Models

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Models

• Communication Information Theory
• Signal Model
• Channel Model

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Model

• Communication Information Theory

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Information Theory Model
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Baseband Processing Inner and Outer Receiver
Modulator

Channnel
Demodultor
Outer Receiver
Inner Receiver Channel Estimator Synchronizer
Equalizer
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Bit-Interleaved Coded Modulation BICM

• Complete Channel State Information (C-CSI)
• Gray Mapping and Interleaving
• Mutual Information (Capacity)
• Partial Channel State Information (P-CSI)
• Channel with Pilot Sequences
• Mutual information using P- CSI
• Example Uniform Channel Sampling
• Extension to MIMO Systems

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Bit-Interleaved Coded Modulation BICM
m-bits define a symbol
Due to the interleaving the input bits to the
mapper are approx. independent
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16-QAM Constellation Gray Mapping
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R
e

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Capacity C of BICM and CM
CMCoded Modulation .....BICM (Gray Mapping)
Bits/Dimension
SNR
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Perfect Channel State Information C-CSI

• Since the channel is perfectly known it is
  memoryless
• The capacity C? is independent of the channel
  dynamics

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Channel with incomplete State Information P-CSI
Simple Idea Use part of the channel capacity
for channel estimation
Information Sympols
Known Training Sympols
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P-CSI Channel Definition
Completely defines the channel
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P-CSI Capacity C
Using the chain rule of mutual information we
obtain..
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P-CSI Capacity C
The channel has memory. But interleaving...
.......makes it memoryless
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Incomplete Channel State Information P-CSI

• Looks like a channel with perfect state
  information but with decreased useful signal and
  increased noise variance !

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Channel Estimate
By construction, z(k) and z(T) are jointly
gaussian (conditioned on the symbols)
Mean
Variance
Note ... is the LMMSE estimate
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Equivalent P-CSI Channel

• Looks like a channel with perfect channel
  knowledge with decreased useful signal and
  increased noise variance !

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Equival.Partial Channel Knowledge P-CSI
Variance of the channel sample c(k)
Variance of the estimation error e(k)
Variance of the channel estimate
Decreased useful signal
Increased noise variance
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ExampleUniform Channel sampling
Information bits
Channel estimation symbols a(T)
SNR degradation due to channel estimation errors
and to bandwidth reduction
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Performance Degradation
SNR degradation due to channel estimation errors
Bandwith reduction due to bandwidth reduction
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Total Loss Factor ?
?Normalized Doppler-Bandwidth ? Average
Signal-to- Noise ratio F Pilot Symbol Period
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Performance factor ?
It pays to spend more capacity for channel
estimation !
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No Capacity is lost for ?? 0
Sampling rate above Nyquist is required. Here we
have chosen the optimimum rate F(opt)
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MIMO Model
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(No Transcript)
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Extension to MIMO Systems Possible ?

• YES