CAPACITY CAPACITY

CAPACITY CAPACITY

P i G i

• Processing Gain

RF bandwidth W

G

The information Bit Rate

G = = R

– Typically, 20 – 60 dB

– Quantifying the degree of Robustness to interference Q y g g

23

CAPACITY (cont’d) CAPACITY (cont d)

Si l t i ti

• Signal to noise ratio

/ S R /

E N = / 1

( ( ) ) /

b o

t

E N

N W α N S W

= ⋅ + − ⋅

S : received signal power at the BS from a mobile station N

: noise spectral density

W : tx bandwidth

N b f i th ll

W N

N : number of users in the cell α : voice activity

Power limited Æ Soft capacity

) 1 / (

/ ⎟⎟ − −

⎠

⎜⎜ ⎞

⎝

⎛

= ⋅

N N E

R W

W

S N

/

⎟ α

⎜ ⎠

⎝ E

N

CAPACITY (cont’d) CAPACITY (cont d)

If S t i fi it th t ti li k it

• If S goes to infinity, the asymptotic link capacity is given by

⎛ ⎞ ^S

0

1 / 1

b

/ N W R

E N α

⎛ ⎞

= ⎜ ⎟ +

⎝ ⎠

1 ⎛ W R / ⎞

0

1 1

capacity) /

( /

u

b p

N W R

E N G α

⎛ ⎞

= ⎜ ⎟

⎝ ⎠

/

E

N

= α

/N 1 E

W/R

0 b

α +

1 N

25

NEAR FAR EFFECT NEAR-FAR EFFECT

Ideal Near Far Effect

T1

P

Ideal

T1

P

T2

P

Near-Far Effect

2 MS1 PT

MS1

MS2 MS2

d d

d/2 d

P P

P

P

d

( /( 2 ) )

1

4 1

2

= ⋅

R

P

d P d

P

1

2 1 2 1

=

=

=

R R R R

P P I

C

P P

1.25 MHz f

R1

P

R2

P

1 16

1

1 2 1

=

=

⋅

=

R R R

P C

P P

1.25 MHz f

1

2 16 _R

R P

P =

2

16 P

I

POWER CONTROL POWER CONTROL

• Objectives

– Solving the near-far problem g p – Maximizing system capacity

M

• Measures

– Received signal strength

– Received signal to interference ratio (SIR)

27

OPEN LOOP POWER CONTROL OPEN-LOOP POWER CONTROL

• To decide tx power based on the received signal strength g g

• No control by feedback

CLOSED LOOP POWER CONTROL CLOSED-LOOP POWER CONTROL

• By the received power control bits

– By 1 bit: up or down y p

– By multiple bits: multi-level up/down

B d th i d SIR

• Based on the received SIR

– If the received SIR is over the target SIR or not

• 800Hz (IS-95), 1500Hz (WCDMA)

29

OUTER LOOP POWER CONTROL OUTER-LOOP POWER CONTROL

• Changing the target SIR value

– Target SIR is varying according to the conditions g y g g such as channel, speed, etc.

– Adaptively following the target SIR Adaptively following the target SIR – For 1% PER (packet error rate)

1 it d f

• 1 unit down: for a success

• 99 units up: for an error

EXAMPLE EXAMPLE

31

RAKE RECEIVER

RAKE RECEIVER

Orthogonal Frequency Orthogonal Frequency

Division Multiplexing p g

Fourier Transform Fourier Transform

Given a varying signal s(t) in the time-domain, the spectral components S(f) are obtained as follows:

∫ ^{⋅ −}

= s t e dt

f

S ( ) ( ) ^{j 2 π ft}

Æ For a fixed frequency f, the integral tells us how much of that harmonic is present in the signal s(t).

And vice versa:

∫ ^{j 2 f}

∫ ^⋅

= S f e df

t

s ( ) ( ) ^{j 2 π ft}

Useful Theorems Useful Theorems

• Theorems – Time delay

– Frequency translation – Convolution

– Convolution – Multiplication

• Transforms – Rectangular – Constant

τ

τ τ ^f

t ⎟ ↔ sinc

⎠

⎜ ⎞

⎝ Π ⎛ – Constant

– Impulse

⎠

⎝

3

Multi Carrier Modulation Multi-Carrier Modulation

t

Channel impulse

Data on

t

impulse

response _f

f

single carrier ^t

subch. 1

t

f

f

f

f₀ f₁ f₂ f₃ Multicarrier

t

subch. 2

t

f

u t ca e with 4 subchannels

subch. 3

t

f

f

Time domain Frequency domain

subch. 4

t

Time domain Frequency domain

SCM vs MCM SCM vs. MCM

„

Single Carrier Transmission g

„

Symbol duration < delay (multipath) spread

= BW of Tx Signal > BW of Channel

Î Severe ISI High complexity (Rake receiver Equalizer) Î Severe ISI, High complexity (Rake receiver, Equalizer)

„

Multi-Carrier Modulation

„

Frequency division multiplexing (for a single user)

„

Frequency division multiplexing (for a single user)

„

Divide a wideband channel into narrow subchannels

„

Serial-to-Parallel conversion, Parallel transmission

Î

Low symbol rate at each subchannel

Î

Low symbol rate at each subchannel

ƒ

Frequency selective channel Æ Flat narrowband channel

ƒ Less ISI

ƒ No need for complex multi-tap time-domain equalizerNo need for complex multi tap time domain equalizer

ƒ Possibly simple 1-tap frequency domain equalizer

ƒ

More sensitive to frequency offset

ƒ

Large PAPR

5

g

FDM vs OFDM FDM vs. OFDM

Saving of bandwidth

(a) Conventional multicarrier FDM

• By using the overlapping multi-carrier modulation, we can save (b) Orthogonal multicarrier (OFDM)

y g pp g ,

almost 50% of bandwidth

Common to FDM & OFDM Common to FDM & OFDM

• Split a high-rate data stream into a number of lower rate streams

– Transmitted simultaneously over a number of subcarriers

• Symbol duration increases for the lower rate parallel y p subcarriers

– Relative amount of dispersion is decreased p

7

FDM FDM

• No requirement for carrier spacing

– If the spacing is sufficiently large to guarantee no overlapping or negligible interference from neighboring bands

negligible interference from neighboring bands

• Receive method - filtering

f

BPF

f

f

f

FDM Transmit FDM-Transmit

9

OFDM OFDM

t f

• Transmitting sin soidal signals ith an integer m ltiple of c cles (time

T t 1/T

• Transmitting sinusoidal signals with an integer multiple of cycles (time domain)

Î carrier spacing is exactly 1/T, where T is the symbol duration Æ 1/T is the minimum spacing (Frequency domain)

Æ 1/T is the minimum spacing (Frequency domain)

• Maintaining and exploiting the orthogonality property when modulating and demodulating the signal

Î no need for filtering Î no need for filtering

Æ but sensitive to frequency & timing offset

Time Domain Representation Time Domain Representation

1.5

0 0.5 1

A *

B *

0 10 20 30 40 50 60 70 80 90 100

-1.5 -1 -0.5

C *

0 10 20 30 40 50 60 70 80 90 100

∫

Data

symbols _{(T 1)}

∫

∫

∫

=

=

T T

dt t t

A

A dt t t

A

0 )

2 sin(

2

* ) sin(

) sin(

2

* ) sin(

symbols _{(T = 1)}

⎧

∫

if

0 2 2

f f

T

dt e

T

e

∫

∫

= +

= +

+

T T

dt t t

C t B

A dt t t

C t B

t A

0 )

sin(

2 )}

3 sin(

) 2 sin(

{

) sin(

2 )}

3 sin(

) 2 sin(

) sin(

{

⎪⎩

⎪ ⎨

⎧

=

−

=

= 0 , if | | if

,

k k

T f n

f f f

T

j j

11

Frequency Domain Representation Frequency Domain Representation

„

For blue curve, when it is at its peak value

„

The other curves have a zero value at that point Î This means orthogonality in frequency domain

f

1/T 1/T

2/T 3/T

4/T 5/T

OFDM Signal Waveform OFDM Signal Waveform

„

An OFDM signal

„

An OFDM signal

„

A sum of subcarriers that are modulated

„

By using phase shift keying (PSK) or quardrature amplitude modulation (QAM) design parameters

l QAM b l

d

™

: complex QAM symbols : the number of subcarriers

th b l d ti d

N

: the symbol duration : carrier frequency T

f

13

Signal Reconstruction Signal Reconstruction

∫

=

k

s t e dt

d T

0

)

1 (

~

2

e

j t T

π

⎛ ⎞

⎜ ⎟

⎝ ⎠ n t( ) ²

e

j t T

π

⎛− ⎞

⎜ ⎟

⎝ ⎠

∫

∫

d0

d

0

d~ d~

2 ( 1)

e

N t

j T

π −

⎛ ⎞

⎜ ⎟

⎝ ⎠

2 ( 1)

e

N t

j T

π −

⎛− ⎞

⎜ ⎟

⎝ ⎠

∫

0

∫

d1

−1

dN

) (t s

d1

1

~

−

dN

∫

Tt j i N

i

e d t

s

s 1 2π

)

( ⁼ ∑

i

i

e d t

s

0

)

( ∑

=

Similarity to DFT Similarity to DFT

N 1 i

T t j i N

i

i

e d t

s

s 1 2

π

0

)

( ∑

=

=

„

IDFT of QAM input symbols N

„

If continuous signal is sampled at the rate N/T

„

That is , time t is replaced by nT/N

1 1

0 )

(

1 2

∑

^d

^N

N_s

π

1 ,

, 1 , 0 ,

) (

0

−

=

= ∑

=

N n

e d n

s

i

i

L

15

Multipath Fading Multipath Fading

H

) ( f H

OFDM Signal through Channel OFDM Signal through Channel

17

Signal after Channel Signal after Channel

„

In receiver

„

In receiver,

„

Received signal is sampled and then DFT is applied

1 nk

N

1 ,

, 1 , 0 ,

)

1

(

0

~

=

= −

−

∑

^{r n e k N}

d N

j nk N

n

k

L

π

„

where

k

1 ,

, 1 , 0 ,

) (

1 2

0

−

= +

= ∑

=

N n

n e

d H n

r

j kn N

k

k

k

L

π

Narrowband channel response in frequency domain of k-th sub-carrier Å constant over the frequency band of each sub-carrier

OFDM Signal in Discrete Time OFDM Signal in Discrete-Time

„

With sampling rate of 1/T

=N/T

1 1

0 0

( ) exp 2 ( ), 0,1,..., 1

N N

kn

k k N

k k

j kn

x n X X W N IDFT n N

N π

− −

−

= =

⎛ ⎞

= ∑ ⎜ ⎝ ⎟ ⎠ = ∑ = × ^X = −

1 1

1

⎛ j 2 k ⎞ 1

1

0 0

1 2 1 1

( ) exp ( ) ( ), 0,1,..., 1

N N

kn

k N

n n

j kn

X x n x n W DFT k N

N N N N

π

− −

= =

⎛ ⎞

= ∑ ⎜ ⎝ − ⎟ ⎠ = ∑ = ^X = −

exp 2

W

= ⎛ ⎜ ⎝ − j π ⎞ ⎟ ⎠

„

Equivalent to the Discrete Fourier transform (DFT)

N

p j

⎜ N ⎟

⎝ ⎠

IDFT DFT

X

P/S S/P

(0) x

(1) x

X

) (n

n ⁰

X ~

1

X ~

IDFT DFT

1

X

P/S S/P

… … …

( 1) x N −

…

1

~

−

X

19

FFT instead of DFT FFT instead of DFT

• N-point IDFT require a total of N

multiplications

• Use IFFT to reduce complexity !!

™ Radix-2 FFT algorithm Æ (N/2)log

(N) multiplications

™ Radix 4 FFT : (3/8)N(log (N) 2) complex multiplications

™ Radix-4 FFT : (3/8)N(log

(N)-2) complex multiplications

•

N=8, Radix-2 FFT

OFDM Modulation OFDM Modulation

sub

sub sub

21

OFDM Mod/Demod Using FFT

OFDM Mod/Demod Using FFT

Guard Time Guard Time

• To eliminate inter-symbol interference (ISI) almost completely

• A guard time is introduced for each OFDM symbol

• Guard time is chosen larger than the expected delay spread such that Guard time is chosen larger than the expected delay spread, such that

multipath components from one symbol cannot interfere with next symbol

• Guard time could consist of no signal at all

– The problem of intercarrier interference (ICI) would arise

• ICI is a crosstalk between subcarriers – No longer orthogonal No longer orthogonal

23

Guard Interval Guard Interval

• ISI from the previous symbol in multi-path fading p y p g

• Guard interval insertion between 2 successive OFDM symbols – To eliminate ISI almost completely in block processing OFDM

transmission

transmission

Zero Valued Guard Time Zero-Valued Guard Time

No

Subcarrier #1 w/o delay ISI

d l d b i #2

Signal from previous symbol

delay

delayed subcarrier #2

previous symbol on the subcarrier #2

FFT integration time Guard time

= 1/carrier spacing FFT integration time Guard time

OFDM symbol time ICI

25

ICI

Cyclic Extension Cyclic Extension

• The OFDM symbol is cyclically extended in the The OFDM symbol is cyclically extended in the guard time

– To eliminate ICI

– Delayed replicas of OFDM symbol always have an

integer number of cycles within FFT interval as long as

h d l i ll h h d i

the delay is smaller than the guard time

• Multipath signals with delays smaller than the guard

ti t ICI

time cannot cause ICI

• The orthogonality becomes lost if multipath delay

b l th th d ti

becomes larger than the guard time

• OFDM symbol time = guard time + FFT interval

Cyclic Prefix (CP) Cyclic Prefix (CP)

27

OFDM Signal Processing OFDM Signal Processing

IFFT d l t bl k f i t QAM l

• IFFT modulates a block of input QAM values onto a number of subcarriers in transmitter

In the recei er

• In the receiver

– The subcarriers are demodulated by an FFT FFT is almost identical to an IFFT

– FFT is almost identical to an IFFT

• Possibly the same hardware for both transmitter and receiver

and receiver

– IFFT can be made using an FFT by conjugating input and out of FFT and dividing the output by the FFT size g p y

• Synchronization process is needed in receiver

– Frequency offset, timing, location of symbol boundary q y g y y

Block Diagram Block Diagram

DAC RF TX

QAM

IFFT (TX) S/P

Pilot insertion

P/S

extension and windowing

IFFT (TX) FFT (Rx)

QAM

P/S S/P

extension

QAM

P/S

ADC

RF RX

Frequency

Synchronization

29

OFDM Signal

OFDM Signal

Windowing Windowing

• Need for indo ing

• Need for windowing

– The out-of-band spectrum of unfiltered QAM sub- carriers decreases rather slowly, according to sinc y, g function

• For larger number of subcarriers

Spectrum goes down more rapidly in the beginning – Spectrum goes down more rapidly in the beginning – The sidelobes are closer together

• Windowing can be applied to the individual Windowing can be applied to the individual OFDM symbols

– To make the spectrum go down more rapidly

• Windowing makes the amplitude go smoothly to zero at OFDM symbol boundaries

31

Symbol Shaping Symbol Shaping

ACI dj t h l i t f

ACI: adjacent channel interference

Time Domain Windowing Time Domain Windowing

„

Time Domain Windowing

„

Lower complexity than digital filtering

„

Raised-cosine window

⎧ 0 5 0 5 ( /( T )) 0 ≤ ≤ T

⎪ ⎪

⎩

⎪⎪ ⎨

⎧

+

≤

≤

− +

≤

≤

≤

≤ +

+

=

sym sym

sym sym

sym sym

sym sym

T t

T T

T t

T t T

T t

T t

t w

) 1 (

)), /(

) cos((

5 . 0 5 . 0

,

0 . 1

0 )),

/(

cos(

5 . 0 5 . 0 ) (

α α

π

α

α α

π π

⎩

prefix d

sym T T

T = +

sym sym

sym T T

T^' = +α

Td

TG

CP i−thSymbol

Tsym

α αTsym

prefix T

33

PSD by Shaping

PSD by Shaping