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COE 341 Data Computer Communications

(T061)Dr. Radwan E. Abdel-Aal

- Chapter 5
- Signal Encoding Techniques

Where are we

Chapter 7 Data Link Flow and Error control

Data Link

Chapter 8 Improved utilization Multiplexing

Physical Layer

Chapter 6 Data Communication Synchronization,

Error detection and correction

Chapter 4 Transmission Media

Transmission Medium

Chapter 5 Encoding From data to signals

Chapter 3 Signals and their transmission over

media, Impairments

Agenda

- Overview
- Implementation of the 4 encoding combinations

introduced in chapter 3 - Encoding Digital Data as Digital Signals
- Encoding Digital Data as Analog Signals
- Encoding Analog Data as Digital Signals
- Encoding Analog Data as Analog Signals

Four Data/Signal Combinations

4

3

2

1

Encoding Techniques

- 1. Digital data as digital signal
- 2. Digital data as analog signal Converter

(Modem) - 3. Analog data as digital signal Converter

(Codec) - 4. Analog data as analog signal
- In general
- When the outcome is a digital signal we use an

Encoding process - When the outcome is an analog signal we use a

Modulation process - But we call the modulation of analog signal by

digital data shift-keying

Encoding

x(t)

g(t)

g(t)

Encoder

Decoder

Analog Data

Analog Data

Digital Signal Transmission

Modulation

Shift in frequency

Shift back in frequency

m(t)

s(t)

Modulator

Demodulator

m(t)

Analog Data

Analog Data

Analog Signal Transmission

fc

fc

Higher frequency

Baseband

Link

Source

Destination

Baseband

Encoding and Modulation Remarks

- Encoding is simpler and less expensive than

modulation - Encoding into digital signals allows use of

modern digital transmission and switching

equipment - Basis for Time Division Multiplexing (TDM)
- Modulation shifts baseband signals to a higher

region in the frequency spectrum (needs same fcs

at both ends) - Basis for Frequency Division Multiplexing (FDM)
- Optical fibers and unguided media and can carry

only analog signals

Terminology

- Unipolar Signals
- Binary data represented by signals of the same

polarity, e.g. 0 5 V, 1 10 V ? DC content - Bipolar (Polar) Signals
- Binary data represented by signals of opposite

polarity, e.g. 0 5 V, 1 -5 V ? ideally Zero DC

content

Terminology, Contd.Data rate and Signaling rate

- Not always Tb Ts !!
- Multi-symbol transmission (M

4, 8, ) Tb lt Ts - Return to zero (RZ) codes Ts lt Tb

- Mark and Space
- Binary 1 and Binary 0 respectively
- Duration of a bit (Tb)
- Time taken for transmitter to emit
- a data bit
- Data rate, R ( 1/Tb)
- Rate of data transmission
- Measured in bits per second (bps)
- Duration of a Signal Element (Ts)
- Minimum duration of a signal pulse
- Modulation (signaling) rate, D (1/Ts)
- Rate at which the signal level changes with time
- Measured in bauds signal elements per second

Example Two different coding methods

- Data rate 1/1ms
- 1 M bps
- (in both cases)
- Signaling Rate for NRZI 1/1ms
- 1 M bauds
- Signaling Rate for Manchester 1/0.5ms
- 2 M bauds

Tb

Ts

Ts

Interpretation of the Received Signal

Interpreting Received Signals

- Requirements at RX
- Determine timing of bits Bit start and end

(When to look) ?

Need Synchronization (Chapter 6)

- Detect signal levels at mid-bit points
- Compare signal level with a threshold level to

decide on data - Factors affecting successful signal

interpretation - (Affect bit error rate)
- Bandwidth
- Signal to noise ratio
- Data rate
- Also Encoding/Modulation scheme, e.g. binary or

multi-level

1. Digital Data, Digital Signal

- Digital signal
- Voltage/current pulses having a few discrete

levels (2 levels for binary) - Each pulse is a signal element
- Binary data is encoded into those signal elements

Encoding SchemesEncoding Mapping data to signal

elements

- Schemes for encoding digital data as digital

signals - The Nonreturn to Zero (NRZ) Group
- Nonreturn to Zero-Level (NRZ-L)
- Nonreturn to Zero Inverted (NRZI)
- The Multi-level Binary Group
- Bipolar-AMI (Alternate Mark Invert)
- Pseudoternary
- The Bi-Phase (RZ) Group
- Manchester
- Differential Manchester
- Scrambling Group
- B8ZS (Bipolar with 8-Zeros Substitution)
- HDB3 (High Density Bipolar 3-Zeros)

Why so Many Encoding Schemes? Aspects of

comparison between schemes

- Signal Spectrum Desirable Features
- Small high frequency content Reduces effective

bandwidth - No dc component Allows ac transformer/capacitor

coupling, required sometimes for electrical

isolation - Concentrate
- signal power in
- the middle of
- the bandwidth
- Avoids problems
- at BW edges, e.g.
- delay distortion.

2

Aspects of comparison between schemes

- Clocking
- Synchronizing RX to TX can be achieved using
- An external clock,
- or better
- A built-in synchronizing mechanism in the signal

itself! (so, a code with many signal transitions

is better) - Error detection
- Mostly handled by higher layers, e.g. data link

control - But error detection capabilities built into the

signal encoding scheme would help! - ? Advantage Implemented much faster (in

hardware)

Comparison of Encoding Schemes, contd.

- Performance with interference and noise
- Some encoding schemes perform better than others

- e.g. with differential encoding data is encoded

as signal transition/no signal transition, and

data detection at RX is less affected by noise - Cost and complexity
- Some codes require signaling at a rate greater

than the data rate (e.g. RZ) - At higher signaling rates this requires higher

bandwidth, faster circuits, etc. (larger costs)

NRZ GroupPros and Cons

- Pros
- Easy to implement
- Modest bandwidth requirements
- Cons
- Large DC component
- Poor TX-RX synchronization
- e.g. No signal transitions for long strings

of all 0s (so few edges are available for

synchronization) - Used for magnetic recording
- Not used much for signal transmission

The RZ Solution

- Advantages of RZ
- Lower DC content (signal spends more time around

0V) - Guarantees an edge per bit (Better TX-RX

synchronization) - Disadvantages of RZ
- Higher frequency content
- More difficult to implement

NRZ Spectrum

? Power Spectral Density, Watt/Hz

1.5

B8ZS,HDB3

NRZ-L, NRZI

1

AMI, Pseudoternary

0.5

Mean square voltage per unit bandwidth

Manchester, Differential Manchester

0

1

0

0.5

1.5

2

Frequency relative to data rate (binary data)

-0.5

Normalized frequency (f/R)

NRZ-L Non return to Zero-Level

- Two different signal voltages for the 0 and 1

data bits - Voltage level is constant (no return to zero, so

no signal transition) for the full duration of

the data bit interval - e.g. 0 V for zero and a positive voltage for one
- More often, negative voltage for one data value

and positive for the other (bipolar signal)

(Why?) - An example of absolute encoding

Mapping data directly to signal levels

NRZI Nonreturn to Zero Invert

- Still constant voltage level for bit duration of

(hence NRZ) - But data is encoded as presence or absence of

signal transition at the beginning of bit time - Transition (low to high or high to low) Denotes

binary 1 - No transition Denotes binary 0
- This is an example of differential encoding

Encoding data as a change/no change in signal

level

Differential Encoding

- Data is represented by signal transitions rather

than signal levels - Advantages
- With noise, signal transitions (or lack of them)

are detected more easily than signal levels ?

Better noise immunity - In complex transmission layouts, it is easy to

accidentally lose sense of polarity

RX

- Effect of swapping terminals on
- NRZ-L
- NRZI

_

The Multilevel Binary Group

- Uses more than two signal levels (3 in this case)
- Signal is multi-level but data is still binary!
- Bipolar-AMI (Alternate Mark (1) Inversion)
- 0 data is represented by no line signal
- 1 data represented by positive or negative pulse
- The 1 pulses alternate in polarity (why? 2

reasons!) - Advantages
- No net dc component (for any data sequence!)
- Lower bandwidth than NRZ
- No loss of sync with a long string of 1z

(but zeros still a

problem- Will try to solve it later) - Alteration of pulse polarity also useful for

error detection

Pseudoternary

- Opposite of Bipolar-AMI
- 1 represented by no line signal
- 0 represented by alternating positive and

negative pulses - Could be called Bipolar-ASI (Why?)
- No advantage or disadvantage over bipolar-AMI

Bipolar-AMI and Pseudoternary

Multilevel Spectrum

The Multilevel Binary Group Advantages

WK 9

- No net dc component
- Spectrum centered at the middle of the BW
- Lower bandwidth than NRZ
- No loss of sync with a long string of 1z

(but zeros still a

problem- Will try to solve it later) - Alteration of pulse polarity also useful for

error detection Next

Bipolar-AMI and Pseudoternary

1. All Single Pulse Errors- Detected

3. Double Pulse Error- Undetected

Adding

Canceling

2. Double Pulse Error- Detected

Disadvantages of Multilevel Binary

N Log2 (M)

No. of bits sent during each signal element

No. of signal levels used

- Coding scheme not as efficient as NRZ
- We send only one bit at a time (1 or 0 data)

? Only M 21 2 signal

levels should be enough, but we are sending 3

levels gt 2 ! - We use 3 signal levels ? Enough to represent

log23 1.58 bits gt 1 bit ! - Receiver Design and Noise Performance
- Now receiver must distinguish between three

signal levels (A, -A, 0) ? Need better receiver

design - Requires approximately 3dB higher SNR for the

same probability of bit error (bit error rate)

Performance with noise NRZ Vs AMI

Multi-Level Binary (AMI)

NRZ

A

A

In both cases signal level is 2A pk2pk

Noise level needed to cause an error

0

-A

-A

- For the same error rate AMI requires higher SNR

noise (lower noise)

- ? i.e. higher Eb/N0
- (for same B and R)
- (hence the 3 dBs difference
- between the two curves)
- For the same SNR (same Eb/N0 )
- AMI has higher error rate
- i.e. AMI has poorer performance with noise

The Biphase Group (2 signal phases per bit)

- Manchester
- Transition in middle of each bit period
- Transition serves both as a clock edge and data

representation - Low to high represents 1
- High to low represents 0
- Used by the IEEE 802.3 specification for Ethernet

LAN (short distances) - Differential Manchester
- Dedicated mid-bit transition used only for

clocking - Data representation is at start of bit
- No transition at start of a bit period represents

1 - Transition at start of a bit period represents 0

(Inverts on 0s

opposite of NRZI) - An example of differential encoding
- Used by IEEE 802.5 specification for Token Ring

LAN

Examples of Self-Clocking Codes

Manchester Encoding

- Mandatory transition in middle of each bit

period - ? Low to high represents 1
- ? High to low represents 0
- Transitions at start of bit only where required

Any error detection capabilities??

Note This is not differential

Data Representation Points

Differential Manchester Encoding

- Mandatory midbit transition for clocking
- Data represented by transition or no transition

at bit start - ? Transition (either direction) represents 0
- (Invert on zeros)
- ? No transition represents 1

Any error detection capabilities??

Data Representation Points

Biphase Group Spectrum

Note higher frequency content

Biphase Pros and Cons

- Pros
- Guaranteed mid bit transitions
- Synchronization facility (self clocking codes)
- Ideally no dc component (using bipolar signals)
- Error detection
- Detecting absence of expected (mandatory)

transitions - Cons
- At least one transition per bit time and possibly

two - Modulation (signaling) rate as high as twice that

of NRZ - So, requires more bandwidth
- Therefore, used over shorter distances (in LANs)

Data rate Modulation (signaling) rate

- Data rate, R 1/Tb bps
- Signaling Rate, D 1/Ts bauds
- If we use k signal elements per bit, then
- Signaling (modulation) rate, D Data rate, R

(bit/s - x k (signal elements/bit)
- Signal elements/s (bauds)

3 bits TXed

Data

Signal

k1

6 signal transitions 6 signal elements

Ts

Ts

Signal

k2

k 6/3 2

- k No. of signal elements/bit
- No. of signal transitions (both ways) No.

of bits

transmitted, n - (over a given period of n Tbs)

Comparison of k for various encoding schemesat

various data bit sequences

k2

e.g., here k 1.5 i.e. baud rate D is

1.5 x data rate R

Digital data, Digital signal Encoding

Bipolar -AMI

Pseudoternary

Use plot to verify values of k in Table 5.3 on

previous

Scrambling Group B8ZS, HDB3Modifications on

Bipolar Multilevel codes

- Use bit scrambling to replace data bit sequences

that would otherwise produce a constant signal

voltage, with a more appropriate bit sequence

producing signal changes - Helps overcome constant DC problems with

Multilevel Binary codes (poor synch) - So, a filling (replacement) bit sequence is

inserted where necessary - Criteria for a Filling sequence
- Should produce enough transitions for

synchronization - Must be recognized by receiver for replacement

with original data - Not likely to be generated by noise

(difficult for

noise/interference to produce it) - Should occupy the same bit length as original

data (so no extra

overhead in the data rate)

Scrambling Group B8ZS, HDB3

- Advantages
- No long sequences of zero level line signal
- No dc component
- No reduction in useful data rate (No extra data

sent) - Built-in error detection capability

B8ZS

- Bipolar With 8 Zeros Substitution
- Improvement on bipolar-AMI
- If an octet of 8 zeros and the last pulse

preceding was positive ()Transmitter encodes

the 8 zeros as 000-0- - (how many level changes does this introduce?)
- If an octet of 8 zeros and last voltage pulse

preceding was negative (-) Transmitter encodes

as 000-0- - (shown in Fig. 5.6)
- Each insertion has two intentional violations of

the basic AMI code rule (violations alternate in

polarity- no net DC added) - 000-0-
- -000-0-
- A strange event ? unlikely to be caused by noise
- Receiver should detect it and interpret as an

octet of 8 zeros (original data) - No additional data sent ? No penalty on genuine

data rate

B8ZS

-000-0-

- See how the insertion satisfies the 5

requirements - Detectable at RX
- Difficult for noise to generate
- Introduces transitions
- Does not introduce DC (alternate violations)
- Error detection capability

V Violation B Bipolar (Valid)

HDB3

- High Density Bipolar 3 Zeros
- Also based on bipolar-AMI
- 4th zero always replaced with an intentional code

violation - String of four zeros replaced with either
- 1 pulse -000- or 000 (violation with preceding

pulse) - or 2 pulses -00 or -00- (internal violation

within the insertion) - What determines whether 1 or 2 pulses?
- Successive insertion violations must alternate in

polarity (why?) -00000000 ?

-000-00 or 00000000 ? 000-00- - With insertions separated by n 1 pulses The

new insertion is determined by the following

rules (Table 5.4) - If n is even, with last pulse p ( or -) ? p00p
- If n is odd, with last pulse p ( or -) ? 000p

HDB3

V Violation B Bipolar (Valid)

-000-00

1s

Even number of 1s after last substitution, with

the last pulse () ? p00p ? -00-

Odd number of 1s after last substitution, with

the last pulse (-) ? 000p ? 000-

p

p

B8ZS, HDB3 Spectrum

2. Digital Data, Analog Signal Encoding

- e.g. over public telephone system
- 300Hz to 3400Hz
- Use modem (modulator-demodulator)
- Modulation (here called shift keying) manipulates

one or more property of a carrier sine wave - Amplitude shift keying (ASK)
- Frequency shift keying (FSK)
- Phase shift keying (PSK)

Modulation Techniques

Digital Data

Digital Signal

Analog Signals

FSK

Phase shift angles ?

PSK

Amplitude Shift Keying (ASK)

- Values represented by different amplitudes of the

carrier sine wave - Usually, one amplitude is zero
- i.e. presence and absence of carrier
- e.g. switching the light sent through a fiber on

and off - Susceptible to noise and sudden changes in gain
- Up to 1200bps on voice grade lines
- Used over optical fiber

Frequency Shift Keying (FSK)

- Most common form is binary FSK (BFSK)
- The two binary data values represented by two

different frequencies (near and on both sides of

a central carrier frequency fc) - Less susceptible to noise than ASK
- (Same as with FM Radio Frequency can be

detected correctly in the presence of noise

better than amplitude) - Applications
- Up to 1200bps on voice grade lines
- Also used at High frequency radio (3-30 MHz)
- And at even higher frequencies on LANs using

coaxial cables

Dfc

Dfc

fc

f1

f2

FSK

fc

f1 fc- Dfc

f2

f1

Spectrum spread due to chopping

Df

Df

f2 fc Dfc

FSK for digital data on Voice Grade Lines

Full Duplex Communication (in the 2 directions

simultaneously)

Amplitude

Spectrum of signal in one direction

Two Spectra overlap (Some Interference)

Frequency(Hz)

3400

300

1270

2025

Bell Systems 108 Series modem

fc ? for left and right

1070

2225

f1, f2 ?

f1, f2

Dfc ? for left and right

Multiple FSK (MFSK)

To improve BW utilization (efficiency) we send

one of multiple signal symbols (frequencies)

every signal element ? More than 1 bit at a time

- More than two frequencies used
- An example of multi-level coding (M levels)
- Each signalling element conveys more than one bit

(L bits, L log2 M) - This increases bandwidth efficient
- (high BE C/B values) (Higher data rates for

the same signalling rate) - But in general, multi-level coding is more prone

to error due to noise - (Unless you do something about it, e.g.

orthogonally)

Multiple FSK (MFSK)

(Half the frequency separation)

(Dfc before)

i.e. different frequencies

- Frequency separation 2 fd
- Bandwidth Required M (2fd)
- - Minimum Ts (signal element duration) 1/(2fd)
- ? Max signaling rate D 1/Ts 2fd
- ? Max data rate R D L 2fd L

Important Parameters

The closer the two frequencies are, the larger

Ts needed to discriminate between them

Ts

Multiple FSK (MFSK)

Frequency

Data sent

Correction!

kBauds

signaling

2fd50kHz

Bandwidth M (2fd) 8 x 50

400 kHz (lt 2 fc, so OK)

Min Ts 1/ (2fd) 1/50 KHz

20 ms

250kHz

75kHz

425kHz

fc

f1

f8

Max signaling rate 1/Ts 2fd

50 kBauds Max Data rate

Max Signaling rate x L 50 KHz x 3 150 Kbps

Multiple FSK (MFSK)

M 4 L Log2 (M) 2

11

10

01

00

b

Phase Shift Keying (PSK)

- Phase of carrier signal is shifted to represent

data - Binary PSK Absolute
- Two phases (spaced at 180?) represent the two

binary digits

Where d(t) 1 for 1 data and -1 for 0 data

Differential PSK (DPSK)

- Phase shifted relative to the previous signal

element, rather than some reference signal

- 0 Do not reverse phase 1 Reverse phase (as with

NRZI, invert on 1)) - (A form of differential encoding)
- Advantage
- - No need for a reference oscillator at RX to

determine absolute phase

Multi-level PSK (MPSK)

- 4 different phases spaced at ?/2 (90o)
- Multilevel signaling, so
- More efficient use of bandwidth

(i.e higher data rate for the same

signaling rate) - Each signal element represents log2 4 2 bits

-3?/4

1

-1

1

-1

Bit pair transmitted

-?/4

Quadrature PSK (QPSK) Implementation

Quadrature Component

In phase branch (I)

In-phase Component

n 1, 3, 5, 7

I and Q are derived from the 2 bits transmitted

1

Quadrature (90?) branch (Q)

-1

1

-1

- n I Q
- 1 1
- 3 -1 1
- -1 -1
- 7 1 -1

1 ? 1, 0 ? -1

Q

I

Quadrature PSK (QPSK) Implementation

Bits are taken 2 at a time .

Assign bit to I or Q?

1

-1

1

-1

I 1, Q -1

- Started with how many phases?
- 4 phases for the price of 2?
- Expect error performance similar to
- BPSK!

Quadrature Amplitude Modulation (QAM)

Constellation

- An extension of the QPSK just described
- Combines both ASK and PSK
- For example, ASK with 2 levels and
- PSK with 4 levels give 4 x 2 i.e. 8-QAM
- M 8, L 3
- Up to M256 is possible
- Large bandwidth savings
- But some susceptibility to
- noise
- QAM used on asymmetric
- digital subscriber line
- (ADSL) and some wireless
- systems

M8, L 3

True Multilevel PSK (MPSK)

- Can use more phase angles and more than one

amplitude - For example, 9600 bps modems use 12 phase angles,

four of which have 2 amplitudes - Gives 16 different signal elements ? M 16 and

L log2 (16) 4 bits - Every signal element carries 4 bits

(Data sent 4 bits at a time) - Baud rate D required is only 9600/4 2400 bauds

(required BW is low i.e. can use on a voice

grade lines!) - Complex signal encoding allows high data rates to

be sent on voice grade lines having a limited

bandwidth

Performance of D-A Modulation Schemes

a. Performance without noise

- Here, bandwidth requirement is the main concern

(should be minimized) - Bandwidth determined by baud rate

Modulated Signal

Modulation ? Filtering ? Transmission

r Filtering Coefficient

m(t)

x(t)

s(t)

Modulator

Filter (r)

Transmitted Signal

(Shift Keyer)

To TX

digital Data

Filter Truncates BW

Modulated Analog Signal

Filtered, band-limited signal

0 lt r lt1

fc

Carrier Signal

Larger r gives larger Transmission BT

Signaling rate D bauds

Data rate R bps

e.g.

(Limited Transmitted bandwidth, BT Hz), e.g.

(Wide, ? bandwidth)

Performance of Modulation Schemes

- Performance without noise Transmission

Bandwidth (BT) Requirement

- We would like to optimize the use of available

bandwidth - i.e. send data at a high rate with the minimum

bandwidth possible - Define the Bandwidth (or spectral) Efficiency, BE

as - Although it is Efficiency, BE can be greater

than 1

Performance of Digital-Digital (Binary)

Modulation Schemes

a. Performance without noise Bandwidth

Efficiency BE

- Example NRZ and NRZI
- Transmitted BW is similarly truncated
- Transmission Bandwidth is given
- approximately by
- D R only for binary, therefore
- and therefore BE is

Larger r

r 0 BT 0.5R

r 1 BT R

Performance of D-A (Binary) Modulation Schemes

a. Performance without noise Bandwidth

Efficiency BE

- For BASK and BPSK
- BT directly related to the (signaling,

modulation, baud) rate, D - where r is the filtering coefficient 0lt r lt1
- With binary encoding (not multilevel), D R, so
- Bandwidth Efficiency, BE

Performance of D-A (Binary) Modulation Schemes

a. Performance without noise Bandwidth

Efficiency BE

- For BFSK
- Frequency of signal is changed by Df, about fc

(i.e. 2 Df) - BT is a function of both Df and the (signaling)

modulation rate, D - With binary encoding (not multilevel), D R, so
- Therefore BE is

Performance of D-A (Binary) Modulation Schemes

a. Performance without noise Bandwidth

Efficiency BE

- For BFSK, contd.
- Two extreme cases
- Df gtgt R (when fc is large)
- Df ltlt R (when fc is small)

, similar to that for BASK, BPSK

Performance of D-A (Multi-level) Modulation

Schemes

a. Performance without noise Bandwidth

Efficiency BE

- For MPSK M phases, L bits/signal element
- BT directly related to the (signaling) modulation

rate, D - where r is the filtering coefficient 0lt r lt1
- With M-level encoding,

, so - Bandwidth Efficiency, BE

Same as for BPSK

For multilevel, L 2 and r 1, so BE 1

So, BE is directly proportional with L

Performance of D-A (Multi-level) Modulation

Schemes

a. Performance without noise Bandwidth

Efficiency BE

- For MFSK M Frequencies, L bits/signal element
- At maximum signaling rate D 2fd
- Bandwidth Efficiency, BE

(Equation 5.11 in textbook)

Bandwidth Efficiency (BE) Data

- BE R/BT

Filtering Coefficient, r

Performance of D-A Modulation Schemes

b. Performance with noise ASK, FSK, PSK, QPSK

- Bit error rate (BER) Plotted Vs Eb/N0 (dBs)
- Curves to the left give better performance
- Lower S/N required for same Error rate
- Lower Error rate obtained for same SNR
- Why QPSK and PSK give the same performance?
- 2 phase levels (1,-1) in both cases
- Remember QPSK gave 4 phase levels for the price

of 2!

Performance of D-A Modulation Schemes

b. Performance with noise MFSK, MPSK

Larger M ? Poorer error performance

Larger M ? Better error performance!

Orthogonal FSK

As expected

Eb/N0 in terms of the bandwidth efficiency

(BE)(for binary transmission)

BT is the Transmission Bandwidth

Example

- What is the bandwidth efficiency (BE) for ASK and

PSK, for a bit error rate (BER) of 10-7 on a

channel with a SNR of 12dB ?

- For ASK (binary) At BER 10-7, Eb/N0 14.3

dBs - Substituting in

- BEASK,FSK -14.3 12 -2.3 dBs ? R/BT 10-.23

0.6 - However, for PSK ? Eb/N0 11.3 dBs)
- BEPSK R/BT 1.2 (doubled 3dB higher-

improvement)

3. Analog Data, Digital Signal

- Digitization
- Conversion of analog data into signals suitable

for the digital mode of transmission/storage - The digital data can be transmitted digitally as

is (e.g. NRZ-L) - Or converted to a more appropriate digital code,

e.g. Manchester - Or even converted to analog signal for

transmission, e.g. ASK

All supported by

Digital Signal (NRZ-L)

Codec

Or

Digital Mode of Transmission

- Will study two Types of Codec
- Pulse Code Modulation (PCM)
- Delta Modulation (DM)

Code Converter

Digital Signal (Manchester)

Or

Analog signals Carry data!

(Shift Keyer)

Analog Signal (ASK)

Two basic tasks to be performed by a digitizer

Analog is continuous in both time and

amplitude Must discretize it in both!

Digital Out

Digitizer (Codec)

Analog In

- 1. Sampling in time

- 2. Quantization in amplitude

L bits (sent serially)

Number of quantization levels 2L, where L is

the number of bits allowed for the digital output

2. Quantization To a finite number of levels in

amplitude

PAM Samples

Signal values Between samples Are ignored- lost!

Digitizing the PAM Samples ? PCM

1. Sampling at discrete points in time

Maximum sampling interval allowed 1/(2fmax)

Where fmax is the maximum frequency in the analog

signal

2fmax is the minimum acceptable sampling rate

Sampling

- Nyquist Sampling Theorem
- If a signal is sampled at regular intervals at a

rate higher than twice the highest signal

frequency fmax, the samples contain all the

information in the original signal - Original signal may be reconstructed from these

samples using an ideal low-pass filter - Example Voice data limited to 4000Hz
- Requires sampling at a rate of at least
- 8000 sample per second

Quantization using 4 bits

Analog signal is band-limited, with bandwidth (0

to B Hz)

24 16 signal levels, numbered 0 to 15

Quantization

Signal Amplitude, Volts Vmax 16 V

PAM Sample

Quantization Error ?½ LSB

Level numbers starting from 0

Transmitted Serial Code representing the value

of the PAM Samples

1 LSB

Sampling rate 2B sample/s

Data Rate 2B x 4 bps

Each PAM sample is assigned the number of the

nearest quantization level and the corres.

digital code is transmitted

Must finish sending the n bits of the code within

the sampling interval .before the next sample

starts!

Pulse Code Modulation (PCM)

- Start with the analog sampled pulses (Pulse

Amplitude Modulation, PAM) - Assign each sample a digital value ( number of

the closest quantization level) - n 4 bit system gives M 16 levels (M 2n)
- Quantization error or noise
- Larger for small M (number of levels)
- Approximations mean it is impossible to recover

the original signal exactly - SNR for quantization error using n bits is
- Each additional bit used for quantization

increases SNR by about 6 dB (a power

factor of 4) - 256 quantization levels n 8 bits, SNR ? 50 dBs

- ? Quality comparable with analog transmission
- Voice 2 x 4000 8000 samples per second, with

of 8 bits per sample, this is a data rate of

80008 64 kbps

PCM Example

- Suppose we want to encode an analog signal that

has voltage levels 0 5 V using 2-bit PCM (n 2

bits) (M 22 4 levels) - We divide the max voltage level into four

intervals, so the size of each interval is

5/41.25 V - Level intervals 0-1.25, 1.25-2.5, 2.5-3.75,

3.75-5 - We select the quantization levels at the middle

of each level interval - i.e. selected levels are 0.625, 1.875, 3.125,

4.375 - This guarantees a maximum quantization error

of ½ (5V /4) 0.625 (1/2 LSB) - and quantization SNR 6 x 2 1.76 13.76 dB

Problem with Linear (Uniform) Encoding

- Absolute quantization error for each sample is

the same regardless of signal level - Signals with lower amplitudes are relatively more

distorted - One Solution make quantization levels not evenly

spaced (denser for low amplitudes) - i.e. higher number of quantization steps for

lower amplitudes and smaller number for larger

ones - Reduces overall signal distortion
- This is Nonlinear Encoding

Effect of Nonlinear Coding

Non linear Encoding

Linear Encoding

Nonlinear Encoding

Quantization error is fixed- same for both

weaker and stronger signals

Weaker signals have smaller quantization errors

Companding An analog solution to the problem

- Effect of nonlinear coding can also be reduced by

companding the analog signal before a linear

digital encoding - Compressing-expanding
- At TX More gain for weak
- signals than for strong
- signals- before encoding
- At RX Reverse
- operation (de-companding?)
- How would the de-companding
- curve look like?

No Companding (Linear encoding)

Example (Problem 5-20)

- Consider an audio signal with spectral components

in the range of 300 to 3000 Hz. Assuming a

sampling rate of 7000 samples per second will be

used to generate the PCM signal - 7000 gt 2 x 3000 ? OK
- To obtain a quantization SNR of 30 dB, what is

the number of uniform quantization levels needed? - (SNR)dB 6.02 n 1.76 30 dB
- n (30 1.76)/6.02 4.69
- Always round off to the next higher integer ? n

5 bits ? 25 32 quantization

levels - What is the data rate required?
- R 7000 samples/sec ? 5 bits/sample 35 Kbps

PCM How costly in terms of BW?

- For good voice reproduction
- PCM ? 128 levels (7 bits per sample)
- Voice bandwidth (baseband) 4 KHZ
- Data rate should be 2 x 4000 x 7 56 kbps
- Analysis of Bandwidth requirement
- PCM digital transmission requires 56 kbps
- Using Nyquist channel capacity criterion, this

data rate requires a bandwidth of ? 28 KHz - (B C/2 R/2 56/2 28)
- Base bandwidth of voice signal 4 KHz
- 28 KHz 7 x 4 KHz
- i.e. PCM digital encoding requires a Nyquist

bandwidth which is 7 times the bandwidth of the

baseband signal! - ( n Bbaseband) ? PCM is costly in bandwidth,

especially with lager n!

PCM Performance, Contd.

- Nevertheless, digital encoding continues to grow

in popularity, because they allow - Use of repeaters No cumulative noise
- Time-division multiplexing (TDM) without the

inter modulation noise of the alternative analog

scheme (FDM) - Use of the more efficient digital switching

techniques in networks - Solution Compression and more efficient coding

can be used to overcome the problem of the larger

data rates (and BW) required by digital encoding

Delta Modulation A cheaper alternative to PCM

- An attempt to reduce complexity (and large R) for

PCM - Analog input is approximated by a staircase

function - Move up or down one fixed amplitude increment (?)

at each sample interval to track changes in the

analog waveform - A single bit stream is produced to approximate

the derivative of the analog signal rather than

its amplitude - Generate a 1 if staircase goes up (slope ive)
- Generate a 0 if staircase goes down (slope - ive)
- Transmit this sequence of 1,0 data (1-bit per

sample) - Receiver uses this bit stream to reconstruct the

staircase waveform and approximate the original

analog waveform

Delta Modulation - example

Quantization

Lower for larger d

Larger for larger d

Sampling

1010 ...Alternating slope ? Signal is level

Digital O/P (Only 1 bit/sample!)

1 ive slope ? Signal increasing

0 - ive slope ? Signal decreasing

Delta Modulation - Implementation

- At mid sampling interval, compare the analog

input to current value of the approximating

staircase function - If input exceeds staircase function, transmit a 1

and increment staircase by ? for the next sample - Otherwise generate a 0 and decrement staircase by

? for the next sample - Output of the DM is a binary bit sequence to be

used for generating the staircase function at RX - Reconstruct staircase function at receiving end

and smooth by a low pass filter to reconstruct an

approximation of the analog signal

Delta Modulation - Implementation

gt

lt

Generated Staircase

Transmitted bit sequence

Generated Staircase

At Source

Staircase Generator

Reconstructed Staircase

Generated Staircase

Received bit sequence

To filtering Analog Waveform Reconstruction

At Destination

Delta Modulation Important Design Parameters

- Two important parameters in DM scheme
- Size of amplitude step (d) assigned to each

binary digit - Must be chosen to produce a balance between two

types of errors or noise (conflicting

requirements) - When waveform changes rapidly, slope overload

noise increases with a smaller d - When waveform changes slowly, quantizing noise

increases with a larger d (the usual quantization

error) - Sampling rate, increasing it
- Improves the accuracy of the scheme
- But increases the data rate requirement
- Main advantages of DM
- Lower data rate required (1 bit samples!)
- Simple to implementation
- Disadvantage
- Larger quantization errors (lower SNR) compared

to PCM

4. Analog Data, Analog Signals

WK 11

- Modulation
- Combining an input signal m(t) and a carrier at

frequency fc to produce signal s(t) with

bandwidth centered at fc - We had to use a form of modulation (shift keying)

to represent digital data as analog signals. - But why modulate signals that are already analog?
- Higher frequency may be needed for effective

transmission - For unguided transmission impossible to send low

frequency baseband signals, e.g. speech, as

required antennas would have dimensions in

kilometers! - Allows implementing frequency division

multiplexing (FDM)

Types of Analog Modulation

Carrier

Modulating Signal

X(t)

Signal to be Transmitted, x(t)

Modulated Signals

Amplitude Modulation (AM)

A ? x(t)

- Angle Modulation
- Phase, PM

f ? x(t)

A sin (wt) f(t) wt

2. Frequency, FM

f ? x(t)

Effect of modulation on signal power?

Effect of modulation on signal BW?

Amplitude Modulation (AM)

- Simplest form of modulation
- Accos 2pfct is the carrier,
- and x(t) Amcos 2pfmt is the input modulating

signal - Modulated signal expressed as
- na is the modulation index (0 lt na ? 1)
- Added 1 is a DC component to prevent loss of

information - there will always be a carrier - Scheme is known as double sideband transmitted

carrier (DSBTC)

Amplitude of modulated wave

Portion of the modulating signal

Units of na?

DSBTC Amplitude Modulation - Example

- Given the amplitude-modulating signal x(t)Amcos

2pfmt , find s(t) - Resulting signal has three components
- One at the original carrier frequency fc
- A pair of additional components (side bands),
- each spaced fm Hz from the carrier
- Envelope of resulting signal
- With na lt1, envelope is exact reproduction of the

modulating signal, - So it can be recovered at receiver by a low pass

filter - With na gt1, envelope crosses the time axis and

information is lost

Ac

Am/2

Am/2

Two Sidebands contain modulating signal power

fc

fm

fm

So, keep na ? 1

DSBTC Amplitude Modulation - Examples

MatLab Simulations

Different vertical scales for the 3 plots

Modulating Signal fm ?

Am ?

Carrier fc ?

Ac ?

Envelope

Modulated Signal

na ?

na 0.5/1 0.5

(10.5cos2pit) (1nacos2pit)

DSBTC Amplitude Modulation - Example

Maximum modulation allowed (na 1)

na 1/1 1

DSBTC Amplitude Modulation - Example

Beyond maximum modulation allowed (na gt 1)

na 2/1 2 (gt1) (not allowed)

Spectrum of DSBTC signal

Modulating signal has a single frequency, fm

fc 40 Hz fm 1 Hz Ac 2 V Am 2 V na

Am/Ac 1

2

1

Spectrum of an DSBTC signal

Let modulating signal have a bandwidth 0-B

Hz (Baseband)

- Spectrum of AM signal is original
- carrier plus spectrum of original
- signal translated on both sides of fc
- Portion of spectrum f gt fc is
- upper sideband
- Portion of spectrum f lt fc is
- lower sideband
- Bandwidth Requirement 2B
- Example voice signal 300-3000Hz
- With fc 60 KHz
- Upper sideband is 60.3-63 KHz
- Lower sideband is 57-59.7 KHz
- Bandwidth Requirement 2 fmmax

Bandwidth of Modulated Signal

Note orientation of the two sidebands

Note Modulating signal amplitude does not affect

bandwidth of modulated signal . But affects its

power (next)

DSBTC Amplitude Modulation

DSBTC

- Total transmitted power Pt in modulated s(t) is

given by - Pc is transmitted carrier power
- na should be maximized (but lt1) to allow

transmission of more power in sideband signals

that carry information - Modulated signal contains redundant information

(duplicate side bands) - Only one of the sidebands is enough for restoring

the modulating signal - Possible ways to economize on transmitted power
- SSB single sideband, uses a filter at TX to pass

only one of the sidebands the carrier, saves on

BW ( B) - SSBSC single sideband suppressed carrier, uses a

filter to select only one of the sidebands

(without the carrier), saves on BW ( B) - DSBSC double sideband suppressed carrier,

carrier is not transmitted, no saving on BW (

2B) - Suppressing the carrier may not be OK in some

applications, e.g. ASK, where the carrier can

provide TX-RX synchronization.

Note Modulating signal amplitude affects power

of modulated signal

Am na Ac

DSBSC Double Sideband Suppressed Carrier -

Example

- Signal is expressed as

Suppressed Carrier

Angle Modulation

What parameters can I change to change the

angle of the modulated signal?

- Includes
- Frequency modulation (FM) and
- Phase modulation (PM)
- Modulated signal is given by
- Phase modulation (PM) (the direct way)
- Instantaneous phase is proportional to the

modulating signal - np is the phase modulation index
- Frequency modulation (FM) (the indirect way)
- Instantaneous angular frequency deviations from

wc is proportional to the modulating signal, - and we have
- So make the derivative of f proportional to

modulating signal - nf is the frequency modulation index

Total Angle

Units of np? Units of nf?

Angle Modulation

- The total phase angle of s(t) at any instant is

2pfctf(t) - Instantaneous phase deviation from that of the

carrier is f(t) - Phase Modulation (PM)
- f(t) npx(t), instantaneous phase variations are

directly proportional to m(t) - Frequency Modulation (FM)
- Instantaneous angular frequency, , can be

defined as the rate of change of total phase - So, for the modulated signal, s(t)
- In FM, f(t) is made proportional to x(t)

? f(t) nf x(t) - So, instantaneous frequency deviations from the

carrier frequency are proportional to x(t).

? df (t) (nf/2p)

x(t)

df (t)

Phase Modulation (PM)- Example

- Derive an expression for a phase-modulated signal

s(t) and its instantaneous frequency given Ac

5V, and the modulating signal - x(t) 3 sin 2pfmt
- We know that s(t)
- For PM, f (t) is given by
- Then s(t) is
- Instantaneous frequency of s(t) is

np is Radians/Volt

Peak frequency deviation for the PM signal

Note Frequency variations in s(t) phase-lead

x(t) amplitude variations by 90?

Frequency Modulation FM

- From equations opposite,
- Peak frequency deviation DF is given by
- Where Am is the peak value of the modulating

signal x(t) - An increase in the amplitude Am of x(t)
- increases DF ? increases bandwidth requirement

BT - But average power level of the FM modulated

signal is fixed at AC2/2, (does not increase with

Am) - i.e. in Frequency Modulation (angle modulation in

general), Am affects the BW but not the power

budget - While in Amplitude Modulation, Am affects the

power budget but not the bandwidth

Frequency Modulation - Example

- Derive an expression for a frequency-modulated

signal s(t) with Ac 5V, given the modulating

signal - x(t) 3 sin 2pfmt
- The FM modulated signal s(t) is
- For FM, f(t) is given by
- Then f(t) is
- We have
- Substituting for DF we get

nf is (Radians/s)/Volt

But frequency varies as f, i.e. as sin not as

cos !!

Bandwidth Requirement

- All AM, FM, and PM result in a modulated signal

whose bandwidth is centered around fc - Let B be the bandwidth of the modulating signal

(0-B Hz) - AM gives only sums differences of frequencies

with fc, and we have BT 2B for DSB systems - Angle modulation includes a term of the form

cos(cos()) which is a nonlinear term producing

a wide range of frequencies fcfm, fc2fm,

(the Bessel function) - i.e. Theoretically, an infinite bandwidth is

required to transmit an FM or PM signal

Practical Bandwidth Requirement for Angle

Modulation

For AM

- Carsons Rule of thumb
- Since ? is gt 0, both FM and PM require a larger

bandwidth than AM (2B) - For FM, BT 2DF 2B

DF is the peak frequency deviation

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