1. Communication System Overview
Gwo-Ruey Lee

2. Outlines
Communication System
Digital Communication System
Modulation

3. Communication System 1/6 Input Transducer Transmitter Channel Receiver
Output Transducer

4. Communication System 2/6 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.

5. Communication System 3/6 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

6. Communication System 4/6 Channel Different forms
The signal undergoes degradation from transmitter to receiver
Noise, fading, interference……

7. Communication System 5/6 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

8. Communication System 6/6 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

9. Digital Communication System
1/6

10. Digital Communication System
2/6
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

11. Digital Communication System
3/6
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

12. Digital Communication System
4/6
Error Control Coding
Linear block code
Convolutional code
RS code
Modulation Coding
Trellis code
Turbo code

13. Digital Communication System
5/6
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

14. Digital Communication System
6/6
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

15. Modulation 1/10 Analog Modulation Pulse Modulation Digital ModulationAM FM PM
Pulse Modulation
PAM / PPM / PCM / PWM
Digital Modulation
ASK
FSK
PSK
QAM
Carrier:
Amplitude
Frequency
Phase

16. Modulation 2/10 Mapping Modulation type
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)

17. Modulation 3/10 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

18. Modulation
4/10
An example of signal-space diagram for 8-PSK

19. Modulation 5/10 Phase shift keying where BPSK QPSK with Gray code
M-ary PSK
where

20. Modulation
6/10
BER versus SNR curves in AWGN channel using BPSK, QPSK, 8-PSK,16-PSK .

21. Modulation 7/10 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

22. Modulation
8/10
An example of signal-space diagram for 16-square QAM.

23. Modulation
9/10
QAM

24. Modulation
10/10
BER versus SNR curves in AWGN channel using BPSK/QPSK, 16QAM, 64QAM, 256QAM.

25. Communication System Overview
Readings
Any book about communications

26. Random Process/ Stochastic Process

27. Outlines 1/10 Basic Concepts Stationary Process
Transmission over Linear Time-Invariant (LTI) Systems

28. Basic Concepts 2/10 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…..

29. Basic Concepts 3/10 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.)
Real line

30. Basic Concepts 4/10 Random Process (r.p.) r.v.
A random process is the mapping of the outcomes in into a set of real valued functions of time, called sample function
r.v.
: ensemble
: sample function
(or a realization)
: r.v.
: numerical value

31. Basic Concepts 5/10 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

32. Basic Concepts 6/10 Classification of random process
Continuous random process
Discrete random process
Continuous random sequence
Discrete random sequence

33. Basic Concepts 7/10 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.)

34. Basic Concepts 8/10 Autocovariance Cross-correlation
If and are orthogonal 
If and are statistically uncorrelated 

35. Basic Concepts 9/10 Crosscovariance
The autocorrelation function of a real WSS process is

36. Basic Concepts
10/10
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.

37. Stationary Process 1/9 Stationary Stationary Process
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

38. Stationary Process 2/9 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

39. Stationary Process
3/9
A example of 2nd-order stationary

40. Stationary Process 4/9 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.

41. Stationary Process 5/9 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.

42. Stationary Process 6/9 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 )

43. Stationary Process 7/9 Wide-Sense Cyclostationary
A random process with and is wide-sense cyclostationary if
Its mean satisfies
Its a.F. satisfies

44. Stationary Process 8/9 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

45. Stationary Process 9/9 The relationship between ergodic and stationary
Ergodic  stationary (True)
Ergodic  stationary (Fault)

46. Transmission over LTI Systems
1/3
Linear Time-Invariant (LTI) Systems

47. Transmission over LTI Systems
2/3
Assumptions:
and are real-valued and is WSS.
The mean of the output
The cross-correlation function

48. Transmission over LTI Systems
3/3
The A.F. of the output
The PSD of the output

49. Random Process/ Stochastic Process
Readings
Communication Systems, 4th edition, Simon Haykin, Wiley
Chapter 1 – 1.1 ~1.7, 1.8