Ch 7Principles of Digital Data Transmission

ENGR 4323/5323Digital and Analog Communication

Engineering and PhysicsUniversity 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

Line Coding

3

On-Off (RZ)

Polar (RZ)

Bipolar (RZ)

On-Off (NRZ)

Polar (NRZ)

Digital Communication Systems

Multiplexer

- Time Division

- Frequency Division

- Code Division

4

Digital Carrier Modulation

- Amplitude Modulation

- Frequency Modulation

- Phase Modulation

Digital Communication Systems

5

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.

Line Coding

6

Property of Line Code- Transmission Bandwidth

- Power Efficiency

- Error Detection and Correction Capacity

- Favorable Power Spectral Density

- Adequate Timing Content

- Transparency

PSD of Line Codes

7

𝑆 𝑦 ( 𝑓 )=|𝑃 ( 𝑓 )|2𝑆𝑥 ( 𝑓 )

𝑦 (𝑡 )=∑ 𝑎𝑘𝑝 (𝑡−𝑘𝑇𝑏 )

The PSD will depend on the line code pattern x(t) and the pulse shape p(t).

PSD of Line Codes

8

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.

h𝑘=𝑎𝑘

𝜖

ℛ �̂�= lim𝑇→ ∞

1𝑇 ∑

𝑘𝑎𝑘

2 (1 − 𝜏𝜖 )

ℛ �̂�=𝑅0

𝜖𝑇 𝑏¿¿

𝑅0= lim𝑁→ ∞

1𝑁∑

𝑘𝑎𝑘

2=~𝑎𝑘

2

|𝜏|<𝜖

PSD of Line Codes

9

ℛ𝑥 (𝜏 )= 1𝑇 𝑏

∑𝑛=− ∞

∞

𝑅𝑛𝛿 (𝜏 −𝑛𝑇 𝑏)

𝑅1= lim𝑁→ ∞

1𝑁∑

𝑘𝑎𝑘𝑎𝑘+1=~𝑎𝑘𝑎𝑘+1

𝑅𝑛= lim𝑁→ ∞

1𝑁 ∑

𝑘𝑎𝑘𝑎𝑘+𝑛=~𝑎𝑘𝑎𝑘+𝑛

To find , let ε0

The PSD is the FT of

PSD of Line Codes

10

𝑆𝑥( 𝑓 )= 1𝑇 𝑏 [𝑅0+2∑

𝑛=1

∞

𝑅𝑛𝑐𝑜𝑠 (𝑛2𝜋 𝑓 𝑇𝑏) ]𝑆 𝑦 ( 𝑓 )=|𝑃 ( 𝑓 )|2𝑆𝑥( 𝑓 )

𝑆 𝑦( 𝑓 )=|𝑃 ( 𝑓 )|2

𝑇𝑏 [𝑅0+2∑𝑛=1

∞

𝑅𝑛𝑐𝑜𝑠 (𝑛2𝜋 𝑓 𝑇 𝑏 )]

𝑅𝑛= lim𝑁→ ∞

1𝑁 ∑

𝑘𝑎𝑘𝑎𝑘+𝑛=~𝑎𝑘𝑎𝑘+𝑛

Again Rn is

PSD of Polar Signaling

11

𝑆 𝑦( 𝑓 )=|𝑃 ( 𝑓 )|2

𝑇𝑏

𝑅0= lim𝑁→ ∞

1𝑁∑

𝑘𝑎𝑘

2= lim𝑁→ ∞

1𝑁 ∑

𝑘1=1

𝑅𝑛= lim𝑁→ ∞

1𝑁 ∑

𝑘𝑎𝑘𝑎𝑘+𝑛=0 1 or -1 with equal

probability

For rectangular pulse shape 𝑝 (𝑡 )=Π ( 2𝑡𝑇𝑏 )

𝑃 ( 𝑓 )=𝑇 𝑏

2𝑠𝑖𝑛𝑐( 𝜋 𝑓 𝑇𝑏

2 )𝑆 𝑦 ( 𝑓 )=

𝑇𝑏

4𝑠𝑖𝑛𝑐 2( 𝜋 𝑓 𝑇 𝑏

2 )

PSD of Polar Signaling

12

𝑆 𝑦 ( 𝑓 )=𝑇𝑏

4𝑠𝑖𝑛𝑐 2( 𝜋 𝑓 𝑇 𝑏

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.

Constructing a DC Null in PSD by Pulse Shaping

13

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 ( 𝑓 )=∫− ∞

∞

𝑝(𝑡 )𝑒− 𝑗2𝜋 𝑓𝑡 𝑑𝑡

𝑃 (0)=∫− ∞

∞

𝑝 (𝑡 )𝑑𝑡=0

Read On-Off Signaling

PSD of Bipolar Signaling

14

𝑅0= lim𝑁→ ∞

1𝑁∑

𝑘𝑎𝑘

2

𝑅1= lim𝑁→ ∞

1𝑁 [𝑁4 (−1 )+ 3𝑁

4(0 )]=− 1

4

Half the time aK equals 0 and the other half time equals either 1 or -1.

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.

𝑅0=12

for

PSD of Bipolar Signaling

15

𝑆 𝑦 ( 𝑓 )=𝑇𝑏

4𝑠𝑖𝑛𝑐 2( 𝜋 𝑓 𝑇 𝑏

2 ) 𝑠𝑖𝑛2 (𝜋 𝑓 𝑇 𝑏 )

𝑆 𝑦( 𝑓 )=|𝑃 ( 𝑓 )|2

𝑇𝑏 [𝑅0+2∑𝑛=1

∞

𝑅𝑛𝑐𝑜𝑠 (𝑛2𝜋 𝑓 𝑇 𝑏 )]𝑆 𝑦 ( 𝑓 )=

|𝑃 ( 𝑓 )|2

2𝑇𝑏[1 −𝑐𝑜𝑠 (2𝜋 𝑓 𝑇𝑏 ) ]

𝑆 𝑦( 𝑓 )=|𝑃 ( 𝑓 )|2

𝑇𝑏𝑠𝑖𝑛2 ( 𝜋 𝑓 𝑇𝑏 )

PSD of Bipolar Signaling

16

𝑆 𝑦 ( 𝑓 )=𝑇𝑏

4𝑠𝑖𝑛𝑐 2( 𝜋 𝑓 𝑇 𝑏

2 ) 𝑠𝑖𝑛2 (𝜋 𝑓 𝑇 𝑏 )

- 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.

High-Density Bipolar (HDB) Signaling

17

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.

Pulse Shaping

18

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.

Nyquist 1st criteria for Pulse Shaping

19

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, …)

𝑝 (𝑡 )={ 1 𝑡=00𝑡=±𝑛𝑇 𝑏

𝑇 𝑏=1𝑅𝑏

Nyquist 1st criteria for Pulse Shaping

𝑃 ( 𝑓 )={ 1|𝑓 |< 𝑅𝑏

2− 𝑓

𝑥

12 [1−𝑠𝑖𝑛𝜋 ( 𝑓 −𝑅𝑏 /2

2 𝑓 𝑥)]|𝑓 −

𝑅𝑏

2 |< 𝑓 𝑥

0|𝑓 |>𝑅𝑏

2+ 𝑓

𝑥

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 )={ 1𝑛=0 ,10 for  all   other  𝑛

Information Sequence

Samples y(kTb)

Detected sequence

1 1 0 1 1 0 0 0 1 0 1 1 1

1 1 0 1 1 0 0 0 1 0 1 1 1

1 2 0 0 2 0 -2 -2 0 0 0 2 2

Nyquist 2nd criteria Duobinary Pulse

The minimum bandwidth pulse that satisfiesthe duobinary pulse criterion and (b) its spectrum.

𝑝 (𝑡 )=𝑠𝑖𝑛 (𝜋 𝑅𝑏 𝑡 )

𝜋 𝑅𝑏𝑡 (1 −𝑅𝑏 𝑡 )

𝑃 ( 𝑓 )= 2𝑅𝑏

𝑐𝑜𝑠( 𝜋 𝑓𝑅𝑏 ) Π ( 𝑓

𝑅𝑏 )𝑒− 𝑗 𝜋 𝑓 /𝑅𝑏

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⨁𝐷3𝑇⨁𝐷5𝑇 𝑆=𝑇⨁ (𝐷3𝑇⨁𝐷5𝑇 )

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 01 0 1 0 0 0 10 1 0 1 0 0 11 1 1 0 1 0 10 1 1 1 0 1 01 0 1 1 1 0 00 0 0 1 1 1 00 0 0 0 1 1 1 0 1 0 0 0 1 10 1 1 0 0 0 00 0 1 1 0 0 1T=101110001101001

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= log2 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 PSK

PSD of FSK

PSD of ASK

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 ASK and noncoherent Detection

M-ary shift keying can send Log2 M bits each time by transmitting any one of M signals.

M-ary FSK and noncoherent Detection

where

and

Choice of the Frequencies for FSK

Large leads to bandwidth waste, whereas small is prone to detection error due to transmission noise interference.

To minimize error detection the choice of should be large enough to make the FSK modulating signals orthogonal over the period Tb.

The choice of will determine the performance and bandwidth of the FSK modulation.

∆ 𝑓 =𝑓 𝑀− 𝑓 1

2=1

2(𝑀−1 )𝛿 𝑓

∫0

𝑇 𝑏

𝐴𝑐𝑜𝑠 (2𝜋 𝑓 𝑚 𝑡 ) 𝐴𝑐𝑜𝑠 (2𝜋 𝑓 𝑛𝑡 ) 𝑑𝑡=0 𝛿 𝑓 =1

2𝑇 𝑏𝐻𝑧

Comparison between ASK and FSK

ASK does not require increase in bandwidth but the power increase linearly with M.

FSK does not require increase in power but the bandwidth increase linearly with M (compared with binary FSK or M-ary ASK).

M-ary PSK

𝜑𝑃𝑆𝐾 (𝑡 )=𝐴𝑐𝑜𝑠 (𝜔𝑐𝑡+𝜃𝑚 ) 𝑚=1 ,2 , …,𝑀

𝜃𝑚=𝜃0+2𝜋𝑀 (𝑚−1 )

M-ary PSK symbols in the orthogonal signal space: (a) M = 2; (b) M = 4; (c) M = 8.

𝜃0=2𝜋𝑀

𝜃0=180𝜃0=90 𝜃0=45

M-ary PSK

𝜑𝑃𝑆𝐾 (𝑡 )=𝑎𝑚√ 2𝑇𝑏

𝑐𝑜𝑠𝜔𝑐𝑡+𝑏𝑚√ 2𝑇 𝑏

𝑠𝑖𝑛𝜔𝑐𝑡 0 ≤ 𝑡<𝑇𝑏

𝜓 1 (𝑡 )=√ 2𝑇𝑏

𝑐𝑜𝑠𝜔𝑐𝑡 𝜓 2 (𝑡 )=√ 2𝑇 𝑏

𝑠𝑖𝑛𝜔𝑐𝑡

𝜑𝑃𝑆𝐾 (𝑡 )=𝑎𝑚𝜓 1 (𝑡 )+𝑏𝑚𝜓 2 (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 )=𝑎𝑖𝑝(𝑡 )𝑐𝑜𝑠𝜔𝑐𝑡+𝑏𝑖𝑝 (𝑡)𝑠𝑖𝑛𝜔𝑐𝑡 0 ≤ 𝑡<𝑇𝑏

𝑟 𝑖=√𝑎𝑖2+𝑏𝑖

2 𝜃𝑖=𝑡𝑎𝑛−1 𝑏𝑖

𝑎𝑖

p(t) is a properly shaped baseband pulse.A simple choice is a rectangular.

𝑝𝑖 (𝑡 )=𝑟 𝑖𝑝 (𝑡 )𝑐𝑜𝑠 (𝜔¿¿𝑐𝑡−𝜃 𝑖)¿

16-point QAM (M = 16).

QAM or Multiplexing