modern wireless chapter 5 communication spread ...yfahuang/ex0387ch05.pdf1 (5.5) ch05-11 modern...

1

CH05-1

Modern Wireless CommunicationsModern Wireless Communications

Modern Wireless

Communication

Simon Haykin, Michael Moher

CH05-2


Chapter 5

Spread Spectrum and Code-

Division Multiple Access

CH05-3


• 5.1 Introduction

• 5.2 Direct-Sequence Modulation– 5.2.1 The Spreading Equation

– 5.2.2 Matched-Filter Receiver– 5.2.3 Performance with Interference

• 5.3 Spreading Codes

– 5.3.1 Walsh-Hadamard– 5.3.2 Orthogonal Variable Spreading Factors (OVSF

– 5.3.3 Maximal-Length Sequences– 5.3.4 Scramblers– 5.3.5 Gold Codes

– 5.3.6 Random Sequences

• 5.4 The advantages of CDMA for Wireless– 5.4.1 Multiple-Access Interference

– 5.4.2 Mutlipath– 5.4.3 RAKE Receiver

– 5.4.4 Fading Channels– 5.4.5 Summary of the Benefits of DS-SS

Contents

CH05-4


• 5.5 Code Synchronization

• 5.6 Channel Estimation

• 5.7 Power Control: The Near-Far Problem

• 5.8 FEC Coding and CDMA

• 5.9 Multiuser Detection

• 5.10 CDMA in a Cellular Environment

• 5.11 Frequency-Hopped Spread Spectrum

– 5.11.1 Complex Baseband Representation of FH-SS

– 5.11.2 Slow-Frequency Hopping

– 5.11.3 Fast-Frequency Hopping

– 5.11.4 Processing Gain

Contents

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5.1 Introduction

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• CDMA

– Multiple-access technique, individual terminals use spread-spectrum and occupy all spectrum when they transmit.

• Spread spectrum

– Direct sequencing (DS)

– Frequency hopping (FH)

2

CH05-7


5.2 Direct-Sequence Modulation

CH05-8


• 5.2.1 The Spreading Equation

• 5.2.2 Matched-Filter Receiver

• 5.2.3 Performance with Interference

CH05-9



5.2.1 The Spreading Equation

CH05-10


• BPSK signal

• Symbol-shaping function

• For rectangular pulse shape, transmit spectrum is given by

• For a direct-sequence signal, the symbol-shaping function is

which is called spreading factor

( ) ( ) Tt tgEbts b ≤≤= 0~ (5.2)

( )otherwise

TtTtg

≤≤

=

0

0'

1(5.3)

( ) ( )fTcTfSg

2sin= (5.4)

( ) ( ) ( )∑=

−=Q

q

cc qTtgqctg1

(5.5)

CH05-11


• For DS modulation, the pulse shape is a sequence of shorter rectangular pulses called chips, the function of chip shape is

( )otherwise

TtTtg

c

c

≤≤

=

0

0'

1(5.6)

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5.2.2 Matched-Filter Receiver


3

CH05-13


• Received signal

• Optimum receiver corresponds to the processing

• Optimum processing

( ) ( ) ( )twtstx ~~~ += (5.7)

( ) ( )dttstxy

T

∗

∫= ~~

0

(5.8)

( ) ( )

( ) ( ) ( )

η+=

+=

=

∫ ∫

∫

∗

∗

b

T T

b

T

Eb

dttgtwdttgEb

dttgtxy

0 0

2

0

~

~

(5.9)

CH05-14


• The mean of the noise sample ηis zero and the variance is given by

• In AWGN, the transmission performance of DS spread

spectrum is identical to the nonspread system.

• The signal-to-noise ratio with optimum detection is

( ) ( ) ( ) ( )[ ] ( ) ( )

( ) ( ) ( ) ( )∫ ∫ ∫

∫ ∫∫

==−=

=

=

∗

∗∗∗

T T T

T TT

NdttgNdtdssgtgstN

dtdssgtgswtwEdttgtwE

0 0 0

0

2

00

0 0

2

0

2 ~~~

δ

ση

(5.10)

[ ]( )0

2

2

N

EyESNR b==

ησ(5.11)

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5.2.3 Performance with Interference


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• DS modulation advantage: reduced receiver sensitivity to interference.

• To explain this, complex envelope is

• Received signal, including interferer, is given by

• Jamming term

( ) tfje

T

At ξπξξ

2~ −= (5.13)

( ) ( ) ( ) ( )twttstx ~~~~ ++= ξ (5.14)

( ) ( )∫∗=

T

dttgty0

~ξξ

(5.15)

CH05-17


• After multiplication by de-spreading sequence, the jamming tone becomes

• The corresponding spectrum is give by

• To estimate the contribution of jammer to the noise after demodulation, we assume:– The frequency offset is small– The noise bandwidth of the integrate and dump circuit is 1/T

( ) ( ) ( )

( ) ( )

( ) ( ) Tt eqTtgqcT

A

qTtgqceT

A

tgeT

Atgt

Q

q

tfj

cc

Q

q

cc

tfj

tfj

≤≤−=

−=

=

∑

∑

=

−∗

=

∗−

∗−∗

0

~

1

2

1

2

2

ξ

ξ

ξ

πξ

πξ

πξξ

(5.16)

( ) ( )( )

( )( )c

cg

TffcQ

A

TffcQ

TQ

T

AfS

ξξ

ξξ

ξ

+=

+××=

2

2

2

sin

sin

(5.17)

CH05-18


• Equivalent noise contribution of jamming is given by the frequency-

domain equation

• In nonspread system, the interference power after the integrate-and-dump circuit is

• In a DS-SS system, the interference is reduced by the processing gain PG relative to its effect in a nonspread system.

( ) ( )

TP

A

TQ

A

dffSfS

G

pg

ξ

ξ

ξξσ

≈

×≈

= ∫∞

∞−

1

2

(5.18)

( )( ) ( )

T

A

dffStffcA px

ξ

ξξσ

≈

+= ∫∞

∞−

22sin

(5.19)

4

CH05-19


5.3 Spreading Codes

CH05-20


• With TDMA, the users are time orthogonal, with FDMA, the users

are approximately frequency orthogonal, with CDMA, the users areapproximately code orthogonal

• To achieve this orthogonality, a different symbol-shaping function is assigned to each user k

• The approximate orthogonality of gj(t) and gk(t) for different time

offsetsτcan be expressed as

• Additional self-orthogonality requirement that minimizes a number of practical channel and receiver effects is

( ) ( ) ( ) Tt0 qTtgqctgQ

q

cckk≤≤−=∑

=1

(5.20)

( ) ( ) ( ) kj for dttgtgR kjjk ≠≈+= ∫∞

∞−

∗ 0ττ (5.21)

( ) 00 >≈ ττ for Rkk(5.22)

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CH05-22


5.3 Spreading Codes

5.3.1 Walsh-Hadamard sequences

CH05-23


• To construct a Walsh-Hadamard sequence, we begin with

sequences of length 2

• A four orthogonal sequences of length 4 from the sequences of

length 2

• In general, we may construct 2n orthogonal sequences of length 2n

from sequences of length 2n-1 by operation

−=

11

111

H(5.25)

−=

−−

−−

11

11

nn

nn

nHH

HHH (5.27)

−−

−−

−−=

−=

1111

1111

1111

1111

11

11

2HH

HHH (5.26)

CH05-24


5.3.2 Orthogonal Variable Spreading

Factors (OVSF)

5.3 Spreading Codes

5

CH05-25


CH05-26


• Suppose we need OVSF codes of length n1 and n2, with n1 < n2. The algorithm for constructing OVSF codes is

1. Construct Hn1 by the usual Walsh-Hadamard algorithm.

2. Choose one row of the matrix Hn1 as the code of length 2n

1. Let H'n1

represent the Hadamard matrix with the selected row removed.

3. Continue the Walsh-Hadamard algorithm with H'n1; that is,

4. Then continue until the desired H'n2is constructed

5. Choose any row of H'n2as the spreading code of length 2

n2

6. If a third code is needed, continue in a similar manner

−=+ ''

''

'

1

11

11

1

nn

nn

nHH

HHH (5.29)

CH05-27


5.3.3 Maximal-Length Sequences

5.3 Spreading Codes

CH05-28


• Sequences having properties similar to random sequences but can be generated simply at both the transmitter and receiver.

• Can be generated by Shift register

• Maximal-length sequences have five important properties:

1. Length property: Each maximal length sequence is of length 2m-1.

2. Balance property: Each maximal length sequence has 2m-1ones and 2m-1-1 zeros.

3. Shift property:

1. The modulo-2 sum of an m-sequence and any circular-shifted version of itself produces another circular-shifted version of itself.

4. Subsequence property: Each maximal sequence contains a subsequence of 1,2,3,…,m-1 zeros and ones.

5. Autocorrelation property.

CH05-29


• Define the circular autocorrelation function

• Normalized autocorrelation

• Each maximal-length sequence provides 2m-1 approximately

orthogonal sequences obtained by different (circular) time shifts of the original sequence.

• Given the irreducible polynomial

A shift register for m-sequence can be constructed

( ) ( ) ( ) ( )( )QkqcqcQ

kRQ

q

jj mod1 1

0

+= ∑−

=

(5.30)

( )

≠−

=

=0k

Q

0k

kR jj1

1

(5.31)

011

2

2

1

1 =+++++ −−

−− xcxcxcx

m

m

m

m

mK (5.32)

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6

CH05-31


5.3.4 Scramblers

5.3 Spreading Codes

CH05-32


• Prevent transmission of long strings of zeros and ones that may appear in raw data.

• Long strings of 0 and 1 cause

– difficulties for circuits tracking

– Peaks in transmit spectrum �excessive

interference.

CH05-33


CH05-34


5.3.5 Gold Codes

5.3 Spreading Codes

CH05-35


• Gold codes are created by summing the output of the two m-sequence generators to produce a new 0-1 sequence.

• The cross-correlation of the Gold codes is approximately bounded by

• For select pairs of maximal-length sequences, we can generate 2m-1 distinct gold codes

( ) kj QQ

R jk ≠+≤21

τ (5.33)

CH05-36


7

CH05-37


5.3.6 Random Sequences

5.3 Spreading Codes

CH05-38


• For random sequences, we define cross-correlation of two sequence as

• The autocorrelation function of random sequence is given by

• If we compute the cross-correlation properties, we can get

( )

= ∑

=+

Q

q

kqqxy yxQ

EkR1

1 (5.34)

( ) k all for kRxy 0= (5.36)

( )

[ ] [ ]

[ ]

==

≠=×=

=

=

∑

∑

∑

=

=+

=+

Q

q

q

Q

q

kqq

Q

q

kqqxx

0k xEQ

1

0k xExEQ

yxQ

EkR

1

2

1

1

1

0001

1

(5.35)

CH05-39


• The average cross-correlation energy of 2 random sequences is give by

• The interference power between two random sequences is inversely proportional to the length of the sequence.

[ ]

Q

Q

yxQ

yxyxQ

E

yxQ

ERE

Q

m

Q

m

mm

Q

q

Q

m

mmqq

Q

q

qqxy

1

111

1

1

1

12

1

22

2

1 12

2

1

2

=

×=

=

=

=

∑

∑

∑∑

∑

=

=

= =

=

(5.37)

CH05-40


5.4 The advantages of CDMA for Wireless

CH05-41


• Effect on multiple-access performance when spreading codes are not perfectly orthogonal.

• 5.4.1 Multiple-Access Interference

• 5.4.2 Multipath Channels

• 5.4.3 RAKE Receiver

• 5.5.5 Fading Channels

• 5.4.5 Summary of Benefits of DS-SS

CH05-42


5.4.1 Multiple-Access Interference


8

CH05-43


• Received complex baseband signal of synchronous CDMA

• The individual transmitted signals reflect their respective data and spreading waveforms, given by

• The output is given by

( ) ( ) ( ) Tt0 twtstxK

k

kk ≤≤+=∑=1

~~~ α (5.38)

( ) ( )tgEbts kbkk =~ (5.39)

( ) ( )

( ) ( )

Tt0 RbEEb

dtsgsgEbEb

dttgtxy

K

k

kkkbb

K

k

T

kbkkb

T

≤≤++=

++=

=

∑

∑ ∫

∫

=

=

∗

∗

2

1111

2 0

1111

0

1~

αηα

αηα

(5.40)

CH05-44


• Average amplitude at correlator output is given by

• The variance of output is

[ ] [ ]

b

b

K

k

kkkbb

Eb

Eb

RbEEEEbyE

11

11

0

1111

00

α

α

αηα

=

++=

++= ∑

=

(5.41)

[ ][ ]

[ ] [ ]

( ) [ ]

∑

∑∑

∑∑

∑∑

=

= =

∗∗

= =

∗∗∗

==

∗

+=

−+=

++=

+

+=

−=

K

k

kkb

K

k

K

l

lklkb

K

k

K

l

lklklkb

K

k

kkkb

K

k

kkkb

REEN

RREkEN

RREbbEEN

RbERbEE

yEYE

2

2

1

2

0

2 2

110

2 2

110

2

2

1

2

11

2

1

22

1

0

Re2

α

δαα

αα

ααηη

σ γ

(5.42)

CH05-45


• From Eq.(5.37), we can have

• Contribution of multiple-access term to the noise variance

given by

• The transmitters are power controlled, which means

• 1st and 2nd order statistics of MAI contribution to noise

[ ]Q

RE jk

12

≈ (5.43)

∑=

≈K

k

kbMAIQ

E2

22 1ασ (5.44)

k all for k

1=α (5.45)

[ ]b

2

MAIbMAI EQ

K and EbyE

1011

−==−= σαµ (5.46)

CH05-46


• Signal-to-interference-pulse-noise ratio

• Degradation

[ ]( )

gb

b

b

b

b

Y

DN

E

N

E

Q

KN

E

EQ

KN

E

yESINR

0

0

0

0

2

2

11

1

1

=

−+

=

−+

=

=σ

(5.47)

1

0

11

−

−+=

N

E

Q

KD b

g

(5.48)

CH05-47



5.4.2 Mutlipath

CH05-48


• Complex envelope of channel impulse response is given by

• Define windowed channel spectrum by

• By Nyquist smapling theorem, the time domain equivalent of

HR(f) can be represented by {hn}

( )∑=

−=L

l

ll tth1

)(~

τδα (5.49)

( )( )

<

=otherwise

Rf fHfH c

R0

2/ (5.50)

( ) ( )( )∑∞

−∞=

−=n

ccnw RntRchth sin (5.51)

9

CH05-49


• With Rc=1/Tc, the chip rate, by the convolutional sampling theorem, the received signal is

( )

( ) ( )

( ) ( )∑

∑

=

∞

−∞=

+−=

+−=

+⊗=

'

0

~

~

)(~)(~)(~~

L

l

cl

l

cl

wmp

twlTtsh

twlTtsh

twtsthtx

(5.52)

CH05-50


5.4.3 RAKE Receiver


CH05-51


• Operating in multipath environments.

• The output of each delay element is processed by a single-

user receiver.

• This receiver has (L+1) fingers and gets the name “RAKE”from its resemblance to common garden rake.

• The output of ith finger

( ) ( )

( )

( )∑

∫∑

∫ ∑ ∫

∫

≠

∗

−

−=

−

− =

−

−

∗∗

−

−

∗

+−+≈

++−=

+++−=

+=

il

igglbbi

icc

iTT

iT

L

ol

l

iTT

iT

L

l

iTT

iT

cccl

iTT

iT

ci

ilRhEbEbh

dttgiTlTtsh

dttgiTtwdttgiTlTtsh

dttgiTtxy

c

c

c

c

c

c

c

c

η

η)()(~

)()(~)(~

~

0(5.53)

CH05-52


• If the delay spread of channel is much less than the symbol

period T, then

• Contribution of self-interference to total noise for the first

finger is

• If spread code has cross-correlation properties similar to

random codes, then we can approximate result

( )( ) ( ) ( )∫ −≈−− ∗T

ggc ilRdttgTiltg0

(5.54)

( )∑=

+=L

l

cgglbY lTRhEN1

22

0

2σ (5.55)

( )∑ ∑≠ ≠

≈jl jl

lcggl hQ

lTRh222 1

(5.56)

CH05-53


• The final estimate of data is given by weighted sum of output of each finger of RAKE receiver

which is called maximal-ratio combining (MRC)

• The resulting output signal-to-noise ratio is

∑ ∑

∑

= =

=

+≈

=

L

l

L

l

lllb

L

i

ii

hbhE

yhy

0 0

*2

1

*

η

(5.57)

[ ]( )

0

0

2

0

2

0

2

0

2

2

2

N

hE

hN

hEyE

SNR

L

l

lb

L

l

l

L

l

lb

Y

∑

∑

∑

=

=

=

=

==σ

(5.58)

CH05-54


5.4.4 Fading Channels


10

CH05-55


• Assumption: Transmission systems are usually designed such that channel is approximately constant, at least over the duration of a symbol interval.

• Therefore, the fading performance of single-user spread spectrum BPSK or QPSK is same as non-spread case.

• For the transmission of coherent BPSK over a single-ray Rayleigh-fading transmission path, BER performance is

• BPSK performance is given by

• With second-order diversity, there is an approximate squaring of the bit error rate

04

1

NEP

b

e ≈ (5.59)

L

b

eNEL

LP

−≈

04

112(5.60)

CH05-56


CH05-57


5.4.5 Summary of the Benefits of DS-

SS


CH05-58


Important features in a multiple-access system

1. Spectral density of transmitted signal is reduced by factor equal to processing gain.

2. Effect of interference by processing gain.

3. Under ideal conditions, there is no difference in BER performance between spread and non-spread forms of BPSK or QPSK.

4. In multipath channels, if it is treated as interference, its effect can be reduced by processing gain.

5. Multipath can improve receiver performance by capturing the energy in paths having different transmission delays.

6. In fading channels, spread-spectrum receiver can obtain important advantage in diversity by using RAKE receiver.

7. Choice of spreading codes is critical to reduce multiple-access interference and multipath self-interference.

CH05-59


5.5 Code Synchronization

CH05-60


11

CH05-61


• Assume spreading code is transmitted repeatedly

• Complex baseband receieved signal prior to chip filters

• Output of sampling device

• Partial correlation

( ) ( )

( ) ( )2TtT eTtgE

Tt0 etgEtx

cfkTj

b

ftj

b

<≤−=

≤≤=

+∆

+∆

φπ

φπ

2

2)(~(5.61)

( ) ( ) ( )

( ) ( )φπ

φπ

+∆

+∆

=

=

c

c

fkTj

b

fkTj

cbc

eQkcE

eTkTgEkTx

2

2

mod

mod~

(5.62)

( ) ( ) ( )( )( )

( ) ( )( )( ) ( )

( ) ( )( )( )∑

∑

∑

∆+

=

∆+

=

+∆

∆+

=

−+≈

−+=

−+=

kk

kk

j

b

kk

kk

fkTj

b

kk

kk

cx

QkkmcQkceE

eQkkmcQkcE

QkkmckTxkC

c

1

1

1

1

1

1

modmod

modmod

mod

10

*'

2

10

*

10

*

1

φ

φπ (5.63)

CH05-62


• Ideally the vale if Cx(k1) should be

• To increase the confidenceof synchronization, we form a decision variable

∆

=otherwise 0

align sequencesthe if keEkC

j

b

ix

'

)(

φ

(5.64)

( )∑=

=1

1

2L

l

lx kCD (5.65)

CH05-63


5.6 Channel Estimation

CH05-64


• In flat-fading channel, a frequency shift will be happened there the

• amplitude and phase of the received signal can be changed.

• The mobile channel effects on phase, frequency and amplitude are slowly time-varying.

• It is critical at receiver performance to have an accurate channel estimation and tracking strategy to tack these variations.

CH05-65


CH05-66


• Channel-tracking algorithm– Reliable data estimates, which involves transmitting

training sequence to adapt the channel estimates initially.

– Bandwidth of low-pass filter must be chosen

appropriately.

– If data stream is channel encoded to operate at a lower

SNR, reliability of the uncoded data at the output of

RAKE receiver is liable to be poor at all times.

12

CH05-67


5.7 Power Control: The Near-Far Problem

CH05-68


• The complex baseband received signal is

• SINR of 1st user is

( ) ( )twtstxK

k

kkc~~)(~

1

+=∑=

α (5.67)

[ ]( )

( )

−

−+

==

−

−+

=

+

=

=

∑

∑

∑

=

=

=

K

k

kb

ggb

K

k

kb

b

K

k

kb

b

Y

KN

E

Q

K

DwhereDN

E

KN

E

Q

KN

E

EQ

N

E

yESINR

2

2

10

2

1

',

0

2

1

2

2

10

2

10

2

1

2

2

0

2

1

2

2

1

111

1

1

111

1

1

α

ααα

α

αα

α

α

α

σ

(5.68)

CH05-69


• Comparing the definition of with definition of , we can see

– The received energy for the desired signal is instead of Eb.

– Difference is that the denominator of included the factor, multiplier applied to the multiple-access interference.

( )∑=

−

K

k

k

K 2

2

11

1

α

α(5.70)

'gD gD

21 bEα

'gD

CH05-70


• Near-far problem: If any of the signal strengths is a greater than the

desired signal(αk>>α1), the multiple-access interference will be

increased.

• Solution for near-far problem: Power control.

• Implementation issues of power control:

– Latency

• Power must be measured at the receiver and then relayed to

the transmitter to adjust the transmit power.

– Accuracy

• Minimal averaging of potentially very noisy signal.

CH05-71


CH05-72


5.8 FEC Coding and CDMA

13

CH05-73


• Forward error correction (FEC) coding increases the bandwidth by a factor of 2 to 3, but includes redundancy.

• Decompose the maximum spreading rate into two parts

• If each FEC-encoded bit is spread by factor Qs, we can write Eq. (5.48) as

• This is the general expression for the degradation due to multiple-access interference when coding is present and unchanged from the uncoded expression.

• However, since the operating Eb/N0 is much lower in coded situation, there is significant improvement in overall performance.

rQQ s

1×=

1

0

1

0

1

0

11

11

11

−−−

−+=

−+=

−+=

N

E

Q

K

rN

E

rQ

K

N

E

Q

KD bbs

s

g(5.72)

CH05-74


• The equation is the general expression for the degradation due to multiple-access interference when coding is present and unchanged from the uncodedexpression.

• Since the operating Eb/N0 is much lower in coded situation, there is significant improvement in overall performance

• FEC coding often provides a form of time tiversity

CH05-75


5.9 Multiuser Detection

CH05-76


CH05-77


• Matched-filter outputs can undergo further processing in the form of

multiuser detection so that the multiple-access interference can be

reduced.

• In synchronous CDMA, an equivalent baseband discrete-time model

for the system over one symbol period is

• For matrix R is the cross-correlation matrix of symbol-shaping waveforms of different users, ijth element of R and the vector of

correlated Gaussian noise samples with element is

[ ]

==≤≤+=

K

T

Kbbb

α

α

α

η

L

MMM

L

L

K

00

00

00

and ,,b whereTt0 2

1

21AARby (5.73,74)

( ) ( ) ( ) ( )∫ ∫∗∗ ==

T T

ijiij dttwtgdttgtgR0 0

i

~ and η (5.75,76)

CH05-78


• Multiuser detection algorithm is to perform the equivalent of interference cancellation

• Method 1:

– Conventional receiver: estimates each user’s bits on basis of sign of individual elements.

• Method 2

– Optimum (maximum-likelihood) detector

• Method 3

– de-correlating detector

{ }ysign=b̂ (5.77)

2minargˆ ARbyb −= b

(5.78)

{ }ysign 1ˆ −= Rb (5.80)

14

CH05-79


5.10 CDMA in a Cellular Environment

CH05-80


• Interference caused by another CDMA signal appears to be

approximately equivalent to additive Gaussian noise.

• Multiple-access interference is directly proportional to channel loading.

• Define intracellular interference as

• Intercellular or other-cell interference is the second type of

interference.

• Define relative other-cell interference factor as

bb EQ

KE

Q

KI ≈

−=

1intracell

(5.81)

intracell

cellother

I

If −= (5.82)

CH05-81


CH05-82


• Ping Pong effect:

– With the mobile terminal switching back and forth between two base stations as the strength of the signal varies at the boundary between two cells.

• The size of relative other-cell interference factor depends on

1. Propagation-loss exponent:

• the larger the propagation loss exponent is, the quicker adjacent-cell interference will be attenuated.

2. Variations in signal strength due to shadowing: • the larger the variation due to shadowing, the greater the

potential is to cause problems.

CH05-83


• 3. The handoff technique between cells:

– Hard handover: • the case where communications are terminated

with one base station immediately upon acquisition of 2nd base station.

• This will result a ping-pong effect.– Soft handover:

• mobile terminal maintains communications with both base stations until one of them becomes significantly stronger than the other.

• This can prevent ping-pong effect.

CH05-84


• Total interference density

• Signal-to-interference-plus-noise at individual receiver

• Cellular CDMA system are often interference limited.

• Substitute Eq.(5.83) into Eq. (5.84), we get

( ) b

cellotherintracell

EQ

Kf

III

+≈

+= −

1

0

(5.83)

+

=

+=

0

00

00

1I

NI

E

IN

ESINR

b

b

(5.84)

( )

++

=

0

011

1

I

N

Q

Kf

SINR (5.85)

15

CH05-85


CH05-86


• Refer to Figure 5.26

– For a constant SINR moving from a noise-limited system to an interference-limited system increases the permissible channel loading.

– For a constant SINR, increasing other-cell interference significantly reduces the permissible channel loading.

– Reducing the SINR required by the receiver can significantly improve the permissible channel loading.

• Cell sectorization:

– Installation of directional antennas as opposed to omnidirectional antennas to improve system capacity

CH05-87


5.11 Frequency-Hopped Spread Spectrum

CH05-88


• Advantages of FH-SS

– High tolerance of narrowband interference.

– Relatively straightforward interference avoidance.

– Current technology-hopped bandwidths on the order of several gigahertz.

• Disadvantages of FH-SS

– Noncoherent detection

– Higher probability of detection

CH05-89


5.11.1 Complex Baseband

Representation of FH-SS


CH05-90


• As DS-SS, complex baseband signal can be expressed as

• For linear modulation, the data modulation is

• For frequency-hopped systems, M-ary FSK will be used, in which case we have

• Hop period is the period when the transmit frequency is constant.

• When hop period larger than the symbol time, multiple data symbols transmitted on each hop, this is called slow-frequency hopping.

( ) ( ) ( ) Tt0 tjtmts kk ≤≤+= θπζ2exp~ (5.86)

( ) Tt0 tgEbtm s ≤≤=)( (5.87)

( ) ( ) Tt0 tfjEtm is ≤≤= π2exp (5.88)

16

CH05-91


• Chip refers to the tone of shortest duration.

• For slow-frequency-hopped system, chip rate = symbol rate.

• For fast-frequency-hopped system, chip rate = hopping rate.

• The tone (signal) which produced by combination of pseudonoise

(PN) code generator output and MFSK modulator output is

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

( )( )( ){ } Tt0 wheretffjE

tfjtmEts

kckis

kcks

≤≤+++=

++=

φζπ

φζπ

2expRe

2expRe

(5.90)

{ }hsc RRR ,max= (5.89)

CH05-92


CH05-93


5.11.2 Slow-Frequency Hopping


CH05-94


{ } jk MRsjk ≠≈−ζζmin

CH05-95


5.11.3 Fast-Frequency Hopping


CH05-96


• Same symbol is transmitted on multiple hops.

• For combining the outputs from multiple hops, two algorithms are:

– Majority logic detector

• Hard decision on symbol is made every hope

• Outs of different hops are combined by choosing the

symbol that appears the most often.

– Noncoherent combining

• Soft measure related to likelihood is used for combining outputs.

• It related to signal energy in a given frequency bin.

17

CH05-97


5.11.4 Processing Gain


CH05-98


• Jammer: intentional interferer

• If jammer spreads its power in interference over the whole spread

bandwidth, the resulting interference density is J0=J/Wss

• Received signal-to-noise ratio

• Processing gain

s

ssG

R

WP = (5.94)

=

=

=

S

ss

ss

s

S

R

W

J

C

WJ

RC

J

ESNR

0

(5.93)

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