Chap2 ofdm basics

DarmstadtUniversity ofTechnology

OFDM Basics for Wireless

Communications

Institute ofMicroelectronicSystems

2VLSI_Comms WS03-04/Generalities L.D. Kabulepa

Single Carrier vs. Multicarrier

Single Carrier

MODMOD

e.g., QAM

TXFilterTX

Filter h(t, τ)h(t, τ) + RXFilterRX

Filter DEMODDEMOD

Noise

Wireless Channel

Databits

Databits

MulticarrierMODMOD TX

FilterTX

FilterRX

FilterRX

Filter DEMODDEMODDatabits

Databits

MODMOD TXFilterTX

FilterRX

FilterRX

Filter DEMODDEMOD

Σ h(t, τ)h(t, τ) +

Noise

Wireless Channel

1

N


Multicarrier Transmission

FSC

tTsymb, SC

f

| h(f)

|2

τ

| h(τ) |2

Single Carrier (SC)

Multicarrier

FSC

t

f| h

(f) |2

F = N

TS = N Tsymb, SC

Basic principle:• Split the transmision bandwidth into many narrow subchannelswhich are transmitted in parallel

• (Ideally) Each subchannel is narrow enough so that it experiences a flat fadingalthough the overall radiopropagation environment is frequency-selective.

The time dispersion effects are less significant as thesymbol duration increases


Benefit of Multicarrier Transmission

The multicarrier transmission allows to achieve high data ratein frequency-selective radio propagation environment

By assuming the same data rate:• Single-Carrier

⇒> CSCsymb,

BT

1Distortion, interference (ISI)

Large amount of signal processingrequired in the equalizer

• Multicarrier

⇒< CSCsymb,

BT N

1No interference

- Data rate can be increased by usinga larger number of subcarriers

- Less equalization effort (as ISI is reducedby a factor N)(BC = Coherence bandwidth)


Benefit of Multicarrier Transmission: Example

• A data rate of 10 Mbit/s is targeted in a multipath radio environment byusing the BPSK modulation. Maximum spread delay = 5 µs

5 Mbit/s with BPSK ⇒ Bandwidth = 5 MHz

• Single Carrier Scenario Tsymb,SC = 0.2 µs ⇒ τmax = 25 Tsymb,SC

• Multicarrier ScenarioNumber of subcarriers: 128Symbol duration = N Tsymb,SC ⇒ τmax = 0.039 NTsymb,SC

⇒ ISI significantly reduced

⇒ Intersymbol-Interference (ISI) is extended over 25 symbols


Orthogonal Multicarrier

Frequency

Orthogonality between the sub-carriers allows their overlappingwhile disabling the occurrence ofcrosstalks.

Thus, a significant power savingcan be achieved by using anorthogonal multicarrier technique

Frequency

Bandwidth saving


Orthogonal Multicarrier (cont‘d)

The orthogonality between the subcarriers can be achieved by letting thetransmit filters gi(t) and the receive filters ri(t) fulfill the following conditions(i ∈ {1, ... , N})

1. Matched filter condition

2. Convolution condition

( ) ( )tTgKtr 0ii −⋅= ∗

( ) ( ) ( )dττthτg0tc nτ jnj, −⋅== ∫+∞

−∞=

( ) ( )⎩⎨⎧

≠=

==−⋅= ∗∞+

−∞=∫ nj,0nj,1

δ dττtgτg nj,nτ j

(Assumption: Perfect synchronization, T0 = 0, K = 1)


Conventional OFDM

OFDM = Orthogonal Frequency Division Multiplexing

• In a conventional OFDM system, the orthogonality between the subcarriersis achieved by means of the discrete Fourier transform (DFT)

• Baseband OFDM signal

• Passband OFDM signal

∑−

=

=1N

0k

t∆fkj2πkas(t)

( )

⎭⎬⎫

⎩⎨⎧

= ∑−

=

+1N

0k

t∆fk fj2πk

CaRes(t)

ak = complex-valued modulated symbols (e.g., QAM)N = number of subcarriersfC = carrier frequencyTs = sampling period, f = subcarrier spacingThe inverse DFT is used at the transmitter side

Tt0, ≤≤

Tt0, ≤≤

STN1

T1∆f ==


Conventional OFDM(cont‘d)1 subcarrier

• The receiver is expected to compute the spectra values at those pointscorresponding to the maxima of individual subcarriers

• As a maximum of a subcarrier corresponds to zeros of other subcarrier,each subcarrier can demolutated independently of the others (by assuminga perfect synchronization)

6 subcarriers


Impact of a Wireless Channel

OFDM Symbol OFDM Symbol OFDM Symbol OFDM Symbol

t

ii-1 i+1 i+2

|h(τ)|2

Symbol (i-1)

Symbol (i)

Interference

Channel PowerDelay Profile


Cyclic Extension

OFDM Symbol OFDM Symbol OFDM Symbol

t

ii-1 i+1

|h(τ)|2

Symbol (i-1)

Symbol (i)

Channel PowerDelay Profile

Cyclic Extension

Tg T

Interference induced bythe channel are canceledby inserting a cylic extensionwith Tg > τmax(at the expense of the dataRate)

GGG G


Circular Convolution

• In the presence of interference induced by the channel

• The cyclic extension (with Tg > τmax) allows to apply the circular convolution

{ } { } { }NNN s(k)DFTh(k)DFTs(k)h(k)DFT ∗≠∗

{ } { } { }NNN s(k)DFTh(k)DFTs(k)h(k)DFT ∗=∗ ˆˆ

∗̂ = Circular Convolution

This property allows the use of a simple equalization scheme in thereceiver

Relationship between transmittedand detected symbol

y(n)H(n)(n)y ⋅=ˆ⇒


OFDM Transceiver

P/SS/P

DFT

S/PP/S

IDFT

ReceiveFilter

ReceiveFilter

TransmitFilter

TransmitFilter

MultipathPropagationEnvironment

+AWGNη

Transmitter

Receiver

Channel

xksk

rkyn

s‘k

Remove CP{


OFDM Drawbacks1. High sensitivity to synchronization errors

Synchronization errors ⇒ Interference, loss of orthogonality

( ) ( ) tf2jefFttf δπδ −⋅−

Timing Errors tf2 C δπ∆Φ =

I

Q

FFT Window

Frequency

Time

tδ

FFT Window

Frequency

Timeff∆ζ

( ) ( ) ( )fffFetf fft2j f ∆ξδ∆ξπ −∗⋅ −

Frequency Offset Errors

∆f f-1 f1 f2f0

ff ∆ζ

fC

Frequency


OFDM Drawbacks(cont‘d)2. Occurrence of very high peak values

A reduction ofthe PAPR is highlydesirable. The higherthe PAPR, the lowerThe efficiency of circuitssuch as power amplifiersand analog-to-digital converters

Peak amplitude

RMS amplitude

time

Amplitude

Peak amplitudeRMS amplitude PAPR = CR2 =

Peak powerAverage power

CR =

CR: Crest Factor PAPR: Peak-to-Average Power Ratio


OFDM Drawbacks(cont‘d)

MPX

Tx Analog

DAC

ShapingFilter

Inter-polation

DLC(MAC)DLC

(MAC)

ScramblingEncoding

Interleaving

Mapping I F F

T

AppendCyclicPrefix

S/P

P/SInter-

polationShaping

Filter

DAC

Tx Analog

MPX

AppendPreambles

I/QMod.

DAC

DACDAC

DAC

I/QMod.

LO1 LO2

PA TransmitFilter

Nonlinear effects generatedby the power amplifiermay introduce intercarrier-interfrence and thus destroythe orthogonality

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Chap2 ofdm basics