College of Information & Communications
0
Wireless everywhere!
Hanyang University
Digital Communications(by B. Sklar)
Sung Ho Cho
(Voice) 02‐2220‐0390(Cellular) 011‐412‐5178
E‐mail: [email protected]
1
College of Information & Communications Hanyang University
Wireless everywhere!
Contents
Signals and SpectraFormatting and Baseband TransmissionBandpass Modulation and DemodulationChannel CodingModulation and Coding Trade‐offsSpread‐Spectrum Techniques
College of Information & Communications
2
Wireless everywhere!
Hanyang University
Signals and Spectra
3
College of Information & Communications Hanyang University
Wireless everywhere!
Analog & Digital Communications
Analog Communications
Digital Communications
Modulation
AnalogInformation
Channel Demodulation
AnalogInformation
DigitalInformation
Channel
DigitalInformation
ADCModulation DAC
Waveguide
WaveguideWire
Free space
Demodulation
4
College of Information & Communications Hanyang University
Wireless everywhere!
Why Digital?
More reliableMore flexibleSimpler
Example: A Regenerative Repeater
5
College of Information & Communications Hanyang University
Wireless everywhere!
A Typical Digital Communication System
Format SourceEncode Encrypt Channel
Encode Multiplex Modulate FrequencySpread
MultipleAccess XMT
Format SourceDecode Decrypt Channel
DecodeDe‐
multiplexDe‐
modulateFrequencyDespread
MultipleAccess RCV
InformationSource
SourceBits
ChannelBits
From OtherSources
To OtherDestinations
ChannelBits
SourceBits
Channel
InformationSink
DigitalInput
DigitalOutput
SynchronizationBitStream
DigitalWaveform
Adaptation CarrierErrorCorrection
Protection PrivacyCompanion SocietyMake‐up WeightControl
6
College of Information & Communications Hanyang University
Wireless everywhere!
Brief Description of Digital Communication Systems
7
College of Information & Communications Hanyang University
Wireless everywhere!
Notations (1/3)
Information Source:AnalogDiscrete
Textual Message:A sequence of charactersEx)
Character:A member of an alphabet or set of symbolsASCII, EBCDIC, MorseEx)
Binary Digit (Bit):The fundamental information unit“1” and/or “0”
8
College of Information & Communications Hanyang University
Wireless everywhere!
Notations (2/3)
Bit stream:A sequence of binary digitsOften called a “baseband signal”Ex) 7‐bit ASCII
Symbol:A digital messageA group of k bits M = 2k (M = size of the alphabet)Baud = symbol rateEx)
9
College of Information & Communications Hanyang University
Wireless everywhere!
Notations (3/3)Digital Waveform:
A voltage of current waveform that represents a digital symbolEx)
Data Rate:Bit rate Rb: Rb = 1/Tb (bits/s) (Tb = Bit duration)Symbol rate (Baud) R : R = 1/T (symbols/s) (T = Symbol duration)Relationship between Rb and R:
R = Rb / k or Rb = kR = R log2M
Performance Criteria (Figure of Merit):Analog communications:
SNR, Percent distortion, Mean‐square errorDigital Communications:
BER, SEP, Bandwidth efficiency
10
College of Information & Communications Hanyang University
Wireless everywhere!
Classification of Signals (1/3)
Deterministic Signal vs. Random Signal
Periodic Signal vs. Nonperiodic Signal
Analog Signal vs. Discrete Signal
Energy Signal vs. Power SignalEnergy signal:
Power signal:
Finite energy, but zero average power
Finite power, but infinite energy
11
College of Information & Communications Hanyang University
Wireless everywhere!
Classification of Signals (2/3)
Impulse FunctionsDirac Delta Function:
Kronecker Delta Function
Unit Step Functions
⎩⎨⎧
≠=
≠0001
)(tt
tδ
∫∞∞−
=1)( dttδ
t
1
)(tδ
⎩⎨⎧
≠=
=0001
)(nn
nδn
1
)(nδ
⎩⎨⎧
<≥
=−== ∫∫∞
∞− 0001
)()()( 0 tt
dtdtu t ττδττδ
⎩⎨⎧
<≥
=−== ∑∑∞
=−∞= 0001
)()()(0 n
nknknu
k
n
kδδ
u(n)
t
u(t)
1
n
1...
12
College of Information & Communications Hanyang University
Wireless everywhere!
Classification of Signals (3/3)
Some Mathematics:
For any x(t) or x(n)
)()( ttudtd δ= )()( 00 ttttu
dtd
−=− δαα
)()1()( nnunu δ=−−
)()( tt −= δδ )()( nn −= δδ
)()()()( 000 tttxtttx −=− δδ
)()()()( 000 nnnxnnnx −=− δδ
ττδτ dtxtx )()()( −= ∫∞∞−
)()()( knkxnxk
−= ∑∞
−∞=δ
)()( tt −=− τδτδ )()( nkkn −=− δδ
13
College of Information & Communications Hanyang University
Wireless everywhere!
Spectral Density
Energy Spectral Density (ESD):
Total Energy:
Power Spectral Density (PSD):
For periodic signals
For nonperiodic signals
Average Power:
Fourier series coefficient
Truncated version
14
College of Information & Communications Hanyang University
Wireless everywhere!
Autocorrelation
For energy signals:
For power signals:
15
College of Information & Communications Hanyang University
Wireless everywhere!
Random Variables
Random Variable X: “A functional relationship between a random event and a real number”
Distribution Function:
Probability Density Function (pdf):
Computation of Probability Using pdf:
16
College of Information & Communications Hanyang University
Wireless everywhere!
Ensemble Averages
Mean Value (or Expected Value):
Moment:
Variance:
17
College of Information & Communications Hanyang University
Wireless everywhere!
Random ProcessesX(t): A representation of the random variable as a function of time
Ensemble of the Random Processes:
Mean of the Random Process:
Autocorrelation Function:
Ensemble Average
Time Average
18
College of Information & Communications Hanyang University
Wireless everywhere!
StationarityStrict‐Sense Stationary (SSS): All the statistics do not change with time.
Wide‐Sense Stationary (WSS):
Autocorrelation of a WSS Process:
19
College of Information & Communications Hanyang University
Wireless everywhere!
Time Averaging and Ergodicity
Ergodic Process: Time Average = Statistical Average
Ergodic in the Mean:
Ergodic in the Autocorrelation Function:
20
College of Information & Communications Hanyang University
Wireless everywhere!
PSD and Autocorrelation (1/3)
21
College of Information & Communications Hanyang University
Wireless everywhere!
PSD and Autocorrelation (2/3)
Example 1:
22
College of Information & Communications Hanyang University
Wireless everywhere!
PSD and Autocorrelation (3/3)
Example 2:
23
College of Information & Communications Hanyang University
Wireless everywhere!
Noise in Communication Systems
A zero‐mean Gaussian random process n(t):
24
College of Information & Communications Hanyang University
Wireless everywhere!
White Noise
PDF:
Autocorrelation:
Average Power: