Communication System Overview

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Communication System Overview

• Gwo-Ruey Lee

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Outlines

• Communication System
• Digital Communication System
• Modulation

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Communication System
1/6

• Input Transducer
• Transmitter
• Channel
• Receiver
• Output Transducer

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Communication System
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• Input transducer
• Messages can be categorized as analog (continuous
  form)or digital (discrete form).
• The message produced by a source must be
  converted by a transducer to a form suitable for
  the particular type of communication system
  employed.

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Communication System
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• Transmitter
• The purpose of the transmitter is to couple the
  message to the channel.
• Modulation
• For ease of radiation
• to reduce noise and interference
• For channel assignment
• For multiplexing or transmission of several
  message over a single channel
• To overcome equipment limitation

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Communication System
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• Channel
• Different forms
• The signal undergoes degradation from transmitter
  to receiver
• Noise, fading, interference

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Communication System
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• Receiver
• The receiver is to extract the desired message
  from the received signal at the channel output
  and to convert it to a form suitable for the
  output transducer
• Demodulation

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Communication System
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• Output Transducer
• The output transducer completes the
  communication system
• The device converts the electric signal at its
  input into the form desired for the system user

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Digital Communication System
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Digital Communication System
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• Source Encoder/ Decoder
• The purpose of source coding is to reduce the
  number of bits required to convey the information
  provided by the information source.
• The task of source coding is to represent the
  source information with the minimum of symbols.
• High compression rates (Good compression rates)
  make be achieved with source encoding with
  lossless or little loss of information.
• Source Coding
• Fixed-length coding
• Pulse-code modulation (PCM)
• Differential Pulse-code modulation (DPCM)
• Variable-length coding
• Huffman Coding/ entropy coding

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Digital Communication System
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• Channel Encoder/ Decoder
• A way of encoding data in a communications
  channel that adds patterns of redundancy into the
  transmission path in order to lower the error
  rate.
• The task of channel coding is to represent the
  source information in a manner that minimizes the
  error probability in decoding.
• Error Control Coding
• Error detection coding
• Error correct coding

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Digital Communication System
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• Error Control Coding
• Linear block code
• Convolutional code
• RS code
• Modulation Coding
• Trellis code
• Turbo code

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Digital Communication System
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• Synchronization
• Symbol/ Timing synchronization
• Frequency synchronization
• Carrier frequency synchronization
• Sampling frequency synchronization
• Two basic types of synchronization
• Data-aid algorithm
• Training sequences
• Preambles
• Non-data-aid algorithm
• Blind

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Digital Communication System
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• Channel Estimation
• A channel estimate is only a mathematical
  estimation of what is truly happening in nature.
• Allows the receiver to approximate the effect of
  the channel on the signal.
• The channel estimate is essential for removing
  inter symbol interference, noise rejection
  techniques etc.
• Two basic types of channel estimation methods
• Data-aid algorithm
• Training sequences
• pilots
• Non-data-aid algorithm
• Blind

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Modulation
1/10

• Analog Modulation
• AM
• FM
• PM
• Pulse Modulation
• PAM / PPM / PCM / PWM
• Digital Modulation
• ASK
• FSK
• PSK
• QAM

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Modulation
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• Mapping
• The process of mapping the information bits onto
  the signal constellation plays a fundamental role
  in determining the properties of the modulation
• Modulation type
• Phase shift keying (PSK)
• Quadrature Amplitude Modulation (QAM)

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Modulation
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• M-ary Phase Shift Keying
• Consider M-ary phase-shift keying (M-PSK) for
  which the signal set is
• where is the signal energy per symbol,
  is the symbol duration, and is the
  carrier frequency.
• This phase of the carrier takes on one of the M
  possible values, namely,
  , where .

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Modulation
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• An example of signal-space diagram for 8-PSK

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Modulation
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• Phase shift keying
• BPSK
• QPSK with Gray code
• M-ary PSK
• where

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Modulation
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• BER versus SNR curves in AWGN channel using BPSK,
  QPSK, 8-PSK,16-PSK .

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Modulation
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• Quadrature Amplitude Modulation
• The transmitted M-ary QAM signal for symbol n can
  be expressed as
• where E is the energy of the signal with the
  lowest amplitude, and , and
  are amplitudes taking on the values
• Note that M is assumed to be a power of 4.
• The parameter a can be related to the average
  signal energy ( ) by

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Modulation
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• An example of signal-space diagram for 16-square
  QAM.

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Modulation
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• QAM

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Modulation
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• BER versus SNR curves in AWGN channel using
  BPSK/QPSK, 16QAM, 64QAM, 256QAM.

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Communication System Overview

• Readings
• Any book about communications

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Random Process/ Stochastic Process
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Outlines
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• Basic Concepts
• Stationary Process
• Transmission over Linear Time-Invariant (LTI)
  Systems

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Basic Concepts
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• Why study random processes?
• Due to the uncertainty of 1. noise and 2. the
  unpredictable nature of information itself.
• Information signal usually is randomlike
• We can not predict the exact value of the signal
• Signal must be distributed by its statistical
  properties.
• Ex mean, variance..

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Basic Concepts
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• Random Variable (r.v.)
• Consider an experiment with sample space . The
  element of are the random outcomes, , of
  the experiment. If to every , we assign a
  real value , such a rule is
  called a random variable (r.v.)

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Basic Concepts
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• Random Process (r.p.)
• A random process is the mapping of the outcomes
  in into a set of real valued functions of
  time, called sample function .

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Basic Concepts
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• Classification of random process
• From the perspective of time
• Random process
• for , t has a continuous of values
• Random sequence
• for , t can take on a finite or
  countably infinite number of values ?
• From the perspective of the value of
• Continuous
• can take on a continuous of values
• Discrete
• Values of are countable

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Basic Concepts
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• Classification of random process
• Continuous random process
• Discrete random process
• Continuous random sequence
• Discrete random sequence

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Basic Concepts
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• 1st-order distributions function
• It describes the instantaneous amplitude
  distribution of a random process
• Mean
• 2nd-order distributions function
• It distributes the structure of the signal in
  the time domain
• Autocorrelation Function (A.F.)

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Basic Concepts
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• Autocovariance
• Cross-correlation
• If and are orthogonal ?
• If and are statistically
  uncorrelated ?

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Basic Concepts
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• Crosscovariance
• The autocorrelation function of a real WSS
  process is

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Basic Concepts
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• The cross-correlation function of two real WSS
  process
• and is
• If and are orthogonal ?
• If and are statistically
  uncorrelated ?
• Power Spectral Density (PSD)
• PSD represents the distribution of signal
  strength (ie, energy or power) with frequency
• The PSD of WSS process is the Fourier
  transform (FT) of the A.F.

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Stationary Process
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• Stationary
• A random process whose statistical properties do
  not change over time
• Stationary Process
• Strictly-Sense Stationary (SSS)
• Wide-Sense Stationary (WSS)
• Strictly-Sense Cyclostationary
• Wide-Sense Cyclostationary

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Stationary Process
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• Strictly-Sense Stationary (SSS)
• A nth-order strictly-sense stationary process is
  a process in which for all , all
  , and all
• Note Mth-order stationary of the above equation
  holds for all .
• Example 2nd-order SSS process ? 1st-order SSS
  process

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Stationary Process
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• A example of 2nd-order stationary

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Stationary Process
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• Wide-Sense Stationary (WSS)
• A random process is wide-sense
  stationary process (WSS) if
• Its mean is constant
• Its A.F. depends only on the time difference.

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Stationary Process
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• The relationship between SSS and WSS
• SSS ? WSS (True)
• SSS ? WSS (Fault)
• 1st-order SSS ?
• 2nd-order SSS ?
• For Gaussian process SSS ? WSS
• Since the joint-Gaussian pdf is completely
  specified by its mean and A.F.

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Stationary Process
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• Strictly-Sense Cyclostationary
• A nth-order strictly-sense cyclostationary
  process is a process in which for all , all
  , and integer m
• ( mT is integer multiples of period T )

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Stationary Process
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• Wide-Sense Cyclostationary
• A random process with and
  is wide-sense cyclostationary if
• Its mean satisfies
• Its A.F. satisfies

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Stationary Process
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• Ergodic Process
• A random process is strictly ergodic process if
  all time and ensemble (statistical) average are
  interchangeable including mean, A.F. PSD, etc.
• A random process is wise-sense ergodic if it it
  ergodic in the mean and the A.F.
• mean ergodic
• A.F. ergodic

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Stationary Process
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• The relationship between ergodic and stationary
• Ergodic ? stationary (True)
• Ergodic ? stationary (Fault)

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Transmission over LTI Systems
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• Linear Time-Invariant (LTI) Systems

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Transmission over LTI Systems
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• Assumptions
• and are real-valued and
  is WSS.
• The mean of the output
• The cross-correlation function

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Transmission over LTI Systems
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• The A.F. of the output
• The PSD of the output

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Random Process/ Stochastic Process

• Readings
• Communication Systems, 4th edition, Simon Haykin,
  Wiley
• Chapter 1 1.1 1.7, 1.8