week1 introductiontodigitalcommunications...
TRANSCRIPT
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EE4601Communication Systems
Week 1
Introduction to Digital CommunicationsChannel Capacity
0 c©2011, Georgia Institute of Technology (lect1 1)
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Contact Information
• Office: Centergy 5138
• Phone: 404 894 2923
• Fax: 404 894 7883
• Email: [email protected] (the best way to contact me)
• Web: http://www.ece.gatech.edu/users/stuber/4601
• Office Hours: TBA
0 c©2011, Georgia Institute of Technology (lect1 2)
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Introduction
Digital communications is the exchange of information using a finite set of signalwaveforms. This is in contrast to analog communication (e.g., AM/FM radio)which do not use a finite set of signals.
Why use digital communications:
• Natural choice for digital sources, e.g., computer communications.
• Source encoding or data compression techniques can reduce the required
transmission bandwidth with a controlled amount of message distortion.
• Digital signals are more robust to channel impairments than analog signals.
– noise, co-channel and adjacent channel interference, multipath-fading.
– surface defects in recording media such as optical and magnetic disks.
• Higher bandwidth efficiency than analog signals.
• Encryption and multiplexing is easier.
• Benefit from well known digital signal processing techniques.
0 c©2011, Georgia Institute of Technology (lect1 3)
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Protocol Stack (cdma2000 EV-DO)Overview 3GPP2 C.S0024 Ver 4.0
Air LinkManagement
Protocol
OverheadMessagesProtocol
PacketConsolidation
Protocol
InitializationState Protocol
Idle StateProtocol
ConnectedState Protocol
Route UpdateProtocol
SessionManagement
Protocol
SessionConfiguration
Protocol
StreamProtocol
SignalingLink
Protocol
Radio LinkProtocol
SignalingNetworkProtocol
ControlChannel MAC
Protocol
Access ChannelMAC Protocol
Reverse TrafficChannel MAC
Protocol
Forward TrafficChannel MAC
Protocol
ConnectionLayer
SessionLayer
StreamLayer
ApplicationLayer
MACLayer
SecurityLayer
PhysicalLayer
SecurityProtocol
AuthenticationProtocol
EncryptionProtocol
Default PacketApplication
Default SignalingApplication
LocationUpdateProtocol
AddressManagement
Protocol
KeyExchangeProtocol
Physical LayerProtocol
FlowControlProtocol
1
Figure 1.6.6-1. Default Protocols 2
3
• This course concentrates on the Physical Layer or PHY Layer.
0 c©2011, Georgia Institute of Technology (lect1 4)
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Cellular Radio Chipset
P r o d u c t B r i e f
A p p l i c a t i o n E x a m p l e Q u a d - B a n d E G P R S S o l u t i o n
Power BusPeripherals
I2CInterface
Power BusBaseband
I2C
AC-Adaptor
Charger
Pre-Charge
VBB2
VRTC
VBB1
VMemory
VBB USB
VBB Analog
VBB I/O Hi
VUSB Host
SM-POWER(PMB 6811)
Control
BB (LR)/Mem/CoproStep down 600 mA
On-chipReference
VBT BB
VRF3 (BT)
VRF Main
VRF VCXO
AmpVDD
LEDDriver
MotorDriver
M
NiMH/LiIonBattery
Power BusBluetooth
Power BusRF
S-GOLD2(PMB 8876)
DA
A
AD
D
I2S / DAII2S SSC
TEAKLite®
GPTU IR-Memory
GSMCipher Unit
RFControl
Speechand Channel
DecodingEqualizer
DA
AD
Speechand Channel
Encoding
8 PSK/GMSKModulator
DA
AD
SRAM
MOVE Copro
DMAC ICUKeypad
USB FSOTG
FastIrDA
MMC/SDIF
CAPCOM
GPTU
RTC
I2C
JTAG
AUXADC
SCCU
FCDP
EBU
GSMTimer
GEA-1/2/3 CGUAFC
GPIOs
ARM®926 EJ-SUSIM
USARTsSSCUSIFCamera
IFDisplay
IF
Multimedia IC IF
FLASH/SDRAM
SMARTi DC+(PMB 6258) GSM 900/1800
GSM 850/1900
AtomaticOffset
Compensation
ControlLogic
SAMFast PLL
850
900
1800
1900
Rx/Tx
Multi ModePA
850900
18001900
I
Q
CLK
DAT
ENA
AFC
RF Control
26 MHz
Car Kit
Earpiece
Ringer
Headset
MU
X
0* #
321
8
54
7
SDC
MMC
6
9
• This course concentrates on the digital baseband;baseband modulation/demodulation.
0 c©2011, Georgia Institute of Technology (lect1 5)
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Course Objectives
1. Brief review of probability and introduction to random processes.
• message waveforms, transmission media or waveform channels, noise andinterference are all random processes.
2. Mathematical modelling and characterization of physical communication
channels, signals and noise.
3. Design of digital waveforms and associated receiver structures for recoveringchannel-corrupted digital signals.
• emphasis will be on waveform design, receiver processing, and perfor-
mance analysis for “additive white Gaussian noise (AWGN) channels.”
• mathematical foundations are essential for effective physical layer mod-
elling, waveform design, receiver design, etc.
• communication signal processing is a key element of this course. Our
focus will be on the “digital baseband” and not the “analog RF.”
0 c©2011, Georgia Institute of Technology (lect1 6)
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Basic digital communication system
source
sink
sourceencoder
sourcedecoder
channelencoder
channeldecoder
digitalmodulator
demodulatordigital
waveformchannel
0 c©2011, Georgia Institute of Technology (lect1 7)
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Some Types of Waveform Channels
• wireline channels, e.g., twisted copper pair, coaxial cable, power line
• fiber optic channels (not considered in this course)
• wireless (radio) channels
– line-of-sight (satellite, land microwave radio)
– non-line-of-sight (cellular, wireless LAN)
• underwater acoustic channels (submarine communication)
• storage channels, e.g., optical and magnetic disks.
– communication from the present to the future.
0 c©2011, Georgia Institute of Technology (lect1 8)
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Mathematical Channel Models
Additive White Gaussian Noise Channel (AWGN):
S (f)nN /2o
-W 0 W
+s(t)
n(t)
r(t) = s(t) + n(t)
Receiver thermal noise can be modeled as spectrally flat or “white.”
Thermal noise power in bandwith W is
No
2· 2 ·W = NoW Watts
At any time instant t0, the noise waveform n(t0) is a Gaussian random variablewith zero mean and variance NoW .
For a given channel input s(t0), the channel output r(t0) is also a Gaussianrandom variable with mean s(t0) and variance NoW .
0 c©2011, Georgia Institute of Technology (lect1 9)
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Mathematical Channel Models
Linear Filter Channel:
c(t)s(t)
n(t)
+*r(t) = s(t) c(t) + n(t)
An ideal channel has impulse response c(t) = αδ(t− t0) and, therefore,
r(t) = αs(t− to) + n(t)
An ideal channel only attenuates and delays a signal, but otherwise leaves itundistorted. The channel transfer function is
C(f) = F [c(t)] = αe−j2πfto, |f | < B
where B is the system bandwidth.
• The magnitude response |C(f)| = α is flat in frequency f .
• The phase response 6 C(f) = −2πfto is linear in frequency f .
0 c©2011, Georgia Institute of Technology (lect1 10)
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Mathematical Channel Models
Two-Ray Multi-path Channel:
Suppose r(t) = αs(t) + βs(t− τ).
Since r(t) = s(t) ∗ c(t), we have c(t) = αδ(t) + βδ(t− τ).
Hence C(f) = α + βe−j2πfτ .
Using |C(f)|2 = C(f)C∗(f), we can obtain
|C(f)| =√
α2 + β2 + 2αβ cos(2πfτ)
Using the Euler identity, ejθ = cos(θ) + j sin(θ), we have
6 (C(f) = −Tan−1β sin(2πfτ)
α+ β cos(2πfτ)
0 c©2011, Georgia Institute of Technology (lect1 11)
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Mathematical Channel Models
Two-Ray Multi-path Channel:
Suppose α = β = 1. Then
|C(f)| =√
2 + 2 cos(2πfτ)
6 C(f) = −Tan−1sin(2πfτ)
1 + cos(2πfτ)
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0.2
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1
1.2
1.4
1.6
1.8
2
fτ
|C(f
)|
0 0.5 1 1.5 2 2.5 3 3.5 4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
fτ
∠ C
(f)
radi
ans
Observe that the multi-path channel is frequency selective.
0 c©2011, Georgia Institute of Technology (lect1 12)
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Mathematical Channel Models
Two-Ray Fading Channel:
Suppose we transmit s(t) = cos(2πfot) and the received waveform is
r(t) = α cos(2πfot) + β cos(2π(fo + fd)t), where fd is a “Doppler” shift.
Using the complex phaser representation of sinusoids, we can write
r(t) = A(t) cos(2πfot+ φ(t))
where
A(t) =√
α2 + β2 + 2αβ cos(2πfdt)
φ(t) = −Tan−1β sin(2πfdt)
α + β cos(2πfdt)
0 c©2011, Georgia Institute of Technology (lect1 13)
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Mathematical Channel Models
Two-Ray Fading Channel:
Suppose α = β = 1. Then
A(t) =√
2 + 2 cos(2πfdt)
φ(t) = −Tan−1sin(2πfdt)
1 + cos(2πfdt)
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0.2
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1
1.2
1.4
1.6
1.8
2
fd t
|A(t
)|
0 0.5 1 1.5 2 2.5 3 3.5 4−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
fd t
φ (t
) ra
dian
s
Observe that the fading channel is time varying.
0 c©2011, Georgia Institute of Technology (lect1 14)
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Shannon Capacity of a Channel
Claude Shannon in his paper “A Mathematical Theory of Communication”BSTJ, 1948, proved that every physical channel has a capacity, C, defined as
the maximum possible rate that information can be transmitted over the channelwith an arbitrary reliability.
Arbitrary reliability means that the probability of information bit error or biterror rate (BER) can be made as small as desired.
Conversely, information cannot be transmitted reliably over a channel at any
rate greater than the channel capacity, C. The BER will be bounded from zero.
The channel capacity depends on the channel transfer function and the receivedbit energy-to-noise ratio (Eb/No).
Arbitrary reliability can be realized in practice by using forward error correction(FEC) coding techniques.
0 c©2012, Georgia Institute of Technology (lect1 15)
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Coding Channel and Capacity
The channel capacity depends only on the coding channel, defined as the portionof the communication system that is “seen” by the coding system.
The input to the coding channel is the output of the channel encoder.
The output of the coding channel is the input to the channel decoder.
In practice, the coding channel inputs are often chosen from a digital modula-
tion alphabet, while the coding channel outputs are continuous valued decision
variables generated by sampling the corresponding matched filter outputs in thereceiver.
Encoder
Decoder
Coding Channel
0 c©2011, Georgia Institute of Technology (lect1 16)
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AWGN Channel
S (f)nN /2o
-W 0 W
+s(t)
n(t)
r(t) = s(t) + n(t)
For the AWGN channel, the capacity is
C = W log2
(
1 +P
NoW
)
W = channel bandwidth (Hz)
P = constrained input signal power (watts)
No = one-sided noise power spectral density (watts/Hz)
No/2 = two-sided noise power spectral density (watts/Hz)
0 c©2012, Georgia Institute of Technology (lect1 17)
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Capacity of the AWGN Channel
Dividing both sides by W
C
W= log2
(
1 +P
NoW
)
= log2
(
1 +Eb
No·R
W
)
R = 1/T = data rate (bits/second)
Eb = energy per data bit (Joules) = PT
Eb/No = received bit energy-to-noise spectral density ratio (dimensionless)
R/W = bandwidth efficiency (bits/s/Hz)
If R = C, i.e., we transmit at a rate equal to the channel capacity, then
C
W= log2
(
1 +Eb
No·C
W
)
or inverting this equation we get Eb/No in terms of C, viz.
Eb
No=
2C/W − 1
C/W
0 c©2011, Georgia Institute of Technology (lect1 18)
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AWGN Channel Capacity
0 c©2011, Georgia Institute of Technology (lect1 19)
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Capacity of the AWGN Channel
Example: Suppose that W = 6 MHz (TV channel bandwidth) and the received
SNR∆= P/(NoW ) = 20 dB. What is the channel capacity?
Answer: C = 6× 106log2 (1 + 100) = 40 Mbps.
Asymptotic behavior: as C/W → 0.Using L’Hopital’s rule
limC/W→0
Eb
No= limC/W→0 2
C/W ln 2
= ln 2
= 0.693
= −1.6dB
Conclusion: It is impossible to communicate on an AWGN channel with arbitraryreliability if Eb/No < −1.6 dB, regardless of how much bandwidth we use.
0 c©2012, Georgia Institute of Technology (lect1 20)
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AWGN Channel Capacity
Power Efficient Region: R/W < 1 bits/s/Hz. In this region we have band-width resources available, but transmit power is limited, e.g., deep space com-
munications.
Bandwidth Efficient Region: R/W > 1 bits/s/Hz. In this region we have
power resources available, but bandwidth is limited, e.g., commercial wirelesscommunications. Note: we still want to use power efficiently, i.e., bandwidth
and power efficient communication
Observe that most uncoded modulation schemes operate about 10 dB from theShannon capacity limit for an error rate of 10−5.
State-of-the-art “turbo” coding schemes can close this gap to less than 1 dB,with the cost of additional receiver processing complexity and delay.
Generally, we can tradeoff power, bandwidth, processing complexity, delay.
0 c©2011, Georgia Institute of Technology (lect1 21)
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What is SNR?
OFDM/OFDMA
CDMA, etc..Gray/SP –
QAM, PSK
BLOCK, CONV,
TRELLIS TURBO
INFO
BITS
coderBit
mapping
Time/
frequency
spreadingp g
Eb/No
bit SNR
Es/No
symbol SNR
Ec/No
chip SNR
Er/No
codebit SNR
Eb = energy per information bit
Er = energy per code bit
E energy per modulated symbolEs = energy per modulated symbol
Ec = energy per spreading chip
The term SNR used by itself is vague:We have Bit-, Code-bit-, Symbol-, Chip-SNR
We always need to compare systems on the basis of Bit-SNR, Eb/No.
0 c©2011, Georgia Institute of Technology (lect1 22)