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Communication System
Lecture 4
Signal space
Lecture 42
What is a signal space?
Vector representations of signals in an N-dimensional
orthogonal space
Why do we need a signal space?
It is a means to convert signals to vectors and vice versa.
It is a means to calculate signals energy and Euclidean
distances between signals.
Why are we interested in Euclidean distances between
signals?
For detection purposes: The received signal is transformed to a
received vectors. The signal which has the minimum distance to
the received signal is estimated as the transmitted signal.
Schematic example of a signal space
Lecture 43
),()()()(
),()()()(
),()()()(
),()()()(
212211
323132321313
222122221212
121112121111
zztztztz
aatatats
aatatats
aatatats




z
s
s
s




)(1 t
)(2 t
),( 12111 aas
),( 22212 aas
),( 32313 aas
),( 21 zzz
Transmitted signal
alternatives
Received signal at
matched filter output
Channel Estimation
Channel Estimation is the process that takes
place before equalization in the communication
system
Types based on the density of Training symbols
Blind Channel Estimation
Semi-Blind Channel Estimation
Pilot Assisted Channel Estimation
Lecture 65
Equalization
ISI due to filtering effect of the communications
channel (e.g. wireless channels)
Channels behave like band-limited filters
)(
)()( fj
cc
c
efHfH 

Non-constant amplitude
Amplitude distortion
Non-linear phase
Phase distortion
Types of Channel
Slow Fading Channel
Channel impulse response variations are slow
Pilot Symbols are transmitted less frequently
Fast Fading
Channel Impulse response variations are fast
Pilot symbols are transmitted more frequently
Examples of Pilots Arrangement for
Slow and Fast Fading Channel in
OFDM
Block-Type Channel Estimation
Block-Type channel Estimation is used for Slow
fading channels
The channel impulse response is assumed
constant for a Block period of time
Comb-Type Channel Estimation
Pilot Symbols are transmitted more frequently for
effective estimation of the rapid channel impulse
variations
The channel Impulse response varies from
OFDM symbol to symbol
Lecture 610
Equalization: Channel examples
Example of a frequency selective, slowly changing (slow fading)
channel for a user at 35 km/h
Lecture 611
Equalization: Channel examples
…
Example of a frequency selective, fast changing (fast fading)
channel for a user at 35 km/h

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Slides4The Communication System midterm Slides

  • 2. Signal space Lecture 42 What is a signal space? Vector representations of signals in an N-dimensional orthogonal space Why do we need a signal space? It is a means to convert signals to vectors and vice versa. It is a means to calculate signals energy and Euclidean distances between signals. Why are we interested in Euclidean distances between signals? For detection purposes: The received signal is transformed to a received vectors. The signal which has the minimum distance to the received signal is estimated as the transmitted signal.
  • 3. Schematic example of a signal space Lecture 43 ),()()()( ),()()()( ),()()()( ),()()()( 212211 323132321313 222122221212 121112121111 zztztztz aatatats aatatats aatatats     z s s s     )(1 t )(2 t ),( 12111 aas ),( 22212 aas ),( 32313 aas ),( 21 zzz Transmitted signal alternatives Received signal at matched filter output
  • 4. Channel Estimation Channel Estimation is the process that takes place before equalization in the communication system Types based on the density of Training symbols Blind Channel Estimation Semi-Blind Channel Estimation Pilot Assisted Channel Estimation
  • 5. Lecture 65 Equalization ISI due to filtering effect of the communications channel (e.g. wireless channels) Channels behave like band-limited filters )( )()( fj cc c efHfH   Non-constant amplitude Amplitude distortion Non-linear phase Phase distortion
  • 6. Types of Channel Slow Fading Channel Channel impulse response variations are slow Pilot Symbols are transmitted less frequently Fast Fading Channel Impulse response variations are fast Pilot symbols are transmitted more frequently
  • 7. Examples of Pilots Arrangement for Slow and Fast Fading Channel in OFDM
  • 8. Block-Type Channel Estimation Block-Type channel Estimation is used for Slow fading channels The channel impulse response is assumed constant for a Block period of time
  • 9. Comb-Type Channel Estimation Pilot Symbols are transmitted more frequently for effective estimation of the rapid channel impulse variations The channel Impulse response varies from OFDM symbol to symbol
  • 10. Lecture 610 Equalization: Channel examples Example of a frequency selective, slowly changing (slow fading) channel for a user at 35 km/h
  • 11. Lecture 611 Equalization: Channel examples … Example of a frequency selective, fast changing (fast fading) channel for a user at 35 km/h