

ij

g g i j

Ai j

= =

- There exists a SNR threshold *i that must be achieved

by each individual MS to ensure certain level of receiver

performance. For two different MSs, this threshold

needs not be the same.


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*ii

for Mi 1

- Repeat writing down the relationship for all MSs. We

can solve for all powers using the Msimultaneous

equations.

Power control is less critical in the forward link if power

consumption is not the main issue. This is because

orthogonal short codes are used and transmission is

symbol synchronous. However, power control still helpsin reducing interference picked up by MSs in

neighboring co-channel cells and the effect of resolvable

multipath.

From the implementation point of view, power control

can be classified into two classes

Open loop: The forward and reverse links are assumedto be symmetric. For example, in this ideal case, MSs

can determine its uplink transmited power according

to its downlink received power. This method only

suitable for the case where path loss and shadowing

which affect the signal propagation change relatively

slow and exhibit reciprocity in the forward and reverse

link.

Closed loop: BS provides continuous feedback to each

MS so that the MS varies transmit power accordingly.

Depending on the speed at which power level control is

performed, closed loop control is used to compensate

either for fast fading + lognormal shadowing or

lognormal fading.



- In practical system, a combination of open- and closed

loop control can be used.

Non-ideal power control

- For perfect power control, the transmitter power should

be identical to the inverse channel variation. However,

due to fast signal fading variations in the channel and

the control loop delay, the transmit signal power does

not follow the inverse channel variations. As a result,there is a significant residual fading in the received

signal after power control.

- In practical system, the received signal power variation

in the BS after power control are approximated by a

lognormally distributed. Through experimental data,

the standard deviation of the lognormal distribution isabout 1 to 2 dB.


9/13



Reverse link Capacity

First we shall consider only a single cell system, Nusers

(MSs) are transmitting and the desired signal arrived at

the BS with received powerP(i.e. ideal power control to

overcome near-far problem, assuming single user

detector is used). The received power isPand the

interference power is (N-1)P. At receiver front end,

1

1

)1( =

=

NPN

PSIR

After the dispreading and the matched filter T

dt0 )( , bit

energy-to-noise ratio is given by

1/)1(

/

=

=

N

G

WPN

RP

N

E b

I

b

where W is the RF bandwidth, bR is the bit rate, G is

known as the processing gain. If the number of MSs

increases, the interference signal increases linearly.

- For a required ( )min

0/ NEb , total number of users

min01

=

N

E

N

G

N

E b

I

b

( )

+=

min0max 1

NE

GN

b

- Increase the number of MSs beyond this threshold only

result in the slight degrading in performance soft

capacity.



- More accurate analysis should consider co-channel

interference, AWGN, imperfect power control,.

Voice activity factor and AWGN

- Silent periods in a voice conversation occupy more time

than nonsilent periods, the ratio is about 60/40.

- Introduce the term voice activity factor . Similarly

for data transmission, data activity factor is defined.

Inter-cell and intra-cell interference

- Each BS in a cellular system receives interference

coming from MSs in the same cell, called intracellinterference. Interference coming from MSs in

neighboring cells is called intercell interference.

- How to evaluate intercell interference?

(1) Consider the MS located at ),( r with respect to

the BS it is communicating with. The desired signal

power received at that BS is given by PPr = , the

transmitted power tp can be obtained using the pathloss model.

(2) The received interference power IP imposed on

the referenced BS can be found from tP and the path

loss model, with the distance between the referenced

BS and MS, obtained from Cosines Rule:


10/13



)cos2(

22

DrDrrI += D is the distance between the two BSs.

(3) The interferenceI

P the MS at the interference

cell to the reference cell BS can be obtained again

from the path loss model.

Irr

Interference user

D

For example, using simple path loss model, the exact

expression fort

P cannot be obtained directly because

0r= is undefined. However, it is not difficult tofigure out that

( , )

n n

I

I I I

P r r P r P

P r r

= =

Assuming circular cell with radius R, the average

interference is roughly given by



- If all MSs perform ideal power control with respect to its

own BS, and assume that all cells have the same sizeand user distribution density. Under these

circumstances, it can be shown that the average

intercell interference normalized to the total average

intra-cell interference can be characterized by a

constant, , known as the interference factor.2

inter

0 0

R

I I P d dr

=

intraI P= (why?)

2

2 20 0 ( 2 cos )

nR

IP r

d drP r D Dr

= = +

- The total intercell interference from all first tier

interfering cells without sectorization is given by 1P ,where

16 = .

Exercise: Write down a general expression for the

interference factor.

Underlaying cell (space)


11/13



More accurate model

- The interference plus noise power spectral 0I ( IN= ) foruserjth communicates to BS0 has to modify

WNPPWIK

kkiki

n

i

K

jkk

kk 0

ceinterferenintercell

11

ceinterferenintracell

1000 ++=

===

)0(1)1( ==== kikiki PP is the voice activity factorfor the ith user in the kth BS. j is the binomial random

variable that model the voice activity. All cells are

havingKMSs.

- When just consider average interference, then the above

expression can be simplified:

WNPPWIK

k kiki

n

i

K

jkk kk 0

ceinterferenintercell

11

ceinterferenintracell

1 000

++= ==

=

Exercise: Assume all cells have uniform user

distribution and can support the same number of users,

N. What is the maximum number of users N each cell

can support to guarantee a Ib NE / of* . Taking into

consideration the voice activity factor, intercell

interfence and assumed perfect power control and

lognormal shadowing..

Exercise : What happen if cluster size greater than 1 is

used? The bandwidth in this case is partition into a

few carrier channels.



Rake Receiver

Multipath channel

1

2

L )(tn

)(2

t

)(tL

)(1 t

)(tr)(ts

+==

L

lil tntsttr

1

)()()()( - for only one user.

where )()()( tctbPts = and )(tl is the time-variantcomplex channel gain of the ith path.

Spread spectrum techniques can improve reception

through using a receiver structure named RAKE

receiver. It inherited the name from the analogy of a

garden rake, whereby the fingers constitute the

resolvable paths. The point where the handle and

fingers meet is where diversity combining takes place.Possible methods of diversity combining are:

Selection combining (SC)

Maximal ratio combining (MRC)

Equal gain combining (EGC)

Combining of the n best signals (SC-n)


12/13



++

+1

1

)1(

b

b

TiiT

)(*

2 t

)(*

tM

)(*

1 t

b)(tr

)( 2*

tc

)(*

Mtc

)( 1*

tc

++

+2

2

)1(

b

b

TiiT

++

+Lb

Lb

TiiT

)1(

( 1)

* *

1

( 1) 2 *

1

( 1)

* *

1

sgn ( ) ( ) ( )

sgn ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

b l

b l

b l

b l

b l

b l

i TM

i l ll iT

i TM

l l l l l iT

i TL

l i l ii iTi l

b t r t c t dt

P t b t c t c t dt

t t c t c t

+ +

= +

+ +

= +

+ +

= +

=

=

+

2

1

sgn ( ) inter-finger interferenceM

l il

dt

t Pb=

= +

We assume there is Mrake fingers ( LM ) is used,

( ) ( ) 0i j

c t c t dt if ji and =1 ifi j= .



1

time

- For optimum performance of the RAKE receiver usingcoherent demodulation, the path attenuation and phase

must be accurately estimated. This estimation is

performed by another process known as channel

estimation.

Soft handover

- CDMA allows each cell to use the same broadbandfrequency channel, eliminating the need for a mobile to

change its freuqency when moving into another cell.

This is the pre-requirement for soft handover.

- In establishing the connection, the mobile detects and

tracks the BS with the highest power. At the same time

the mobile monitors the powers of neighoring BSs. The

second BS is introduced when its power becomes

significant relative to the first BS power. The first BSwill be abondoned only when the first BSs signal

becomes weak relative to second BS.


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A

AB

B



Spectral Overlay Systems

DS spread spectrum systems can share common

spectrum with the currently operating cellular or fixed

microwave systems in order to achieve efficient

bandwidth utilization.

The signals of coexisting users would appear as

narrowband interference in the spectrum of a wideband

signal. This is still possible because spread spectrum

modulation has an inherent ability to reject narrowband

interference. The effectiveness of narrowband

interference rejection depends on the processing gain.

f

CDMA Cellular System

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