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The Communication System midterm Slides
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Communication System
Lecture 4
Lecture 4
Signal space
2
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.
Lecture 4
Schematic example of a signal space
3),()()()(
),()()()(
),()()()(
),()()()(
212211
323132321313
222122221212
121112121111
zztztztz
aatatats
aatatats
aatatats
z
s
s
s
)(1 t
)(2 t),( 12111 aas
),( 22212 aas
),( 32313 aas
),( 21 zzz
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 symbolsBlind Channel EstimationSemi-Blind Channel EstimationPilot Assisted Channel Estimation
Lecture 65
EqualizationISI due to filtering effect of the
communications channel (e.g. wireless channels)Channels behave like band-limited filters
)()()( fjcc
cefHfH
Non-constant amplitude
Amplitude distortion
Non-linear phase
Phase distortion
Types of Channel
Slow Fading ChannelChannel impulse response variations are slowPilot Symbols are transmitted less frequently
Fast FadingChannel Impulse response variations are fastPilot 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
