Spread-Spectrum Technique and its Application to …kom.aau.dk/project/navcom/CourseWebSites/SpreadSpectrum/Lecture... · Spread-Spectrum Technique and its Application to DS/CDMA

Spread-Spectrum Technique andits Application to DS/CDMA

Bernard H. Fleury

Navigation & Communications Section (NavCom)Department of Communication Technology, Aalborg University

DK - 9220 Aalborg, Fredrik Bajers Vej 7 C1e-mail: [email protected]

Spread-Spectrum Technique and its Application to DS/CDMA, Fall 2008 # 1

PRINCIPLES OF SS TECHNIQUE


BLOCK DIAGRAM OF A DIGITAL COMMUNICATION SYSTEM• Transmitter:

Amplification / Filtering

Bit stream

10011

d(t)

t

WaveformModulator

Carrier Modulation &

TS

• Receiver:

Baseband Demodulation

Bit stream

10001

d(t)Waveform Filtering / Amplification &

t

Demodulator

TS


BLOCK DIAGRAM OF A SPREAD SPECTRUM SYSTEM

• SS Transmitter:

• SS Receiver:

Widebandnoise-like

signal

t

GeneratorPseudo-Noise

Bit stream

10011

d(t)

Pseudo-NoiseGenerator

Amplification / FilteringCarrier Modulation &

Filtering/Amplification &Baseband Demodulation

d(t)

10001

Bit stream

Synchronization

WaveformDemodulator

WaveformModulator

TS

tTS

c(t)

c∗(t)


MAIN FEATURES OF THE NOISE-LIKE WIDEBAND SIGNAL c(t)

• Usually, the bandwidth W of c(t) is much higher than the bandwidthB of d(t):

– In military applications: G � WB ≈ 100 . . . 1000

– In UMTS/W-CDMA, G = 4 − 256.

• The signal c(t) appears noise-like and random to any unintendeduser.

• The signal c(t) is easily generated by a device (pseudo-randomgenerator) the initialization setting of which (key) is known only tothe intended transmitter and receiver.

• Synchronization should be easily performed at the intended receiver.


MULTIPLICATIVE BANDWIDTH EXPANSION

��

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��

��

��

P0

frequencyB ≈ 1

Ts

c(t)

d(t) d(t)c(t)

1

Power spectrum of c(t)

Power spectrum of d(t)

Power spectrum of d(t)c(t)

frequency

η =P02B P0

frequencyW + 1Ts

≈ W

P02W

= ηG

W



−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1

Pulse Spectra. Processing Gain = 16

Frequency normalised to the symbol rate

Nor

mal

ised

|S|2

−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1

Tranmitted Spectrum. Processing Gain = 16

BPSK Pulse SpectrumChip Spectrum

Transmitted Spectrum



−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1



Nor

mal

ised

|S|2

−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1






The ratio

G � W

B= W · Ts

is called the spreading factor (SF), spreading gain or processing gain of theSS system.


ADVANTAGES OF SS TECHNIQUE


ADVANTAGES OF SS SYSTEMS

The following five items apply for large SF.1. Privacy.

It is a computational burden for an unintended user to demodulate aSS signal.

2. Low probability of intercept.Because of the low level of its power spectrum, a SS-signal can be“hidden” in the background noise.This feature makes a SS signal difficult to be detected by anunintended user.

3. High tolerance against interference.

• Intentional interference (jamming).• Unintentional interference (multiuser interference in a multiuser

communication system).


ADVANTAGES OF SS SYSTEMS3. High tolerance against interference (cont’d).

��

��

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��

��

��

��

��

��

��

��

��

��

P

P

Bandwidth expansion

Bandwidth compression

Bandwidth expansion

Baseband digital signal

Baseband spread digital signal+ interference

Baseband digital signal+ residual interference

J

B W f

W f

B f

J



3. High tolerance against interference (cont’d).

Signal-to-interference power ratio after bandwidth compression(also called de-spreading):

SIRd =P

J· G = SIRi · G

In dB:[SIRd]dB = [SIRi]dB + [G]dB

SIRi: Input signal-to-interference ratio.SIRd: Signal-to-interference ratio after despreading.

Interference reduction is proportional to the spreading factor G.



4. Multiple access operation (CDMA).

2B 2B

2B 2B

η2

2W

c2(t)

η2

η1/Gη2/G

Lowpassfilter

Lowpassfilter

η1

2W

2W

η2/G

2B

η1/G

2B

c1(t)

d1(t)

d2(t)

d1(t)

d2(t)

η2/G

η1/G

η1 η1

η2η2

c∗2(t)

c∗1(t)



−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1



Nor

mal

ised

|S|2

−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1






−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1



Nor

mal

ised

|S|2

−3 −2 −1 0 1 2 30

0.2

0.4

0.6

0.8

1






5. Diversity processes exploited in SS technique.


MAIN TYPES OF SS TECHNIQUES


DIRECT SEQUENCE (DS) SS SYSTEM

t−B B

f

Power spectrum of d(t)

t

Ts

d(t) · c(t)

Data waveform d(t)

PN sequencegenerator

c(t)

P

η = P2B

t

Tc = Ts/N

P

Power spectrum of d(t) · c(t)

η/Gf

W ≈ 1Tc

Power spectrum of c(t)

f1/2W

1

W

B ≈ 1Ts


TIME-FREQUENCY OCCUPANCY OF A DS-SSSIGNAL

2W f0

f

t


FREQUENCY HOPPING (FH) SS SYSTEM

Tsd(t)

d(t) · c(t)

Data waveform d(t)

Digital FrequencySynthesizer

PN-SequenceGenerator

c(t) = exp{j2πfc(t)t}

0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

Ts

Th

�{d(t

)·c

(t)}

0 1 2 3 4 5 6−1.5

−1

−0.5

0

0.5

1

1.5

Ts

Th

�{c(

t)}


TIME-FREQUENCY OCCUPANCY OF A FH-SS SIGNAL

Occupied time−frequency slot

2W f0

f

t

2B

Th

Processing gain, G = WB


MULTI-CARRIER CDMA

Com

bine

r



fc[M ]

fc[2]

fc[1]

chip #1

chip #2

chip #M

fc[2]

fc[1]

fc[M ]

chip #1

chip #2

chip #M

Synchronized

Transmitter Receiver

bit stream

Code vectorCode vector

bit streamModulator Demodulator


ACCESS TECHNIQUES


ACCESS TECHNIQUES

Frequency

Time

Code

Frequency

Time

Code

Frequency

Time

Code

User 1

User 2

User 3 User 1 User 2 User 3

User 1

User 2

User 3

FDMA TDMA CDMA


DUPLEX TECHNIQUES

Downlink (DL)

Uplink (UL)

duplexseparation

FDD

DL DL DLUL UL UL

TDD

time

frequency

TDD frame


THEORY AND APPLICATION OF PSEUDO RANDOMBINARY SEQUENCES


PROPERTIES OF RANDOM BINARY SEQUENCESLet us consider a set S of periodic sequences of same length N .

Example:

S = {(000111101011001), (010011010111100)}

In order for these sequences to be “pseudo-random” or “pseudo-noise(PN)” sequences, they have to satisfy the following properties:

• Balance Property

For each sequence in S the relative frequencies of “0” and “1”approximately equal 1

2 each.

• Run Property

For each sequence in S the relative frequencies of runs “0 0 . . . 0︸︷︷︸m

”

and “1 1 . . . 1︸︷︷︸m

” of length m approximately equal 12m each.


PROPERTIES OF RANDOM BINARY SEQUENCES (CONT’D)

• Shift Property

The numbers of disagreements and agreements between each se-quence in S and its cyclically shifted versions are approximately thesame.

0 0 0 1 1 1 1 0 1 0 1 1 0 0 11 0 0 1 0 0 0 1 1 1 1 0 1 0 1− + + + − − − − + − + − − + +

+ = agreement- = disagreement


PROPERTIES OF RANDOM BINARY SEQUENCES (CONT’D)

• Separation Property

The numbers of disagreements and agreements between any twosequences in S or their cyclically shifted versions are approximatelythe same

0 0 0 1 1 1 1 0 1 0 1 1 0 0 10 0 1 1 0 1 0 1 1 1 1 0 0 0 1+ + − + − + − − + − + − + + +

+ = agreement- = disagreement


AUTOCORRELATION OF BINARY SEQUENCES

Let a = (a0, . . . , aN−1), an ∈ {−1,+1} denote a binary sequence oflength N . Example: a = (1, 1, 1,−1, 1,−1,−1).

Let a(l) denote the l-times cyclicly right-shifted version of a. Example:a(2) = (−1,−1, 1, 1, 1,−1, 1)

Autocorrelation of a:

Ra(l) =N−1∑n=0

ana(l)n

Example:

l = 2 a 1 1 1 −1 1 −1 −1a(2) −1 −1 1 1 1 −1 1a · a(2) −1 −1 1 −1 1 1 −1 Ra(2) = −1


AUTOCORRELATION OF BINARY SEQUENCES

7

-1

Ra(l)

l

Ra(l) is a measure of the resemblance between the sequence a and itsl-times cyclicly right-shifted version a(l).

Ra(l) = # of agreements- # of disagreementsbetween a and a(l).

Properties of Ra(l):1. Ra(0) = N .2. |Ra(l)| ≤ Ra(0) = N .


CROSSCORRELATION OF BINARY SEQUENCES

Let a = (a0, . . . , aN−1) and b = (b0, . . . , bN−1) denote two binarysequences of length N .

Crosscorrelation of a and b:

Ra,b(l) =N−1∑n=0

anb(l)n

Ra,b(l) is a measure of the resemblance between a and b(l)n .

|Ra,b(l)| = N ⇔ a = ±bRa,b(l) = 0 ⇔ a and b are orthogonal


CROSSCORRELATION OF BINARY SEQUENCES

Example:

a = (−1,−1,−1,+1,−1,+1,+1)b = (−1,+1,−1,−1,−1,+1,+1)

-1

l

3

-5

Ra,b(l)


WELCH BOUNDWe consider a set S of binary sequences of length N :

ab

S

S contains M sequencesof length N

Welch bound:

max∀l �=cN

{|Ra,a(l)|} ,max∀l

{|Ra,b(l)|} ≥ N

√M − 1

MN − 1= Rc

For M largeRc ≈

√N

The Welch bound gives a lower bound on the minimum resemblancebetween any arbitrary shifted, distinct versions of any two selected se-quences in S.


PSEUDO-NOISE SEQUENCES


LINEAR FEEDBACK SHIFT REGISTER (LFSR)

1 0 0 0 0

Modulo−2 adder

Output

Clockpulses

Example n = 5-stage LFSR sequence generator.

Output from the LFSR generator:

00001︸︷︷︸init.

01011101100011111001101001


LINEAR FEEDBACK SHIFT REGISTER

Output

Clockpulses

am f1 f2 f3 fn

am−1 am−2 am−3 am−n

• The coefficients fi equal ’0’ or ’1’.• The contents of the shift registers equal ’0’ or ’1’.• The LFSR is entirely described by its characteristic polynomial:

f(x) = 1 + f1x + f2x2 + · · · + fnxn


PROPERTIES OF SEQUENCES GENERATED BY LFSRS

• A sequence generated by a LFSR is periodic with length N , where

N ≤ 2n − 1.

• If N = 2n−1, then the sequence is referred to as a maximum-length(ML) sequence or pseudo-noise (PN) sequence.

• A LFSR generates a PN sequence if, and only if, its characteristicpolynomial is primitive.


PROPERTIES OF PN-SEQUENCES

PN sequence of length N = 2n − 1.

Example: n = 5, N = 31 : a = (0000101011101100011111001101001).

• Balance propertyNumber of “1” : 2n−1.Number of “0” : 2n−1 − 1.

• Run property– Number of runs of consecutive “0” or “1” : 2n−1.– 1

2 of them have length 1.– 1

4 of them have length 2.– · · ·– 2−(n−2) of them have length n − 2.– 1 run of length n − 1: “ 0 · · · 0︸︷︷︸

n−1 times

”.

– 1 run of length n: “1 · · · 1︸︷︷︸n times

”.


PROPERTIES OF PN-SEQUENCES

• Shift property

Ra(l) ={

N, l = 0−1, l = 1, . . . , N − 1 (1)

Example: N = 31.

31

0

-1 l

Ra(l)

31


PROPERTIES OF PN-SEQUENCES (CONT’D)

Proof of (1):

Given the binary sequence a and the circularly shifted version a(l), bothwith period N , the auto-correlation Ra(l) can be written as

Ra(l) = A(a, a(l)) − D(a, a(l))

where

A(a, a(l)) � # of term-by-term agreements between a and a(l)

D(a, a(l)) � # of term-by-term disagreements between a and a(l)

Notice thatA(a, a(l)) + D(a, a(l)) = N.


PROPERTIES OF PN-SEQUENCES (CONT’D)

Let W (a) be the Hamming weight of a. Then,

D(a, a(l)) = W (a ⊕ a(l)).

Thus,Ra(l) =

(N − W (a ⊕ a(l))

)− W (a ⊕ a(l)).

For ML sequences,

W (a ⊕ a(l �=iN)) = W (a) = (N + 1)/2.

Hence,

Ra(l = iN) = N − 2W (a ⊕ a(l))= N − 2W (a)= −1. �


NUMBER OF PRIMITIVE POLYNOMIALS

n N = 2n − 1 Np(n)2 3 13 7 24 15 25 31 66 63 67 127 188 255 169 511 4810 1023 60

n N = 2n − 1 Np(n)11 2047 17612 4095 14413 8191 63014 16383 75615 32767 180016 65535 204817 131071 771018 262143 806419 524287 27594

Np(n) = φp(2n−1)n , φp(m) Euler totient function (number of integers less

than m which are relatively prime to m).


CORRELATION PROPERTIES OF PN SEQUENCES

l

N

l

lag lExample: N = 31, Np(5) = 6 different PN sequences.


PREFERRED PAIRS OF PN SEQUENCES

The crosscorrelation between a preferred pair is three-valued:

Let {a, b} be a preferred pair of length N = 2n − 1, n odd orn = 2 mod 4.

ThenRa,b ∈ {−t(n),−1, t(n) − 2}

where

t(n) =

{1 + 2

n+12 , n odd

1 + 2n+2

2 , n = 2 mod 4

Example: n = 5Ra,b ∈ {−9,−1,+7}


DEFINITION AND PROPERTIES OF GOLD SEQUENCES

Let {a, b} be a preferred pair of PN sequences of length N = 2n − 1.

Set of Gold sequences:

{a, b, a ⊕ b, a ⊕ b(1), . . . , a ⊕ b(N−1)}

Number of Gold sequences: N + 2 = 2n + 1.

Let c and c′ denote two Gold sequences from the above set.

• Autocorrelation property:

Rc(l){

= N, l = 0∈ {−t(n),−1, t(n) − 2} l = 1, . . . , N − 1


DEFINITION AND PROPERTIES OF GOLD SEQUENCES

• Crosscorrelation property:

Rc,c′(l) ∈ {−t(n),−1, t(n) − 2}

Comparison with Welch bound for large N

max |Rc,c′(l)|l �=0, for c=c′

= |t(r)| ≥

≥{ √

2 · 2n/2 =√

2Rc, n odd2 · 2n/2 = 2Rc, n = 2 mod 4


GOLD SEQUENCESA Gold sequence is generated by modulo-2 addition of two preferred pairsequences.

pulsesClock Output

am

bm

am−2am−1 am−3 am−n

bm−nbm−3bm−2bm−1

f ′1 f ′

2 f ′3

f1 f2 f3 fn

f ′n

cm


GOLD SEQUENCES

2 3 4 51

2 3 4 51

f2(x) = 1 + x2 + x3 + x4 + x5

seq2: N = 25 − 1 = 31 chips

f1(x) = 1 + x2 + x5

seq1: N = 25 − 1 = 31 chips

N = 31 chips

Sequence 1: 1111100011011101010000100101100Sequence 2: 11111001001100001011010100011100 shift combination: 00000001111011011111011101000101 shift† combination: 0000101010111100001010000110001...30 shift combination: 1000010001000101000110001101011

† Cyclic shift of sequence 2 to the left.


GOLD SEQUENCES

0 10 20 30 40 50 60−10

−5

0

5

10

15

20

25

30

35

lag l

Ra(l

)

0 10 20 30 40 50 60−10

−8

−6

−4

−2

0

2

4

6

8

10

lag l

Ra,b(l

)


THEORY AND APPLICATION

OF

PSEUDO-NOISE (PN)/MAXIMUM LENGTH (ML)SEQUENCES


DEFINITION OF A FIELD

Let us consider a set F of elements endowed with two operations:Addition ”+” and Multiplication ”·”.

• F is a field if the following properties hold:

– F is a commutative group w.r.t. the addition “+”;

– F\{0} is a commutative group w.r.t. the multiplication “·”;– Distributive law: for a, b, c ∈ F , a · (b + c) = a · b + a · c.

• Finite field or Galois field (GF): F is finite.

– the residue class of any prime integer p forms a GF denotedby GF (p);

– the number of elements in any finite GF equals pm where p is aprime integer and m is a natural number, i.e. q = pm.

• Infinite field : F has infinite elements, e.g. the field of real numbers.


IRREDUCIBLE POLYNOMIAL OVER GF(2)

A polynomial f(x) = f0 + f1x + . . . + fnxn over GF (2), i.e. f0, . . . , fn ∈GF (2) is irreducible if it has positive degree (i.e. > 0) and it cannot be fac-torized into the product of other polynomials with lower positive degrees.

Example: Find the irreducible polynomials over GF (2) of degree 4.

a. First write all 24 = 16 polynomials over GF (2) of degree 4;

b. Compute all reducible polynomials by computing all products(x3 + a1x

2 + a2x1 + a3)(x + b1) and (x2 + a1x

1 + a2)(x2 + b1x + b2)with a1, a2, a3, b1, b2 ∈ GF (2);

c. Removing the reducible polynomials from the 16 polynomials yieldsthe following irreducible polynomials over GF (2) of degree 4:

f1(x) = x4 + x + 1f2(x) = x4 + x3 + 1f3(x) = x4 + x3 + x2 + x + 1


FIELD GENERATED BY AN IRREDUCIBLE

POLYNOMIAL

Let f(x) be irreducible with degree n and α a root of f(x):f0 + f1α + . . . + fn−1α

n−1 + αn = 0

GF (2n) = {c0 + c1α + . . . + cn−1αn−1; cl ∈ GF (2), l = 1, . . . , n − 1}

Letc1(α) = c1,0(α) + c1,1α + · · · + c1,n−1α

n−1 ∈ GF (2n)

c2(α) = c2,0(α) + c2,1α + · · · + c2,n−1αn−1 ∈ GF (2n)

• Addition

c1(α)+c2(α) = (c1,0⊕c2,0)+(c1,1⊕c2,1)α+· · ·+(c1,n−1⊕c2,n−1)αn−1

• Multiplication

c1(α) · c2(α) = (c1,0 + c1,1α + · · · + c1,n−1αn−1) ·

·(c2,0 + c2,1α + · · · + c2,n−1αn−1)


FIELD GENERATED BY AN IRREDUCIBLE

POLYNOMIAL (CONT’D)

where “powers” of α larger than n are reduced using the identity

αn = fn−1αn−1 + . . . + f1α + f0

Example: Representation of GF (23) generated with f(x) = 1 + x2 + x3.Let α be a root of f(x): α3 = α2 + 1

Elements of GF (23) Vector representation0 0001 001α 010α2 100

α2 + 1 101α2 + α + 1 111

α + 1 011α2 + α 110


PRIMITIVE ELEMENTS

An element of GF(2n) is called a primitive element if its generates GF (2n),i.e. {α0, α1, . . . , α2n−2} = GF (2n)\{0}

Example: α is a primitive element in GF (23)

Powers of α Elements of GF (23)\{0}α0 = 1α1 = αα2 = α2

α3 = α2 + 1α4 = α2 + α + 1α5 = α + 1α6 = α2 + α


PRIMITIVE POLYNOMIAL

Primitive polynomial: An irreducible polynomial f(x) of degree n is said tobe primitive if one of its roots is a primitive element of GF (2n).

Example: The irreducible polynomial of degree 3, f(x) = x3 + x2 + 1, isused to construct GF (23).

Show that f(x) is a primitive polynomial.

a. The roots of f(x) are x = α,α2, α4;

b. The order of these roots is 7 according to

Order of αk =2n − 1

GCD(2n − 1, k),

where GCD(n, k) is the greatest common divisor of n and k.

Therefore these elements are primitive elements of GF (23).

The polynomial f(x) is then a primitive polynomial.


GENERATION OF ML SEQUENCES

Simple Shift Register Generator (SSRG):

D

c1

D

c2

D

cn−1

x1 x2 xn−1 xn

Modular Shift Register Generator (MSRG):

D

c1

D

c2

D

cn−1

x1 x2 xn−1 xn

f(x) = 1 + c1x + c2x2 + · · · + cn−1x

n−1 + xn is primitive.


GENERATION OF ML SEQUENCES (CONT’D)

Alternative representation of shift register:

X(t + 1) = TX(t),

where X(t) = [xn(t), xn−1(t), . . . , x1(t)]T is the state vector.

and T is the characteristic matrix calculated as

TS =

⎡⎢⎢⎢⎢⎢⎢⎢⎣

0 1 0

for SSRG:

· · · 0 00 0 1 · · · 0 00 0 0 · · · 0 0...

......

...0 0 0 · · · 0 11 cn−1 cn−2 · · · c2 c1

⎤⎥⎥⎥⎥⎥⎥⎥⎦

, TM =

⎡⎢⎢⎢⎢⎢⎢⎢⎣

cn−1 1 0 0

for MSRG:

· · · 0 0cn−2 0 1 0 · · · 0 0cn−3 0 0 1 · · · 0 0

......

......

......

c1 0 0 0 · · · 0 11 0 0 0 · · · 0 0

⎤⎥⎥⎥⎥⎥⎥⎥⎦


GENERATION OF ML SEQUENCES (CONT’D)

Example:f(x) = x3 + x2 + 1

SSRG:

D D Dx1 x2 x3 TS =

⎡⎣0 1 00 0 11 1 0

⎤⎦

MSRG:

D D Dx1 x2 x3 TM =

⎡⎣1 1 0

0 0 11 0 0

⎤⎦


GENERATION OF ML SEQUENCES (CONT’D)Let α denote a root of f(x) = x3 + x2 + 1, α3 = α2 + 1.

SSRG MSRGClock Memory State vectors Memory State vectorst = 0 001 1 001 1t = 1 010 α 010 αt = 2 101 α3 100 α2

t = 3 011 α5 101 α3

t = 4 111 α4 111 α4

t = 5 110 α6 011 α5

t = 6 100 α2 110 α6

A MSRG successively generates the ”powers” of α. Thus, the MSRG (andin fact any LSRG) will generate a ML sequence iff f(x) is primitive.


RECIPROCAL POLYNOMIALS

Consider an irreducible polynomial of degree n given by

f(x) = 1 + c1x + c2x2 + · · · + cn−1x

n−1 + xn (2)

Then its reciprocal polynomial f ∗(x) is given by

f∗(x) = xn + c1xn−1 + c2x

n−2 + · · · + cn−1x + 1

= xn · f(x−1) (3)

The sequence generated by an SSRG using f(x) is the same as thesequence generated by an MSRG using f ∗(x).


PN SEQUENCE PHASE SHIFTS

The output sequence of the SSRG can be formally written as

a(x) =g(x)f(x)

, g(x) = g0 + g1x + . . . + gnxn−1.

where gi ∈ GF (2), g(x) ≡ 0.

There are 2n − 1 possible numerator polynomials g(x) that are uniquelyrelated to the 2n − 1 ”phase shifts” of the sequence a(x).

Example: f(x) = 1 + x + x3 and g(x) = 1 + x. By long division we find

1 + x

1 + x + x3= 1 + x3 + x4 + x5 + x7 + x10 + x11 + x12 + . . .

→7−bit period︷︸︸︷

1 0 0︸︷︷︸Initial

conditions

1 1 1 0 1 0 0 1 1 1 0 . . .


PN SEQUENCE PHASE SHIFTS (CONT’D)

Degree of g(x):Because the sequence a(x) is periodic with N , it follows

g(x)f(x)

= a(x) =

First period︷︸︸︷a0 + a1x + . . . + aN−1x

N−1 +a0xN + . . .

= (a0 + a1x + . . . + aN−1xN−1) · (1 + xN + x2N + x3N + . . .)

In modulo-2 arithmetic,

1 + xN + x2N + x3N + . . . =1

1 − xN=

11 + xN

.

Thus,

g(x)f(x)

= a(x) =

b(x)︷︸︸︷a0 + a1x + . . . + aN−1x

N−1

1 + xN.


PN SEQUENCE PHASE SHIFTS (CONT’D)

Relationship among the degrees of f(x), g(x), and b(x):

a(x) =

degree = Dg≤n−1︷︸︸︷g(x)f(x)︸︷︷︸

degree = Df = n

=

degree = Db≤N−1︷︸︸︷b(x)

1 + xN︸︷︷︸degree = N

degree{f(x)} − degree{g(x)} = N − degree{b(x)} ⇒ Db = Dg + N − n.

Knowing the degee of g(x), we can predict the number of 0s at the end ofthe first period, i.e. b(x) ends with

(N − 1) − Db = n − 1 − Dg zeros.


BACK TO THE EXAMPLE

f(x) = 1 + x + x3 and g(x) = 1 + x

• n = 3• Dg = 1• Period: N = 2n − 1 = 23 − 1 = 7• Number of trailing zeros: n − 1 − Dg = 3 − 1 − 1

1 + x

1 + x + x3= 1 + x3 + x4 + x5 + x7 + x10 + x11 + x12 + . . .

→7-bit period︷︸︸︷

1 0 0︸︷︷︸Initial

conditions

1 1 1 0

One trailing zero

1 0 0 1 1 1 0 . . .


SHIFTED SEQUENCES

• Let a0(x) = 1/f(x) denote the reference sequence

• and ak(x) = gk(x)f(x) be the sequence a0(x) cyclically right-shifted by k

bits

Then it can be shown that

gk(x) = xk mod f(x).


SHIFTED SEQUENCES (CONT’D)

Example: Consider the characteristic polynomial f(x) = 1 + x + x3

Shift, k First period, bk gk(x)0 1110100 11 0111010 x2 0011101 x2

3 1001110 1 + x4 0100111 x + x2

5 1010011 1 + x + x2

6 1101001 1 + x2

Unique relationships for a particular shift of a PN sequence:

ak(x), shift k ⇐⇒ gk(x) = xk mod f(x)degree Dg

� �︷︸︸︷bk(x), first period, with n − 1 − Dg zeros at end


SSRG IMPLEMENTATION

• Initial loading: 1

n−1 zeros︷︸︸︷00 . . . 0

0 0 001

cn−1c3c2c1

1f (x)

xf (x)

x2

f (x)xn−2

f (x)xn−1

f (x)

xn−1

f (x)

• Initial loading:

n−1 zeros︷︸︸︷00 . . . 0 1

0 00

cn−1c3c2c1

xf (x)

x2

f (x)xn−1

f (x)

gn(x)f (x)

gn(x)f (x) = xnmodf (x)

f (x)

0 1


PHASE SHIFTING USING MASKS FOR A SSRG

Phase shift network (PSN)

0 0 001

cn−1c3c2c1

Mask

m0 m1 m2 mn−1mn−2

1f (x)

xf (x)

x2

f (x)xn−2

f (x)xn−1

f (x)

xn−1

f (x)

m(x)f (x)


MASK POLYNOMIALS FOR SSRGS

• There is a one-to-one correspondence between the P = 2n−1 differ-ent shifted version of the PN sequence and numerator polynomialsg(x) of degree < n.

• A particular sequence a(x) can be written as

a(x) =g(x)f(x)

=g0 + g1x + . . . + gn−1x

n−1

f(x)

= g0 · 1f(x)

+ g1 · x

f(x)+ . . . + gn−1 · xn−1

f(x)

• Define the mask polynomials

m(x) = m0 + m1x + . . . + mn−1xn−1 ⇔ (m0,m1, . . . ,mn−1)

• To generate the kth shift relative to 1f(x) , select the mask polynomials

m(x) = gk(x) = xk mod f(x)


MASK POLYNOMIALS FOR MSRGS

The kth shift at the output of the MSRG, relative to 1f(x) , is obtained as

follows:1. Find the polynomial gk(x) = xk mod f(x);2. Calculate the sequence:

gk(x)f(x)

=xk mod f(x)

f(x)= a0 + a1x + . . . + an−1 + . . .

3. Select the mask polynomial to be:

m(x) = m0 + m1x + . . . + mn−1xn−1

= a0 + a1x + . . . + an−1xn−1.

The formula for the mask can also be written

m(x) =[xk mod f(x)

f(x)

]deg<n


EXAMPLE: SSRG AND MSRG MASKS

• Primitive polynomial: f(x) = 1 + x + x3

• loading vector: 100

Delay, k SSRG mask MSRG mask

0 g0(x) = 1 ⇒ 100 {g0(x)/f(x)}3 bits = 111

1 g1(x) = x ⇒ 010 {g1(x)/f(x)}3 bits = 011

2 g2(x) = x2 ⇒ 001 {g2(x)/f(x)}3 bits = 001

3 g3(x) = 1 + x ⇒ 110 {g3(x)/f(x)}3 bits = 100

4 g4(x) = x + x2 ⇒ 011 {g4(x)/f(x)}3 bits = 010

5 g5(x) = 1 + x + x2 ⇒ 111 {g5(x)/f(x)}3 bits = 101

6 g6(x) = 1 + x2 ⇒ 101 {g6(x)/f(x)}3 bits = 110


SYNCHRONISATION ISSUES


SYNCHRONISATION

Signal model

+ + +{b(l)}L−1

l=0

Amplification√2P

Delayτ1

Channel noisew(t)

Received signaly(t)

cos(ω0t + θ1)

s(t)

y(t) =√

PTs

L−1∑l=0

b(l) s(t − lTs − τ1)√

2 cos (ω0t + θ1)︸︷︷︸sl(t;τ1,θ1)︸︷︷︸

s(t;τ,θ,b)

+ w(t).

We assume that s(t) has support [0, Ts) and∫ Ts

0

s2(t) dt = 1.

The DS-SS receiver needs to estimate θ1 and τ1.


ML SYNCHRONISATION

Likelihood function for (τ, θ, b) [b = [b(0), . . . , b(L − 1)]]

Λ(τ, θ, b) ∝ exp

{∫ LTs+τ

τ

y(t)s(t; τ, θ, b) dt

}

∝ exp

{L−1∑l=0

b(l)∫ (l+1)Ts+τ

lTs+τ

y(t) sl(t; τ, θ) dt

}

∝L−1∏l=0

exp

{b(l)∫ (l+1)Ts+τ

lTs+τ

y(t) sl(t; τ, θ) dt.

}

∝L−1∏l=0

exp {b(l) z1(l; τ, θ)}

with the definition

z1(l; τ, θ) =∫ (l+1)Ts+τ

lTs+τ

y(t) sl(t; τ, θ) dt.


ML SYNCHRONIZATION (CONT’D)

Likelihood function for (τ, θ)

By averaging over the unknown binary symbols b, while assuming thatthey are i.i.d. we get

Λ(τ, θ) =∫

b

Λ(τ, θ, b) db

=L−1∏l=0

cosh {z1(l; τ, θ)}

Log-likelihood function for (τ, θ)

log Λ(τ, θ) =L−1∑l=0

log cosh {z1(l; τ, θ)} .


NON-DECISION DIRECTED LOOP

Derivative of the log-likelihood function:

d log Λ(τ, θ)dθ

= −L−1∑l=0

z2(l; τ, θ) tanh{z1(l; τ, θ)}with

z2(l; τ, θ) = − d

dθz1(l; τ, θ)

= −∫ (l+1)Ts+τ

lTs+τ

y(t)d

dθsl(t; τ, θ) dt

=∫ (l+1)Ts+τ

lTs+τ

y(t) s(t − lTs − τ )√

2 sin (ω0t + θ) dt

Equating the derivative of the log-likelihood function to zero yields

L−1∑l=0

z2(l; τ, θ1) tanh{z1(l; τ, θ1)} = 0


NON-DECISION DIRECTED LOOP (CONT’D)

Derived receiver architecture [known delay]:

VCOy(t)

s(−t)

s(−t)

∑L−1l=0

sin(w0t + θ1)

cos(w0t + θ1)90o

tanh(·)

tanh(z1(l; τ1, θ1))

z2(l; τ1, θ1))

lTs + τ1

lTs + τ1



Using the approximation tanh(x) ≈ x yields

VCOy(t)

s(−t)

s(−t)

∑L−1l=0

cos(w0t + θ1)

− sin(w0t + θ1)90o z1(l; τ1, θ1)

z2(l; τ1, θ1)

lTs + τ1

lTs + τ1



Costas loop:

VCOy(t)

F (p)

90o

z1(t)

z2(t)

ε(t)

Filters(−t)

Filters(−t)


SQUARING LOOP

Block diagram:

Device

Square−Law

Band−

FilterPass

VCO

PhaseLockedLoop (PLL)

synchronizationstage

LoopFilter

To next

ScalingFrequency

f2

ε(t)z(t)

F (p)

rVCO(t)

y(t) y(t)2


SQUARING LOOP (CONT’D)

Remember,

y(t) =√

PTs

L−1∑l=0

b(l)s(t − lTs − τ1)√

2 cos (ω0t + θ1) + w(t)

This time, we square and bandpass filter the received signal

z(t) = PTs

[L−1∑l=0

s(t − lTs − τ1)

]2

cos[2(ω0t + θ1)] + n(t),

The PLL recovers the carrier phase at 2ω0.


SQUARING LOOP(CONT’D)

VCO output of the PLL:

rVCO(t) ∝ sin 2(ω0t + θ1)

Hence it follows for the error signal at the input of the loop filter:

ε(t) = z(t) · rVCO(t)

= PTs

[L−1∑l=0

s(t − lTs − τ1)2]

cos 2(ω0t + θ1) sin 2(ω0t + θ1) + n(t, φ)

=PTs

2

[L−1∑l=0

s(t − lTs − τ1)2]

sin 2φ + O(2ω0t) + n(t, φ)

where φ � θ1 − θ1.

The loop filter suppresses the terms at 2ω0.


SQUARING LOOP(CONT’D)

Transfer function of the VCO in operator form

2θ1 =1pF (p){ε(t)}

=1pF (p)

{PTs

2

[L−1∑l=0

s(t − lTs − τ1)2]

sin 2φ + ˜n(t, φ)

}.

Phase diagram

ε

π2

−π2

2φ


TIMING SYNCHRONISATION


TIMING SYNCHRONISATION

Pilot sequence with larger SNR

· · · datadata

Pilot chip sequence (unmodulated)

time

Next the DS-SS receiver needs to estimate τ .

Back to our ”one-path” channel:

+ +s(t)

α1

Delayτ1

α1s(t − τ1)

Channel noisew(t)

Received signaly(t)


TIMING SYNCHRONISATION (CONT’D)

We distinguish between

• Acquisition: coarse estimate τ1c of τ1

• Tracking: maintaining fine estimate τ1 of τ1, i.e.

|τ1 − τ1| <Tc

Q= δ


ACQUISITION

Correlation method

s(t) = c(t) is the pilot signal (no data modulation)

τ1c = arg maxτ∈[0,NTc]

∣∣∣∣∣∫ TD

0

y(t)c(t − τ )dt

∣∣∣∣∣2

︸︷︷︸λ(τ)

where TD is the dwell-time.


ACQUISITION (CONT’D)Correlation method

Chooselargestinputsignal

Chooselargestinputsignal

Output

2

2

2

2

2

y(t) = α1c(t − τ1) + w(t)

Number of performed correlation operations: 2N (Q = 2, TD = λTC)


ACQUISITION (CONT’D)

Serial Search

PNGenerator

Threshold

Detector

Yes

No

Tracking

Adjust delay

˛˛˛Z

TD

(·)dt

˛˛˛2y(t) = α1c(t − τ1) + w(t)

c(t − τ1)

τ1



Serial Search: Straight Line

threshold

Uncertainty intervalUncertainty interval



Serial Search Strategies



Single dwell serial acquisition

+Square law

detectorBandpass

filterSignal abovethreshold ?

PN codegenerator

Adjust timing

Yes

No

Tracking∫ t

t−TD

(·) dtn TD



Probability of Detection and False Alarm

Output ofthe correlatorOutput ofthe correlator

Threshold �

τ1 = τ1 τ1 = τ1



Dual dwell serial acquisition

Next hypothesis(delay)

Initial State:Integration time

Verification State:Integration time

Output abovethreshold ?

Output abovethreshold ?

Yes

No

No

Yes

Hypothesis acceptedAcquisition completed

TD1

TD2 > TD1


TRACKING

Early-late gate tracking (coherent)

• The correlation estimate of the delay can be expressed as

τ1 = arg maxτ

{∫TD

y(t)c(t − τ ) dt

}︸︷︷︸

λ(τ)

• This is equivalent to

τ1 = arg zeroτ

{d

dτλ(τ )

}≈ arg zero

τ{λ(τ + δ) − λ(τ − δ)}

≈ arg zeroτ

{∫TD

y(t)c(t − (τ + δ)) dt −∫

TD

y(t)c(t − (τ − δ)) dt

}


TRACKING (CONT’D)

Early-late gate tracking (coherent)

• The early-late gate algorithm attempts to maximize the autocorre-lation between the received and the locally generated PN-sequence.

• The tracking algorithm is a simple gradient search algorithm.

Received power

Timing offset

Early

Currentoperating

point

Late

λ(τ − τ1)

δδτ1 − τ1

[relative to τ1]


TRACKING (CONT’D)

A non-coherent delay-locked loop

+

+

+

Bandpass

Bandpass

Square-lawenvelope detector

Square-lawenvelope detector

-

Loop filterVoltage controlledclock (VCC)

PN code generator

Delay

y(t)

H(p)

H(p)

ε(t)

F (p)

ε+(t)

c(t − τ1 − δ)

ε−(t)

δ

c(t − τ1)

c(t − τ1 + δ)

y+(t)

y−(t)

y+(t)2

y−(t)2


TRACKING (CONT’D)

Output of the bandpass filter:

y±(t) = CV±∫ t

t−TD

c(t − τ1)c(t − τ1 ± δ) dt︸︷︷︸√PTsRc(τ1−τ1±δ)+n±(t,ε)

+n(t)

where n(t, ε) is the so-called self-noise.

Squaring and subtracting the signals from both arms yields

ε(t) = y−(t)2 − y+(t)2

= PTs(C2V−R2

c(τ1 − τ1 − δ) − C2V+R2

c(τ1 − τ1 + δ)) + ntotal(t, ε)


TRACKING (CONT’D)

Transfer function of the VCC in operator notation

τ1

Tc=

F (p)p

{ε(t)}

Provided both multipliers have exactly the same gain,i.e. CV = CV− = CV+

τ1

Tc=

PTsC2VF (p)p

{R2c(τ1 − τ1 − δ) − R2

c(τ1 − τ1 + δ)) + ntotal(t, ε)}


TRACKING (CONT’D)

Linearized model for a delay-locked loop

+ +

loop filter

τ1Tc

εΔ.= τ1−τ1

Tc D(εΔ)

ntotal

PTsCV ± F (p)

1p

τ1Tc

VCC


TRACKING (CONT’D)

Discriminator characteristic

−1 − 1Q −1 + 1

Q − 1Q

−1 δ = TcQ

+1

D(εΔ) = Rc([εΔ − 1Q ]Tc)2 − Rc([εΔ + 1

Q ]Tc)2

1Q

1 − 1Q 1 + 1

Q

εΔ


TRACKING (CONT’D)

Autocorrelation functions of the advanced and retarded PN code

−1 − 1Q −1 + 1

Q− 1Q

+1

1Q

1 − 1Q 1 + 1

Q

εΔ εΔ

Rc([εΔ + 1Q ]Tc) Rc([εΔ − 1

Q ]Tc)


DIVERSITY TECHNIQUES AND RAKE PROCESSING


DIVERSITY TECHNIQUES

• Frequency diversity, transmitting or receiving the signal at differencefrequencies:Especially used in FH-CDMA.

• Path diversity, resolving multipath components and coherently com-bining them:Rake receiver.

• Time diversity, transmitting or receiving the signal at different times:FEC, interleaving.

• Space diversity, transmitting or receiving the signal at different loca-tions:multiple antenna transmission/reception.

• Polarization diversity, transmitting or receiving the signal with differentpolarizations:antennas need to support dual polarization modes.


PATH DIVERSITY

• Selection diversity(SD): take the signal diversity component with thehighest SNR.

• Maximum ratio combining(MRC): all signal diversity componentsare combined such that the SNR is maximized.

• Equal gain combining(EGC): all signal diversity components arephase compensated and combined.


SELECTION DIVERSITY (CONT’D)

Receiver architecture:

Transmittedsignal

Diversity channel #1

Diversity channel #l

Diversity channel #L

MF1

MFl

MFL

Sel

ectl

arge

stS

NR

chan

nel

Z1

γc,1

Zl

γc,l

ZL

γc,L

Userdata

• Zl: Signal at the output of the MF of Branch l;

• γc,l: Instantaneous SNR at the output of MFl.


SELECTION DIVERSITY

Let the average SNR of any diversity channel (path) be

γc = γc,1 = γc,2 = . . . = γc,L = E{α2} Eb

LN0

For Rayleigh distributed α, γc is χ2 distributed with 2 degrees of freedom

pγc,l(γ) =

1γc

e−γγc

The probability that SNRs at all L receivers are below the value λ

P{γc,1, γc,2, . . . , γc,L < λ} =L∏

l=1

P{γc,l < λ} =L∏

l=1

∫ λ

0

pγc,l(γ) dγ

=(1 − e−

λγc

)L



Pdf for the maximum SNR γmax = max{γc,1, . . . , γc,L}

pγmax(γ) =d

dγP{γc,1, γc,2, . . . , γc,L < γ}

=L

γc(1 − e−

γγc )L−1e−

γγc

For BPSK,

Pb = Q

(√2Eb

N0

), Q(x) =

1√2π

∫ ∞

x

e−x2/2dx

and hence,

Pb =∫ ∞

0

Q(√

2γ)pγmax (γ) dγ

=L

2

L−1∑k

(L − 1

k

)(−1)k

k + 1

[1 −

√γc

k + 1 + γc

].



0 5 10 15 2010

−4

10−3

10−2

10−1

100

L=1

L=2

L=3L=4

AWGN

SNR per bit (dB)

Pro

babi

lity

of b

it−er

ror


MAXIMUM RATIO COMBINING

Receiver architecture:

Transmittedsignal

Diversitychannel #1(α1, φ1)

Diversitychannel #l(αl, φl)

Diversitychannel #L(αL, φL)

n1(t)

nl(t)

nL(t)

g1

gl

gL

MF1

MFl

MFL

LX

l=1

Combiner

Z1

Zl

ZL

Z

Userdata

Maximizing the output SNR: g = arg maxg γc(g), g = [g1, . . . , gL].


MAXIMUM RATIO COMBINING (CONT’D)

Instantaneous SNR of the output of the combiner

γc =Eb |∑i αigi|2LN0

∑i |gi|2

Invoking Schwarz inequality∣∣∣∣∣∑i

αigi

∣∣∣∣∣2

≤∑

i

|αi|2∑

j

|gj |2

with equality, if and only if g∗i = ai,i = 1, . . . , L. In this case,

γc =Eb

[∑l |αl|2

]LN0



For Rayleigh distributed α, γc is χ2 distributed with 2L degrees of freedom

pγc(γ) =γL−1

γLc Γ(L)

e−γγc , Γ(x) =

∫ ∞

0

tx−1e−x dx.

and hence

Pb =∫ ∞

0

Q(√

2γ)pγc(γ) dγ = pL

L−1∑l

(L + l − 1

l

)(1 − p)l

p � 12

(1 −

√γc

1 + γc

).



0 5 10 15 2010

−4

10−3

10−2

10−1

100

L=1

L=2

L=3L=4

AWGN

SNR per bit (dB)

Pro

babi

lity

of b

it−er

ror


RAKE RECEIVER CONCEPT

DS-SS receiver for the one path channel

PNGenerator

DetectionDecoding

Delay

c(t − τ1)

c(t)

|h(τ)|

nTs + τ1

τ1 τ

|α1|δ(τ − τ1)

τ1

α∗1

Z (n+1)Ts+τ1

nTs+τ1(·)dt

y(t) = α1c(t − τ1) + w(t) Z1(n)


RAKE RECEIVER CONCEPT (CONT’D)

Estimation of the path gain α1:

Z1(n) =∫ (n+1)Ts+τ1

nTs+τ1

y(t)c(t − τ1) dt

= α1Rc(τ1 − τ1) + W1(n)

Hence,

α1 =Z1(n)Rc(0)

.



PNGenerator

DetectionDecoding

Z (n+1)Ts+τ1

nTs+τ1(·)dt

Z (n+1)Ts+τL

nTs+τL

(·)dt

Z (n+1)Ts+τ2

nTs+τ2(·)dt

τLτ2τ1

Delay line

c(t)

|αL|δ(t − τL)

τ

β1

β2

βL

|α1|δ(t − τ1)

c(t − τ1)c(t − τ2)c(t − τL)

|h(τ)|

τ1 τ2 τL

nTs + τ1

nTs + τ2

nTs + τL

|α2|δ(t − τ2)

· · ·

· · ·

· · ·

· · ·

y(t) =PL

�=1 α�c(t − τ�) + w(t)



Maximum ratio combining:

βl = α∗l , l = 1, . . . , L

Equal gain combining:

βl = exp (j arg(α∗l )) , l = 1, . . . , L


MULTIPLE ACCESS INTERFERENCE

Near-far scenario:

…

…

Base station

K

k

1

2

User of interest

Interfererweak

strong

Remedy: either power control or multiuser detection


POWER CONTROL


OPEN LOOP POWER CONTROL

Duplexer AGC

Measure Rxpower

Adjust Tx power

PA

Mobile station

BTS

Pr1

Pt1

Pr2

Pt2

d

Pt2 = (Pr1)nominal + Pt1 − Pr2︸︷︷︸loss

[dB]


OPEN LOOP POWER CONTROL

• Open loop power control relies on the assumption that the power-loss in the uplink and downlink channels are identical.

• The uplink and downlink channels are separated by 130 MHz in theUMTS system, which far exceeds the coherence bandwidth.Consequently, fluctuation of the channel coefficients in the twobands are uncorrelated and open loop power control fails in com-pensating for fast fading!


CLOSED LOOP POWER CONTROL

User dataMUX

Eb/No, SNRmeasurement

Power controlcommands

adjust Eb/Notarget

Measure Quality

Decoding Despreading& RAKE

PA

AGC

Demultiplexer Decoding

Power controlcommands

user data

Base station closed loop power control functions Mobile station closed loop power control functions

Pt(n)

Pt(n) = Pt(n − 1) + PC(n)

PC(n)


POWER CONTROL FOR THE UPLINK

Closed-loop power control in IS-95:Standard deviation of the residual power adjustment error: 1.1 − 1.5 dB.


STREET CORNER EFFECT

BTS1

BTS2

MS1

MS2

MS3

We expect a system crash in DS/CDMA.


HANDOVER

Intrafrequency Handover

Interfrequency Handover

f1

f1

f1 f1

f1

f1

f1

f2f2

f2f2

f3

a) b)

Hierarchical cell structure Hot spot cells with several carriers


INTRAFREQUENCY HANDOVER

• The MS is connected to two BS at the same time.

• Separate pilot channel used for signal strength measurements.

• Handover is initiated if signal becomes smaller than a certainthreshold.

• Drawback: This 2nd BS causes additional interference, because dif-ferent cells use different scrambling codes.


INTERFREQUENCY HANDOVER

• Using slotted downlink transmission, the MS can perform measure-ments on other frequencies.

• The regular 10 ms-frame is compressed in time, either by puncturingor by reducing the spreading factor with a factor of 2. During theremaining idle time of 5 ms, the MS can carry out interfrequencymeasurements.

Time

Instantaneous power

Normal transmission Slotted Transmission

Idle time


UMTS W-CDMA


MAIN REQUIREMENTS FOR UMTS RADIO ACCESS

PART

Delay Constrained Delay Unconstrained

Operating Envi-ronment

MaximumUser BitRate

Max BER, Max Delay MaximumUser BitRate

BER

Rural Outdoor 144 kb/s BER=10−3, D=30 ms 144 kb/s 10−3 −10−8

BER=10−6, D=100 msBER=10−7, D=300 ms

Urban/Suburban 500 kb/s BER=10−3, D=30 ms 500 kb/s 10−3 −10−8

Outdoor BER=10−6, D=100 msBER=10−7, D=300 ms

Indoor/Low Range 2 Mb/s BER=10−3, D=30 ms 500 kb/s 10−3 −10−8

Outdoor BER=10−6, D=100 msBER=10−7, D=300 ms


IMT-2000 FREQUENCY ALLOCATION


MULTIPLEX TECHNIQUES

Downlink (DL)

Uplink (UL)

duplexseparation

FDD

DL DL DLUL UL UL

TDD

time

frequency

TDD frame


WIDEBAND CDMA SPECIFICATIONS (FDD,PHYSICAL LAYER)

Multiple access DS-CDMADuplex technique FDDChip rate 3.84 Mchips/sCarrier spacing 5 MHzFrame size 10 msSpreading technique Variable-spreading factor+multi-codeChannel Coding 1/2-1/3 rate convolutional coding

Turbo codingInterleaving Block interleaver with inter-column permutationsModulation QPSK with roll-off factor α = 0.22


UPLINK CHANNELIZATION CODES

Code-tree for generation of Orthogonal Variable Spreading Factor (OVSF)codes

Cch,1,0 = (1)

Cch,2,0 = (1,1)

Cch,2,1 = (1,-1)

Cch,4,0 =(1,1,1,1)

Cch,4,1 = (1,1,-1,-1)

Cch,4,2 = (1,-1,1,-1)

Cch,4,3 = (1,-1,-1,1)

1Cch,1,0 � ,

��

��

��

��

��

��

11

11

0,1,

0,1,

0,1,

0,1,

1,2,

0,2,

ch

ch

ch

ch

ch

ch

C

C

C

C

C

C

The OVSF codes are only orthogonal in the synchronous case.


UPLINK LONG SCRAMBLING CODES

Complex scrambling codes, Gold sequence generator

clong,1,n

clong,2,n

MSB LSBf1(X) = X25 + X3 + 1

f2(X) = X25 + X3 + X2 + X + 1

Notice: no change in signal bandwidth!


UPLINK SHORT SCRAMBLING CODES

The selected codes are defined from the family of periodically extendedS(2) Codes (N=255)

07 4

+ mod n addition

d(i)12356

2

mod 2

07 4b(i)

12356

2

mod 2

+mod 4multiplication

zn(i)

07 4 12356

+mod 4

Mapper

cshort,1,n(i)

a(i)

+ + +

+ ++

+ ++

3 3

3

2

cshort,2,n(i)

f0(X) = X8 + X5 + 3x2 + x2 + 2x

f1(X) = X8 + X7 + X5 + x + 1

f2(X) = X8 + X7 + X5 + X4 + x

S(2) codes supports MU-detection.


DOWNLINK SPREADING

I

Any downlink

physical channel

except SCH

S

�P

Cch,SF,m

j

Sdl,n

Q

I+jQ S

SCH: Synchronisation Channel


DOWNLINK SCRAMBLING CODES

Complex scrambling codes, Gold sequence generator

I

Q

1

1 0

02

2

3

3

4

4

5

5

6

6

7

7

8

8

9

9

17

17

16

16

15

15

14

14

13

13

12

12

11

11

10

10

f1(X) = X18 + X7 + 1

f2(X) = X18 + X10 + X7 + X5 + 1


FORWARD ERROR CORRECTION IN UMTS

Transport Channel Type Coding Scheme CodingRate

Broadcast ch. 1/2Paging ch. Convolutional CodeRandomaccess ch. 1/3, 1/2

Turbo Code 1/3


CONVOLUTIONAL ENCODER

Output 0G0 = 557 (octal)

InputD D D D D D D D




InputD D D D D D D D

Output 1G1 = 753(octal)

(a) Rate 1/2 convolutional coder

(b) Rate 1/3 convolutional coder


TURBO ENCODER


PHYSICAL CHANNELS (FDD)

Physical channels typically consist of a three-layer structure:

• Super frame: A super frame has a duration of 720 ms and consistsof 72 radio frames.

• Radio frame: A radio frame is a processing unit of 10 ms whichconsists of 15 time slots.

• Time slot: A time slot is a unit which consits of fields containing bits.The number of bits per time slot depends on the physical channel(Spreading factor). Length of a timeslot is 667 ms.


EXAMPLE DOWNLINK

TPC

NTPC bits

Slot #1 Slot #2 Slot #i Slot #16

Frame #1 Frame #2 Frame #i Frame #72

0.625 ms, 20*2k

bits (k=0..6)

Pilot

Npilot bitsData

Ndata bits

DPCCH DPDCH

Tf = 10 ms

Tsuper = 720 ms

TFI

NTFI bitsTime slot

Radio frame

Super frame


UPLINK DEDICATED PHYSICAL CHANNELS

• DPDCH: Dedicated Physical Data Channel. This channel is usedto carry dedicated data generated at Layer 2 and above, i.e. thededicated transport channel (DCH). There may be none, one orseveral uplink DPDCH on each Layer 1 connection.

• DPCCH: Dedicated Physical Control Channel. This channel is usedto carry control information generated at Layer 1 such as: pilot bitsfor coherent detection, power control, feedback information, andmultiplexing information of the DPDCH.



Pilot

Npilot bits

TPC

NTPC bits

Data

Ndata bits


Tslot = 2560 chips, 10 bits

1 radio frame: Tf = 10 ms

DPDCH

DPCCHFBI

NFBI bitsTFCI

NTFCI bits

Tslot = 2560 chips, Ndata = 10*2k

bits (k=0..6)

• Pilot: Known pilot bitssupport channel estima-tion for coherent detec-tion.

• TPC: Transmit power-control commands

• FBI: Feedback informa-tion

• TFCI: Optional transportformat combination indi-cator



I

�

j

cd,1 d

Sdpch,n

I+jQ

DPDCH1

Q

cd,3 d

DPDCH3

cd,5 d

DPDCH5

cd,2 d

DPDCH2

cd,4 d

DPDCH4

cd,6 d

DPDCH6

cc c

DPCCH

�

S


DOWNLINK DEDICATED PHYSICAL CHANNELS

• DPDCH and DPCCH are time-multiplexed in downlink.

• The dedicated pilot channel facilitates the use of antennae in down-link.


DOWNLINK DEDICATED PHYSICAL CHANNEL

TPC

NTPC bits


Frame #1 Frame #2 Frame #i Frame #72

0.625 ms, 20*2k

bits (k=0..6)

Pilot

Npilot bitsData

Ndata bits

DPCCH DPDCH

Tf = 10 ms

Tsuper = 720 ms

TFI

NTFI bits

• Pilot: Known pilot bitssupport channel estima-tion for coherent detec-tion.

• TPC: Transmit power-control commands

• TFI: Optional transportformat combination indi-cator


SYNCHRONISATION IN UMTS

The initial Cell Search is carried out in three steps:

• Slot synchronisation using the primary synchronisation channel.

• Frame synchronisation and code-group identification – using thesecondary synchronisation channel.

• Scrambling-code identification through symbol-by-symbol correla-tion over the primary CCPCH with all the scambling codes withinthe code group.


UMTS FDD POWER CONTROL SPECIFICATIONS

• Open loop power control– The downlink power is measured on the CCPCH (Common

Control Physical Channel) before the MS transmits the random-access burst.

– Uplink interference level and required SIR is broadcast on theBCCH

• Closed loop power control– Power control commands are sent every 0.625ms.– The step size is 0.5 − 3.0 dB, and is fixed for each cell.– Target SIR is determined by the outer loop.

• Outer loop power control– The target SIR is determined by radio resource management,

i.e. not a physical layer issue.– The SIR level is adjusted according to a quality estimate (FER,

BER, a.s.o).


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