Multi Carrier and of Dm Systems

7/30/2019 Multi Carrier and of Dm Systems

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Orthogonal Frequency DivisionMultiplexing

Cihan TepedelenliogluCihan Tepedelenlioglu

Arizona State UniversityArizona State University

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Overview

Intro to digital communications

Multipath fading and ISI

Elimination of the ISI: Equalization

Basic idea in OFDM

History and context

Advantages and disadvantages of OFDM

Channel estimation and equalization

Bit loading and DMT Diversity issues

Conclusions


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Digital Communications

Transmission of 0s and 1s (as opposed to waveforms)

Tx Channel Rxbits

Tx turns bits into waveforms

Channel is the propagation medium that causes distortions and noise

Rx turns the received distorted waveforms to bits again

It is easier to manipulate and store bits than waveforms; thats whydigital is better.

bit estimates

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Wireless Multimedia Communications


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Current Research Trends

Bottleneck: The wireless channel

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Multipath Fading

Reflections cause vectorial combination of received signal

This results in frequent fading

At high data rates multipath fading isfrequency-selective

If the receiver is in motion we also haveDoppler

Hence

Mobility causes Doppler (time-variations)

High-rate signaling causes intersymbol interference (ISI)


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Discrete-Time Model for ISI In digital comm. multipath channel can be modeled in discrete-time

s(n)p(t) h(t) p(-t)

x(n)

Hencex(n) ands(n) can be related by discrete-time convolution:

noiselnslhnxL

l

+==0

)()()(

Discrete-time baseband equivalent model for the ISI channel

Carrier modulation and demodulation is bypassed in baseband eq.

ISI is also present in wired communications (e.g., ADSL)

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ISI Example

)1()()( += nsnsnx

s(n) = +1, -1, +1, +1, -1, -1 +1

x(n) = , 0, 0, 2, 0, -2, 0

x(n) is Nothing like what was transmitted!!! x(n) can be viewed as the output of an LTI system


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How to Eliminate ISI: Equalization

s(n)h(l) g(l)

w(n)

)( ns

Problems with linear equalization in SC systems:

Requires channel estimation (with training sequences)

Channel inversion

Suffers when channel zeros on the unit circle (no stable inverse)

When the channel is long (high rates) the equalizer must be long (complexity)

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The OFDM Concept

Duality: convolution in time is multiplication in frequency There is no ISI anymore!

The channel is experienced in the frequency domain

)()()(

,,1)()()/2()(

H nnn

NknwnsNkHnz kkk

vsDz +=

=+=


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Cyclic Prefix

Cyclic prefix aids in removing the ISI and diagonalizes the channel CP length should be greater than the channel length

Introduces redundancy

Hence greater the channel length implies more redundancy

Ratio of redundant CP length to

Ncan be minimized by making

Nlarge OFDM symbol length (N) is limited by other considerations such as

9 Complexity (FFT length)

9 ICI effects

9 PAR

DataCP

h

N

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History and Context

Basic idea is to use carriers with orthogonal frequencies

Chang66, Saltzberg67 looked into orthogonal carriers (analog)

Weinstein and Ebert, 1971, thought about using the DFT

Kalet89 proposed assigning more bits to stronger subcarriers to increasedata rates for a given performance (Water-Filling) for wired channels

Hybrids of OFDM and CDMA for wireless communications Fazel97

The OFDM literature is rich

Used in wireless LAN standards (laptops in a hotspot)

DAB/DVB in Europe


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Advantages of OFDM

ISI channel can be handled as if we had a narrow-band system (no ISI)

Reduced complexity equalization

Higher-order constellations can be used on stronger subcarriers Higher data rates for a given BER

Requires channel feedback to the Tx, more feasible for wired comm.

NknwnsNkHnz kkk ,,1)()()/2()( =+=

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Disadvantages of OFDM

Presence of channel zeros on the unit circle Requires coding across subcarriers to recover transmitted symbols

Even if channel zeros are close to the UC, performance degrades due to noise amp.

Time variations Channel variations within one OFDM symbol

Presence of a frequency offset

Oscillator phase noise

High peak to average power ratio (dynamic range of transmitted signal)

NkkICInwnsNkHnz kkk ,,1)()()()/2()( =++=


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Channel Estimation

Pilot symbol insertion in time and frequency

Interpolation can take advantage of channel correlation in time and freq.

NknwnsNknHnz kkk ,,1)()()/2;()( =+=

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Channel Equalization

Noise is amplified when there are channel nulls

Error correction coding is necessary

Channel estimation and equalization is much simpler than SC systems

)/2;(/)()()/2;(/)()(

,,1)()()/2;()(

NknHnwnsNknHnzns

NknwnsNknHnz

kkkk

kkk

+==

=+=


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Bit Loading and DMT for ADSL

NknwnsNkHnz kkk ,,1)()()/2()( =+=

In wired comm. channel is time-invariant

Feasible to feedback the CSI to the transmitter

This enables using higher-order constellations (higher rates) at stronger subcarr

Exploitation of all the channel resources

Similar to water-filling of Shannons Information Theory

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DMT Block Diagram


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DMT Bit Loading

Stronger channels get higher order constellations, thus maximizing rate

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Relation between SNR and Bit Loading

Stronger channels get higher order constellations, thus maximizing rate


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Time Domain Equalizer in DMT

The TEQ shortens the effective channel length, allowing a shorter CP

Implying less bandwidth waste on CP length

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ICI in OFDM

By duality, time variations cause ICI in OFDM for wireless


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PAR in OFDM

In SC comm. the dynamic range of the trans. signal is small

In OFDM,Npoint FFT of symbols are transmitted:

=

=1

0

/2)()(N

k

Nknjensnx

Peak value of |x(n)| is proportional toN

Large dynamic range for transmitted signal Expensive power amplifiers at the Tx

Solutions: Coding to reduce PAR

Use variants of OFDM without IFFT at the transmitter

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Diversity Issues in Wireless OFDM

Diversity improves performance over fading channels

The ISI channel offers multiple copies of the Tx signal

OFDM does not exploit multipath diversity

To get diversity with OFDM Hybrids of OFDM and CDMA

Multi-antenna reception in OFDM

Space-time coding combined with OFDM


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Conclusions

Multipath fading and ISI

Elimination of the ISI: Equalization

Basic idea in OFDM

History and context

Advantages and disadvantages of OFDM

Channel estimation and equalization

Bit loading and DMT

Diversity issues

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Multi Carrier and of Dm Systems