Multi Carrier and of Dm Systems
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Transcript of 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