OFDM – Orthogonal Frequency Division Multiplex

Naftali Chayat

CTO, BreezeCOM

©BreezeCOM, 2000

Overview

• Motivation – the Multipath and its effects

• OFDM principles

• Error Correction Coding

• OFDM-based standards– Broadcast standards – DAB and DVB– LANs & Access – 802.11a and HIPERLAN/2– Baseband – ADSL

High Speed Digital Comm – the curse of multipath

• The traditional way of sending information is serially

• This type of communication is affected by multipath

time

MultipathMultipathMultipathMultipath

time frequency

Effect of Multipath: Inter-Symbol Interference (ISI)

• Each bit becomes distorted by echoes• The symbols disturb each other

Sent data

Data and the echoes

Resulting waveform

Solution 1 - Equalization

• Equalization is building an “inverse filter”• If channel has nulls, you cannot inverse• Decision Feedback Equalizer (DFE) can

handle also channels with nulls– Uses past decisions

• In coded systems past decisions may be unreliable

• In long channels – complexity problem

Solution 2 – Parallel Channels

• Send several long symbols in parallel• Only the edges are corrupted

Sent signal

Received signal

How to send in parallel?

• Use signals at different frequencies• Both sine and cosine – complex exponential

Frequency domain view

• ORTOGONALITY – The peak of each signal coincides with nulls of

other signals

FFT period and Guard Time

• Equispaced in frequency periodic in time

• Send slightly more than one period

Frequency domain

Time domain

Guard timeWaveform sent

FFT period

Guard time and Multipath

• The multipath corrupts the Guard Interval• The FFT region remains undistorted

Sent signal

Received signal

FFT period

symbol

GI

Multipath effect on OFDM

• Each subcarrier is scaled, but they still do not interfere with each other

Sent signal

Received signal

QAM constellations• For multiple bits/symbol – QAM constellations• Gray coding is typically used – neighbors differ

by one data bit only

01 11

1000

11

QPSK=4QAM2 bits/sym

16QAM4 bits/sym

64QAM6 bits/sym

Q

I

Q

I

Q

I

Modulating the subcarriers

• The sine and cosine are multiplied by I and Q and added.

16QAM4 bits/sym

I

Q

QAM in OFDM environment

• Larger constellations require higher SNR

• Some subcarriers are received stronger, while others are received weaker– Some may be completely faded

• Some form of mutual protection is needed Error Correction Coding

Convolutional Codes and the Viterbi Algorithm

• Data bits are passed through a shift register

• The XOR outputs are sent.

• Trellis representation– States are labeled

according to shift register contents

D D

00

01

10

11

00

01

10

11

data

x0

x1

0 00

0 11

1 01

1 10

time n time n+1

Convolutional Codes and the Viterbi Algorithm

• Noisy versions of the sent bits are received.

• Each transition in a trellis is assigned a “likelihood”

• Viterbi Decoder finds out what’s the most likely path through the trellis, yielding the sequence of data bits

00 00

10

00

01

10

11

00

01

10

11

00

01

10

11

00

01

00

1 0 1 1 0 0

Viterbi Algorithm (1)

• How do we get from Metula to Eilat in the shortest way?

• A lot of paths to check• Solution – do it stage

by stage

Metula

Haifa Tveria

Tel Aviv Jerusalem

Ashkelon Beer Sheva

Eilat

100 120140180

65 12011090

70120

210260

Viterbi Algorithm (2)

• Start with Haifa and Tveria – this is trivial:– 120 Km to Haifa

– 70 Km to Tveria

Metula

Haifa Tveria

Tel Aviv Jerusalem

Ashkelon Beer Sheva

Eilat

100 120140180

65 12011090

70120

210260

Viterbi Algorithm (3)

• The shortest route from Metula to Tel Aviv:– Through Haifa:

120+100=220 Km

– Through Tveria: 70+180=250 Km

– Choose through Haifa!

• From Metula to Jerusalem– Through Haifa – 260 Km

– Through Tveria – 190 Km

Metula

Haifa Tveria

Tel Aviv Jerusalem

Ashkelon Beer Sheva

Eilat

100 120140180

65 12011090

70120

210260

220 190

Viterbi Algorithm (4)

• The shortest route from Metula to Ashkelon:– If through Tel Aviv, then also

through Haifa: 220+65=285 Km– If through Jerusalem, then also

through Tveria: 190+90=280 Km– Choose through Jerusalem!

• From Metula to Beer-Sheva– Through Tel Aviv – 330 Km– Through Jerusalem – 310 Km

• Jerusalem is better in both cases

Metula

Haifa Tveria

Tel Aviv Jerusalem

Ashkelon Beer Sheva

Eilat

100 120140180

65 12011090

70120

210260

280310

Viterbi Algorithm (5)

• Finally, to Eilat:– If through Ashkelon, then also

through Tveria and Jerusalem: 280+260=540 Km

– If through Beer-Sheva, then also through Tveria and Jerusalem : 310+210=520 Km

– Choose through Jerusalem!

• Conclusion: the sortest route is Metula – Tveria – Jerusalem – Beer-Sheva – Eilat

• Shortest Distance – 520 Km

Metula

Haifa Tveria

Tel Aviv Jerusalem

Ashkelon Beer Sheva

Eilat

100 120140180

65 12011090

70120

210260

520

QAM to metrics conversion

• For each bit a metric (sign+likelihood) is extracted• The strength of the subcarrier is weighted into the

likelihood estimation

MSB LSBMiddle bit

Interleaving

• Convolutional Codes work well with scattered errors, and perform badly with clustered errors

• Adjacent subcarriers typically fade together• The coded bits are interleaved (reordered)

prior to transmission• Upon reception, metrics are deinterleaved

(reordered back) prior to Viterbi decoding

OFDM Advantages

• For a long multipath – relatively low computational complexity– The FFT algorithm has log(N) ops/sample

complexity

• Integrates well with Error Correction Coding

• Extreme robustness in multipath

OFDM Disadvantages

• The time domain waveform is noise-like– Large peak-to-average ratio (crest factor)

• Dictates large Power Amplifier backoff

• Long symbols impose higher sensitivity to oscillator instabilities – offsets and phase noise

OFDM in Broadcasting Standards

• Digital Audio Broadcasting– 192-1536 subcarriers– QPSK modulation, Convolutional ECC– 1.536 MHz total bandwidth

• Digital Video Broadcasting– 1705 or 6817 subcarriers– QPSK, 16QAM or 64QAM– Convolutional +Reed-Solomon ECC

Single Frequency Network

• All broadcasting transmitters operate at the same frequency and transmit same data

• Received signals have “artificial multipath”

Receiver

Tx 1

Tx 2

Tx 3

ADSL: Asymmetric Digital Subscriber Line – OFDM over copper

• The copper twisted pairs exhibit a response with long tail in time domain.

• Static channel – power and constellation is negotiated per subcarrier according to SNR

• The OFDM is at baseband, not at radio frequencies

• 512 subcarriers, up to 32K-QAM• Trellis coded modulation for ECC

The 802.11a +HIPERLAN/2High Speed Physical Layer

for the 5 GHz band

Frequency Allocations

• USA– 5.15-5.25 GHz (50 mW, indoor)– 5.25-5.35 GHz (250 mW)– 5.725-5.825 GHz (1 W)

• Europe– 5.15-5.35 GHz (100 mW)– 5.47-5.725 GHz (1 W)– Only for the HIPERLAN devices

• Japan– 5.15-5.25 GHz (?)– MMAC W-Eth WG will adopt 802.11a

Main Parameters

• 20 MHz channel spacing– 16.6 MHz signal bandwidth – 5 MHz grid for various regulatory domains

• Multiple data rates- 6 to 54 Mbit/s– support of 6, 12 and 24 Mbit/s rates is mandatory

• OFDM modulation– BPSK, QPSK, 16QAM or 64QAM on each subcarrier– pilot assisted coherent detection

• 802.11 multirate mechanism support

Channelization in US

Data and Pilot subcarriers• 52 non zero subcarriers, spaced 312.5 KHz

– 48 data subcarriers

– 4 pilot subcarriers

• Center frequency subcarrier not used– leakage in quadrature modulators may corrupt the data

OFDM Frame Structure

• Carrier spacing is 312.5 KHz

• Fourier transform performed over 3.2 μsec

• 0.8 microsecond Guard Interval for ISI rejection

GIt1

Data 1

0.8 s +3.2 s = 4.0 s

1. s

GIt1

Data 2

Error Correction Coding

• ECC is a must - some subcarriers may fade• Bit Interleaved Convolutional Coding used

– more robust than trellis in Rayleigh fading

• Industry standard K=7, R=1/2 code– higher coding rates (2/3, 3/4) derived by puncturing

– tail zero bits added to message (trellis termination)

• Interleaver spans one OFDM symbol– latency and complexity considerations

coding rateConstellation1/2 2/3 3/4

BPSK 6 Mbit/s 9 Mbit/sQPSK 12 Mbit/s 18 Mbit/s

16 QAM 24 Mbit/s 36 Mbit/s64 QAM 48 Mbit/s 54 Mbit/s

Supported Rates and Modulations

• Modulation of the data subcarriers by either– BPSK, QPSK, 16QAM or 64QAM– 1, 2, 4, or 6 bits/subcarrier, correspondingly

Preamble Structure• Short sequences in the beginning

– Signal Detection, AGC convergence, Diversity resolution, Timing estimation, Coarse frequency estimation

• Long sequences with Guard Interval– Fine frequency estimation, Channel Estimation

t1 t2 t3 t4 t5 t6 t7 t8 t9 t10

Short training sequence

GI2 T1 T2

Long training sequence

GI

SIGNAL

GI

DATA1

GI

DATA2

10*0.8 sec=8.0 sec 1.6+2*3.2 sec =8.0 sec0.8+3.2sec

= 4.0 sec 4.0 sec

Signal detectionAGC convergenceDiversity selectionCoarse freq. offset estimate

Fine timing acquisitionFine freq. offset estimationChannel estimation

RATE andLENGTHReceived at6 Mbit/s

DATA is received at RATE indicated in the SIGNAL field

Multirate Mechanism Support

• Each Frame has a SIGNAL field in the beginning– Contains RATE and LENGTH

• The SIGNAL is transmitted at the most robust data rate (6 Mbit)– The rest of the packet is at the RATE indicated

• Even if the receiver does not support the RATE of the signal is too weak, it can predict how long the packet will last

• AP can communicate with different stations at different rates

Transmitter Performance Specs

Timing Related Specs

• Short InterFrame Space (SIFS) is 16 usec– Finish decoding, decide you need to reply and put a

signal on air

• Slot Time is 9 usec– Listen, decide that there is no signal and only then

transmit

Data ACK

SIFS

Data

DIFS+n*SlotDIFS=SIFS+2*Slot

Second station detects signal and does

not transmit

Short IFS for ACK gives it priority -

second station yields

SUMMARY

• OFDM is an excellent choice for channels with long multipath

• OFDM has disadvantages with power efficiency and with phase noise tolerance

• OFDM finds applications in many areas:– Broadcasting (DAB, DVB-T)– WLANs (802.11a, HIPERLAN/2)– Baseband over copper (ADSL)