OFDM Basics for Wireless Communications -...

16
Darmstadt University of Technology OFDM Basics for Wireless Communications Institute of Microelectronic Systems

Transcript of OFDM Basics for Wireless Communications -...

Page 1: OFDM Basics for Wireless Communications - KFUPMfaculty.kfupm.edu.sa/.../COE082_543/chap2_OFDM_basics.pdf · Darmstadt University of Technology OFDM Basics for Wireless Communications

DarmstadtUniversity ofTechnology

OFDM Basics for Wireless

Communications

Institute ofMicroelectronicSystems

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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

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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

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4VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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)

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5VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

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6VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

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7VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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)

Page 8: OFDM Basics for Wireless Communications - KFUPMfaculty.kfupm.edu.sa/.../COE082_543/chap2_OFDM_basics.pdf · Darmstadt University of Technology OFDM Basics for Wireless Communications

8VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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 ==

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9VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

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10VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

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11VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

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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⇒

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13VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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{

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14VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

FFT Window

Frequency

Timeff∆ζ

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

Frequency Offset Errors

∆f f-1 f1 f2f0

ff ∆ζ

fC

Frequency

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15VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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

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16VLSI_Comms WS03-04/Generalities L.D. Kabulepa

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