Transcript Ch7 - Department of Engineering and Physics

ENGR 4323/5323
Digital and Analog Communication
Ch 7
Principles of Digital Data Transmission
Engineering and Physics
University of Central Oklahoma
Dr. Mohamed Bingabr
Chapter Outline
• Digital Communication Systems
• Line Coding
• Pulse Shaping
• Scrambling
• Digital Receiver and Regenerative Repeaters
• PAM: M-ARY Baseband Signaling for Higher Data
Rate
• Digital Carrier Systems
• M-ARY Digital Carrier Modulation
2
Digital Communication Systems
On-Off (RZ)
Polar (RZ)
Line Coding
Bipolar (RZ)
On-Off (NRZ)
Polar (NRZ)
3
Digital Communication Systems
Digital Carrier Modulation
Multiplexer
- Amplitude Modulation
- Time Division
- Frequency Modulation
- Frequency Division
- Phase Modulation
- Code Division
4
Digital Communication Systems
Regenerative Repeater
- Used at regularly spaced interval.
- Timing information extracted from
the received signal.
- Transparent line code does not
effect the accuracy of the timing
information.
5
Line Coding
Property of Line Code
- Transmission Bandwidth
- Power Efficiency
- Error Detection and Correction Capacity
- Favorable Power Spectral Density
- Adequate Timing Content
- Transparency
6
PSD of Line Codes
The PSD will depend on the line
code pattern x(t) and the pulse
shape p(t).
𝑦 𝑡 =
𝑎𝑘 𝑝 𝑡 − 𝑘𝑇𝑏
𝑆𝑦 𝑓 = 𝑃 𝑓
2 𝑆 (𝑓)
𝑥
7
PSD of Line Codes
We can express the impulse as a
pulse with narrow width and large
amplitude such that the strength
of the pulse is the same as the
impulse.
𝑎𝑘
ℎ𝑘 =
𝜖
1
𝜏
2
ℛ𝑥 = lim
𝑎𝑘 1 −
𝑇→∞ 𝑇
𝜖
𝑘
𝑅0
|𝜏|
ℛ𝑥 =
1−
𝜖𝑇𝑏
𝜖
1
𝑅0 = lim
𝑁→∞ 𝑁
𝑎𝑘2 = 𝑎𝑘2
𝑘
𝜏 <𝜖
8
PSD of Line Codes
1
𝑅1 = lim
𝑁→∞ 𝑁
1
𝑅𝑛 = lim
𝑁→∞ 𝑁
𝑎𝑘 𝑎𝑘+1 = 𝑎𝑘 𝑎𝑘+1
𝑘
𝑎𝑘 𝑎𝑘+𝑛 = 𝑎𝑘 𝑎𝑘+𝑛
𝑘
To find ℛ𝑥 𝜏 , let ε0 ℛ𝑥 𝜏
1
ℛ𝑥 (𝜏) =
𝑇𝑏
∞
𝑅𝑛 𝛿 𝜏 − 𝑛𝑇𝑏
𝑛=−∞
The PSD 𝑆𝑥 𝑓 is the FT of ℛ𝑥 𝜏
9
PSD of Line Codes
1
𝑆𝑥 (𝑓) =
𝑅0 + 2
𝑇𝑏
∞
𝑅𝑛 𝑐𝑜𝑠 𝑛2𝜋𝑓𝑇𝑏
𝑛=1
𝑆𝑦 𝑓 = 𝑃 𝑓
2 𝑆 (𝑓)
𝑥
𝑃(𝑓)
𝑆𝑦 (𝑓) =
𝑇𝑏
2
∞
𝑅0 + 2
𝑅𝑛 𝑐𝑜𝑠 𝑛2𝜋𝑓𝑇𝑏
𝑛=1
Again Rn is
1
𝑅𝑛 = lim
𝑁→∞ 𝑁
𝑎𝑘 𝑎𝑘+𝑛 = 𝑎𝑘 𝑎𝑘+𝑛
𝑘
10
PSD of Polar Signaling
1
𝑅0 = lim
𝑁→∞ 𝑁
1
𝑅𝑛 = lim
𝑁→∞ 𝑁
𝑎𝑘2
𝑘
1
= lim
𝑁→∞ 𝑁
𝑎𝑘 𝑎𝑘+𝑛 = 0
𝑘
𝑃(𝑓)
𝑆𝑦 (𝑓) =
𝑇𝑏
1=1
𝑘
𝑎𝑘 𝑎𝑘+𝑛 = 1 or -1 with
equal probability
2
2𝑡
For rectangular pulse shape 𝑝 𝑡 = Π
𝑇𝑏
𝑇𝑏
𝜋𝑓𝑇𝑏
𝑃 𝑓 = 𝑠𝑖𝑛𝑐
2
2
𝑇𝑏
𝜋𝑓𝑇𝑏
2
𝑆𝑦 𝑓 = 𝑠𝑖𝑛𝑐
4
2
11
PSD of Polar Signaling
𝑇𝑏
𝜋𝑓𝑇𝑏
2
𝑆𝑦 𝑓 = 𝑠𝑖𝑛𝑐
4
2
- Essential Bandwidth 2Rb Hz
- No capability for error detection or correction
- Nonzero PSD at dc ( f = 0)
- For a given power, Polar signaling has the lowest error
detection probability.
- Transparent
- Rectification of polar signal can help in extracting clock
timing.
12
Constructing a DC Null in PSD by Pulse
Shaping
Split-phase (Manchester or twinned-binary) signal.
Fig. a: Basic pulse p(t) for Manchester signaling.
Fig. b: Transmitted waveform for binary data sequence using
Manchester signaling.
∞
𝑝(𝑡)𝑒 −𝑗2𝜋𝑓𝑡 𝑑𝑡
𝑃(𝑓) =
−∞
∞
𝑃(0) =
𝑝 𝑡 𝑑𝑡 = 0
−∞
Read On-Off Signaling
13
PSD of Bipolar Signaling
1
𝑅0 = lim
𝑁→∞ 𝑁
𝑎𝑘2
𝑘
Half the time aK equals 0 and the other half time equals either 1
or -1.
1
𝑅0 =
2
For R1, the combination of akak+1 = 11, 10, 01, 00. For bipolar
rule the product is zero for the last three combination and -1
for the first combination.
1 𝑁
3𝑁
𝑅1 = lim
−1 +
0
𝑁→∞ 𝑁 4
4
1
=−
4
𝑅𝑛 = 0 for 𝑛 > 1
14
PSD of Bipolar Signaling
𝑃(𝑓)
𝑆𝑦 (𝑓) =
𝑇𝑏
2
𝑃(𝑓)
𝑆𝑦 (𝑓) =
2𝑇𝑏
2
∞
𝑅0 + 2
𝑅𝑛 𝑐𝑜𝑠 𝑛2𝜋𝑓𝑇𝑏
𝑛=1
1 − 𝑐𝑜𝑠 2𝜋𝑓𝑇𝑏
𝑃(𝑓) 2
𝑆𝑦 (𝑓) =
𝑠𝑖𝑛2 𝜋𝑓𝑇𝑏
𝑇𝑏
𝑇𝑏
𝜋𝑓𝑇𝑏
2
𝑆𝑦 𝑓 = 𝑠𝑖𝑛𝑐
𝑠𝑖𝑛2 𝜋𝑓𝑇𝑏
4
2
15
PSD of Bipolar Signaling
𝑇𝑏
𝜋𝑓𝑇𝑏
2
𝑆𝑦 𝑓 = 𝑠𝑖𝑛𝑐
𝑠𝑖𝑛2 𝜋𝑓𝑇𝑏
4
2
- Essential Bandwidth Rb Hz.
- Single error detection capability.
- Zero PSD at dc ( f =0).
- Disadvantage require twice the power as a polar signal needs.
- It is not transparent.
16
High-Density Bipolar (HDB) Signaling
The HDB scheme is an ITU standard. In this scheme the
problem of nontransparency in bipolar signaling is eliminated by
adding pulses when the number of consecutive 0s exceeds N.
(a) HDB3 signal and (b) its PSD.
17
Pulse Shaping
The pulse shape p(t) effect the PSD Sy( f ) more than the choice
of line code.
Intersymbol Interference (ISI): Spreading of a pulse beyond its
allocated time interval Tb will cause it to interfere with
neighboring pulses.
18
Nyquist 1st criteria for Pulse Shaping
Nyquist criteria for pulse shaping to eliminate ISI:
Pulse shape that has a nonzero amplitude at its center and zero
amplitudes at t =  nTb (n =1, 2, 3, …)
1
𝑝 𝑡 =
0
𝑡=0
𝑡 = ±𝑛𝑇𝑏
1
𝑇𝑏 =
𝑅𝑏
19
Nyquist 1st criteria for Pulse Shaping
1
1
𝑓 − 𝑅𝑏 /2
𝑃 𝑓 =
1 − 𝑠𝑖𝑛𝜋
2
2𝑓𝑥
0
𝑅𝑏
𝑓 <
− 𝑓𝑥
2
𝑅𝑏
𝑓−
< 𝑓𝑥
2
𝑅𝑏
𝑓 >
+ 𝑓𝑥
2
Nyquist 2nd criteria for Pulse Shaping
Pulse broadening in the time domain leads to reduction of its
bandwidth. Pulse satisfying second criteria is also knowing as
the duobinary pulse.
𝑝 𝑛𝑇𝑏 =
1
0
𝑛 = 0, 1
for all other 𝑛
Information Sequence
1 1 0 1 1 0 0 0 1 0 1 1 1
Samples y(kTb)
1 2 0 0 2 0 -2 -2 0 0 0 2 2
Detected sequence
1 1 0 1 1 0 0 0 1 0 1 1 1
Nyquist 2nd criteria Duobinary Pulse
𝑠𝑖𝑛 𝜋𝑅𝑏 𝑡
𝑝 𝑡 =
𝜋𝑅𝑏 𝑡 1 − 𝑅𝑏 𝑡
2
𝜋𝑓
𝑓
𝑃 𝑓 =
𝑐𝑜𝑠
Π
𝑒 −𝑗𝜋𝑓/𝑅𝑏
𝑅𝑏
𝑅𝑏
𝑅𝑏
The minimum bandwidth pulse that satisfies
the duobinary pulse criterion and (b) its spectrum.
Scrambling
Scrambler tends to make the data more random by removing
long strings of 1s and 0s. Removing long 0s or 1s help in timing
extraction. However, the main purpose of scrambling is to
prevent unauthorized access to the data.
𝑇 = 𝑆⨁𝐷3 𝑇⨁𝐷5 𝑇
𝑆 = 𝑇⨁(𝐷3 𝑇⨁𝐷5 𝑇)
Scrambling Example
The data stream 101010100000111 is fed to the scrambler.
Find the scrambler output T, assuming the initial content of the
registers to be zero.
Scrambling Example
The data stream 101010100000111 is fed to the scrambler.
Find the scrambler output T, assuming the initial content of the
registers to be zero.
S 1 2 3 4 5 T
1 0 0 0 0 0 1
0 1 0 0 0 0 0
1 0 1 0 0 0 1
0 1 0 1 0 0 1
1 1 1 0 1 0 1
0 1 1 1 0 1 0
1 0 1 1 1 0 0
0 0 0 1 1 1 0
0 0 0 0 1 1 1
0 1 0 0 0 1 1
0 1 1 0 0 0 0
T=101110001101001
0 0 1 1 0 0 1
Digital Receivers and Regenerative
Repeaters
Tasks of Receivers or repeaters:
1. Reshaping incoming pulses by means of an equalizer.
2. Extracting the timing information required to sample
incoming pulses.
3. Making symbol detection decisions based on the pulse
samples.
Time Extraction
Three general methods of synchronization
1- Derivation from a primary or a secondary standard
(transmitter and receiver slaved to a master timing source).
2- Transmitting a separate synchronizing signal (pilot clock)
3- Self-synchronization, where the timing information is
extracted from the received signal itself.
Eye Diagrams: An Important Tool
Three general methods of synchronization
Eye diagrams of a
polar signaling
system using a
raised cosine pulse
with roll-off factor
0.5: over 2 symbol
periods 2Tb with a
time shift Tb/2;
PAM: M-ARY Baseband Signaling for
Higher Data Rate
The information IM transmitted by an M-ary symbol is
𝐼𝑀 = log 2 𝑀 bits
The transmitted power increases as M2.
Example
Determine the PSD of the quaternary (4-ary) baseband signaling
when the message bits 1 and 0 are equally likely.
Digital Carrier Systems
In transmitting and receiving digital carrier signals, we need a
modulator and demodulator to transmit and receive data. The
two devices, modulator and demodulator are usually packaged
in one unit called a modem for two-way (duplex)
communication.
Amplitude Shift Keying (ASK)
(a) The carrier cos ωct.
(b) The modulating signal m(t).
(c) ASK: the modulated signal
m(t) cos ωct.
Digital Carrier Systems (Modulator)
Phase Shift Keying (PSK)
Frequency Shift Keying (FSK)
Spectrum of Modulated Digital Signals
PSD of ASK
PSD of PSK
PSD of FSK
Digital Carrier Systems (Demodulator)
Noncoherent detection of FSK
Coherent detection of FSK
Coherent binary PSK detector
Differential PSK (DPSK)
DPSK allows noncoherent demodulation at the receiver.
The transmitter encodes the information data into the phase
difference θk - θk-1. For example a phase difference of zero
represent 0 whereas a phase difference of  signifies 1.
Transmitter Encoding
Receiver Decoding
Differential PSK (DPSK)
Transmitter Encoding
Receiver Decoding
M-Ary Digital Carrier Modulation
Higher bit rate transmission can be achieved by either reducing
Tb or by applying M-ary signaling; the first option requires more
bandwidth; the second requires more power to keep the error bit
rate within acceptable level.
M-ary shift keying can send Log2 M bits each time by
transmitting any one of M signals.
M-ary ASK and noncoherent Detection
𝜑 𝑡 = 0, 𝐴 𝑐𝑜𝑠 𝜔𝑐 𝑡, 2𝐴 𝑐𝑜𝑠 𝜔𝑐 𝑡, … , M − 1 𝐴 𝑐𝑜𝑠 𝜔𝑐 𝑡
M-ary FSK and noncoherent Detection
𝜑 𝑡 = 𝐴 𝑐𝑜𝑠 2𝜋𝑓𝑖 𝑡
where
𝑓𝑖 = 𝑓1 + (𝑚 − 1)𝛿𝑓 and 𝑖 = 1, 2, … , 𝑀
Choice of the Frequencies for FSK
The choice of 𝛿𝑓 will determine the performance and
bandwidth of the FSK modulation.
𝑓𝑀 − 𝑓1
1
∆𝑓 =
=
𝑀 − 1 𝛿𝑓
2
2
Large 𝛿𝑓 leads to bandwidth waste, whereas small 𝛿𝑓 is prone
to detection error due to transmission noise interference.
To minimize error detection the choice of 𝑓𝑖 should be large
enough to make the FSK modulating signals 𝐴 𝑐𝑜𝑠 2𝜋𝑓𝑖 𝑡
orthogonal over the period Tb.
𝑇𝑏
0
𝐴𝑐𝑜𝑠 2𝜋𝑓𝑚 𝑡 𝐴𝑐𝑜𝑠 2𝜋𝑓𝑛 𝑡 𝑑𝑡 = 0
1
𝛿𝑓 =
𝐻𝑧
2𝑇𝑏
Comparison between ASK and FSK
FSK does not require increase in power but the bandwidth
increase linearly with M (compared with binary FSK or M-ary
ASK).
ASK does not require increase in bandwidth but the power
increase linearly with M.
M-ary PSK
𝜑𝑃𝑆𝐾 𝑡 = 𝐴 𝑐𝑜𝑠 𝜔𝑐 𝑡 + 𝜃𝑚
2𝜋
𝜃𝑚 = 𝜃0 +
𝑚−1
𝑀
𝜃0 = 180
𝑚 = 1, 2, … , 𝑀
2𝜋
𝜃0 =
𝑀
𝜃0 = 90
𝜃0 = 45
M-ary PSK symbols in the orthogonal signal space: (a) M = 2; (b) M = 4; (c) M = 8.
M-ary PSK
𝜑𝑃𝑆𝐾 𝑡 = 𝑎𝑚
𝜓1 𝑡 =
2
2
𝑐𝑜𝑠 𝜔𝑐 𝑡 + 𝑏𝑚
𝑠𝑖𝑛 𝜔𝑐 𝑡
𝑇𝑏
𝑇𝑏
2
𝑐𝑜𝑠 𝜔𝑐 𝑡
𝑇𝑏
𝜓2 𝑡 =
0 ≤ 𝑡 < 𝑇𝑏
2
𝑠𝑖𝑛 𝜔𝑐 𝑡
𝑇𝑏
𝜑𝑃𝑆𝐾 𝑡 = 𝑎𝑚 𝜓1 𝑡 + 𝑏𝑚 𝜓2 𝑡
M-ary PSK symbols in the orthogonal signal space: (a) M = 2; (b) M = 4; (c) M = 8.
Quadrature Amplitude Modulation (QAM)
𝑝𝑖 𝑡 = 𝑎𝑖 𝑝(𝑡) 𝑐𝑜𝑠 𝜔𝑐 𝑡 + 𝑏𝑖 𝑝(𝑡) 𝑠𝑖𝑛 𝜔𝑐 𝑡
0 ≤ 𝑡 < 𝑇𝑏
𝑝𝑖 𝑡 = 𝑟𝑖 𝑝 𝑡 𝑐𝑜𝑠 (𝜔𝑐 𝑡 − 𝜃𝑖 )
𝑟𝑖 =
𝑎𝑖2
+
𝑏𝑖2
𝜃𝑖 = 𝑡𝑎𝑛
−1
𝑏𝑖
𝑎𝑖
p(t) is a properly shaped baseband pulse.
A simple choice is a rectangular.
16-point QAM (M = 16).
QAM or Multiplexing