Chapter 5 Digital Communication SystemsChapter

contents

- 5.1 Overview of Digital Communication Systems
- Transmission schemes, communication link, Adv vs.

Disadv - 5.2 Digital Transmission Pulse Modulation
- Pulse modulation method PWM, PAM, PPM, PCM
- 5.3 Pulse Code Modulation
- PCM operation, sampling, quantization
- 5.4 Information Capacity, Bits, Bit Rate, Baud,

M-ary encoding - 5.5 Digital Modulation
- ASK, FSK. PSK
- 5.6 Applications of Digital Communication Systems

5.1 Overview

- Digital communications is the transfer of

information (voice, data etc) in digital form. - Basic diagram of digital/data communications

5.1 Overview

- If the information is in the analog form, it is

converted to a digital form for transmission. At

the receiver, it is re-converted to its analog

form. - In some case, data needs to be changed to analog

form to suit the transmission line (ex

internet/point-to-point data communication

through the public switching telephone network)

the use of modem - Modem (from modulator-demodulator) is a device

that modulates an analog carrier signal to encode

digital information, and also demodulates such a

carrier signal to decode the transmitted

information - Function of modem at transmitter converts

digital data to analog signal that are compatible

to the transmission line characteristics.

5.1 Overview

- Transmission schemes for analog and digital

signals

5.1.1 Communication links in digital transmission

- Basic protocol of transmission simplex,

half-duplex, full duplex - Classification of communication link
- Synchronous Channel the transmitted and

received data clocks are locked together. This

requires that the data contains clocking

information (self-clocking data). - Asynchronous Channel the clocks on the

transmitter and the receiver are not locked

together. The data do not contain clocking

information and typically contains start and stop

bits to lock the systems together temporarily.

5.1.2 Digital vs Analog Communication Systems

- Advantages
- Noise immunity
- Digital signals are less susceptible than analog

signals to interference caused by noise - Simple determination is made whether the pulse is

above or below the prescribed reference level - Signal processing capability
- Digital signals are better suited than analog

signals for processing and combining for

multiplexing purpose. - Much simpler to store digital signals compare to

analog signals - Transmission rate of digital signals can be

easily changed to suit different environments and

to interface with different types of equipment. - Can also be sample instead of continuously

monitored - A regenerative repeater along the transmission

path prevent accumulation of noise along the

path. It can detect a distorted digital signal

and transmit a new clean signal

5.1.2 Digital vs Analog Communication Systems

- Advantages
- Simpler to measure and evaluate than analog

signals - Easier to compare the error performance of one

digital system to another digital system. - Transmission error can be detected and corrected

more easily and more accurately (error bit

check). This gives very low error rate and high

fidelity. - Digital hardware implementation is flexible and

permits the use of microprocessors and digital

switching. - Ability to carry a combination of traffics, e.g.

telephone signals, data, coded video and

teletext, if the medium has enough capacity.

5.1.2 Digital vs Analog Communication Systems

- Disadvantages
- Bandwidth
- Transmission of digitally encoded analog signals

requires significantly more bandwidth than simply

transmitting the original analog signal. - Circuit complexity
- Analog signals must be converted to digital

pulses prior to transmission and converted back

to their original analog form at the receiver

additional encoding/decoding circuitry. - Requires precise time synchronization between the

clocks in the transmitter and receiver.

5.2 Digital Transmission Pulse Modulation

- Mostly used modulation technique in digital

transmission - Consists of several processes
- Sampling analog information signals
- Converting those samples into discrete pulse
- Transporting the pulses from a source to a

destination over a physical transmission medium - Predominant method of pulse modulation pulse

width modulation (PWM), pulse position modulation

(PPM), pulse amplitude modulation (PAM), pulse

code modulation (PCM) - Pulse Width Modulation (PWM)
- The width (active portion of the duty cycle) of a

constant amplitude pulse is varied proportional

to the amplitude to the amplitude of the analog

signal at the time the signal is sampled. - Maximum analog signal amplitude produces the

widest pulse, and the minimum analog signal

amplitude produces the narrowest pulse. - All pulses have the same amplitude.

5.2 Digital Transmission Pulse Modulation

- Pulse Position Modulation (PPM)
- The position of a constant-width pulse within a

prescribed time slot is varied according to the

amplitude of the sample of the analog signal. - The higher the amplitude of the sample, the

farther to the right the pulse is positioned

within the prescribed time slot. - The highest amplitude sample produces a pulse to

the far right, and the lowest amplitude sample

produces a pulse to the far left. - Pulse Amplitude Modulation (PAM)
- the amplitude of a constant-width

constant-position pulse is varied according to

the amplitude of the sample of the analog signal. - The amplitude of a pulse coincides with the

amplitude of the analog signal - PAM wave resemble the original analog signal more

than the waveforms for PWM or PPM.

5.2 Digital Transmission Pulse Modulation

- Pulse Code Modulation (PCM)
- Analog signal is sampled and then converted to a

serial n-bit binary code for transmission. - Each code has the same number of bits and

requires the same length of time for transmission.

5.2 Digital Transmission Pulse Modulation

Figure Comparing between Pulse modulations

(a) analog signal (b) sample pulse (c) PWM (d)

PPM (e) PAM (f) PCM

5.3 Pulse Code Modulation (PCM)

- Preferred method of communication within the

public switched telephone network (PSTN). - with PCM it is easy to combine digitized voice

and digital data into a single, high-speed

digital signal and propagate it over either

metallic or optical fiber cables. - Refer to figure of simplified block diagram of

PCM system. - At the transmitter
- The bandpass filter limits the frequency of the

analog input signal to the standard voice-band

frequency range of 300 Hz 3000 Hz. - The sample-and-hold circuit periodically samples

the analog input signal and converts those

samples to a multilevel PAM signal. - The analog-to-digital converter (ADC) converts

the PAM samples to parallel PCM codes, which are

converted to serial binary data in the

parallel-to-serial converter. The output to the

transmission line is a serial digital pulses. - The transmission line repeaters are placed at

prescribed distances to regenerate the digital

pulses.

5.3 Pulse Code Modulation (PCM)

- At the receiver
- The serial-to parallel converter converts serial

pulses received from the transmission line to

parallel PCM codes. - The digital-to-analog converter (DAC) converts

the parallel PCM codes to multilevel PAM signals. - The hold circuit is basically a low pass filter

that converts the PAM signals back to its

original analog form - An integrated circuit that performs the PCM

encoding and decoding is called a codec

(coder/decoder)

5.3 Pulse Code Modulation (PCM)

- Block diagram of a single channel, simplex PCM

transmission channel

5.3.1 PCM Sampling

- The function of the sampling circuit
- to periodically sampled the continually changing

analog input and convert those samples to a

series of constant-amplitude pulse that easily be

converted to binary PCM code - 2 basic techniques for the sampling function
- 1) Natural sampling
- Tops of the sample pulses retain their natural

shape during the sample interval. - Difficult for an ADC to convert the sample to a

PCM code due to un-constant voltage. - 2) Flat-top sampling
- Most common method, used in the sample-and-hold

circuit periodically sample the continually

changing analog input voltage and converts those

samples to a series of constant-amplitude PAM

voltage levels.

5.3.1 PCM Sampling

Natural sampling

Flat-top sampling

5.3.2 Sampling Rate

- Sampling is a process of taking samples of

information signal at a rate based on the Nyquist

Sampling Theorem. - Nyquist Sampling Theorem the original

information signal can be reconstructed at the

receiver with minimal distortion if the sampling

rate in the pulse modulation signal is equal or

greater than twice the maximum information signal

frequency. - where fs minimum Nyquist sampling

rate/frequency - fm(max) maximum information signal

frequency

5.3.2 Sampling Rate

- If fs is less than 2 times fm(max) an impairment

called as alias or fold-over distortion occurs.

5.3.3 Quantization

- Quantization process of assigning the analog

signal samples to a pre-determined discrete

level. - The number of quantization levels, L depends on

the number of bits per sample, n where - where L number of quantization level
- n number of bits in binary to represent the

value of the samples - The quantization levels are separated by a value

of ?V that can be defined as - ?V is the resolution or step size of the

quantization level.

5.3.3 Quantization

- Ex

5.3.3 Quantization

- Ex (continue)

5.3.3 Quantization

- Quantization error/Quantization noise error

that is produced during the quantization process

due to the difference between the original signal

and quantized signal magnitudes. - Since a sample value is approximated by the

midpoint of the sub-internal of height ?V, in

which the sample value falls, the maximum

quantization error is ?V/2. - Thus, the quantization error lies in the range (-

?V/2, ?V/2).

5.3.4 Dynamic Range

- the number of PCM bits transmitted per sample

determined by determined by several factors

maximum allowable input amplitude, resolution and

dynamic range. - Dynamic range (DR) the ratio of the largest

possible magnitude to the smallest possible

magnitude (other than 0 V) that can be decoded by

the DAC converter in the receiver. - mathematically expressed
- where DR dynamic range (unitless ratio)
- Vmin the quantum value (resolution)
- Vmax the maximum voltage magnitude that can

be discerned by the - DACs in the receiver

5.3.4 Dynamic Range

- Dynamic range is generally expressed as a dB

value - where DR dynamic range (unitless ratio)
- Vmin the quantum value (resolution)
- Vmax the maximum voltage magnitude that can

be discerned by the - DACs in the receiver
- the number of bits used for a PCM code depends on

the dynamic range. The relationship between

dynamic range and the number of bits in a PCM

code is - and for a minimum number of bits 2n 1 DR

5.3.4 Dynamic Range

- Ex For a PCM system with the following

parameters, determine (a) minimum sample rate (b)

minimum number of bits used in the PCM code (c)

resolution (d) quantization error - Maximum analog input frequency 4 kHz
- Maximum decode voltage at the receiver

2.55V - Minimum dynamic range 46 dB

5.3.4 Coding Efficiency

- Coding efficiency ratio of the minimum number

of bits required to achieve a certain dynamic

range to the actual number of PCM bits used. - number of bits should include the sign bit !

5.3.5 Signal-to-Quantization Noise Ratio

- Generally, the quantization error or distortion

caused by digitizing an analog sample expressed

as an average signal power-to-average noise power

ratio. - For a linear PCM codes (all quantization

intervals have equal magnitudes), the signal

power-to-quantizing noise power ratio is

determined by - where R resistance (ohms)
- v rms signal voltage (volts)
- q quantization intervals (volts)
- v2/R average signal power (watts)
- (q2/12)/R average quantization noise power

(watts) - if R is assume to be equal

5.3.6 Companding

- Companding is the process of compressing and

expanding to improve the dynamic range of a

communication system. - a companding process is done by firstly

compressing signal samples and then using a

uniform quantization. The input-output

characteristics of the compressor are shown

below. - the compressor maps input signal
- increments ?x into larger increments
- ?y for a large input signals.
- 2 compression laws recognized by
- CCITT
- µLaw North America Japan
- A-Law Europe others

5.3.7 Line speed / Transmission bit rate

- Line speed is the transmission bit rate at which

serial PCM bits are clocked out of the PCM

encoder onto the transmission line. - Line speed/transmission bit rate can be expressed

as - Line speed samples/seconds x bits/sample
- line speed transmission rate (bps)
- samples/second sampling rate fs
- bits/sample no of bits in the compressed PCM

code

5.4 Parameters in Digital Modulation5.4.1

Information Capacity

- Information capacity a measure of how much

information can be propagated through a

communication systems and is a function of

bandwidth and transmission time. - represents the number of independent symbols that

can be carried through a system in a given unit

of time - the most basic digital symbol used to represent

information is the binary digit, or bit. - Bit rate the number of bits transmission during

one second and is expressed in bits per second

(bps). - Bit rate is used to express the information

capacity of a system. - mathematically expressed, information capacity I
- refer to slides of chapter 1 !

5.4.2 M-ary encoding

- in an M-ary encoding, M represents a digit that

corresponds to the number of conditions, levels,

or combination possible for a given number of

binary variables. - the number of bits necessary to produce a given

number of conditions is expressed mathematically

as - where N number of bits necessary
- M number of conditions, levels, or

combination possible with N bits - from above, the number of conditions possible

with N bits can be expressed as - Ex with 1 bit ? 21 2 conditions
- 2 bits ? 22 4 conditions
- 3 bits ? 23 8 conditions

5.4.3 Baud and Minimum Bandwidth

- Bit rate refers to the rate of change of

digital information, which is usually binary. - Baud refers to the rate of change of a signal

on a transmission medium after encoding and

modulation have occurred. - Baud can be expressed as
- where Baud symbol rate (baud per second)
- ts time of one signaling element (seconds)
- signaling element symbol
- for a given bandwidth B, the highest theoretical

bit rate is 2B. Using the multilevel signaling,

the Nyquist formulation for channel capacity is

5.4.3 Baud and Minimum Bandwidth

- where fb channel capacity (bps)
- B minimum Nyquist bandwidth (Hertz)
- M number of discrete signal or voltage

levels - above formula can be rearranged to solve for the

minimum bandwidth necessary to pass M-ary

digitally modulated carrier as follow - since N log2M above formula can be expressed as
- where N is the number of bits encoded into each

signaling element (symbol).

5.5 Digital Modulation

- Given an information signal which is digital and

a carrier signal represented as follow - A digitally modulated signal is produced as

follow - If the amplitude (V) of the carrier is varied

proportional to the information signal, ASK

(Amplitude Shift Keying) is produced. - If the frequency (f) of the carrier is varied

proportional to the information signal, FSK

(Frequency Shift Keying) is produced. - If the phase (?) of the carrier is varied

proportional to the information signal, PSK

(Phase Shift Keying) is produced. - If both amplitude and phase are varied

proportional to the information signal, QAM

(Quadrature Amplitude Modulation) is produced.

5.5.1 Amplitude Shift Keying

- digital information signal directly modulates the

amplitude of the analog carrier. - mathematically, the modulated carrier signal is

expressed as follow - (5.5-1)
- where vask(t) amplitude-shift keying wave
- vm(t) digital information (modulating)

signal (volts) - A/2 unmodulated carrier amplitude (volts)
- ?c analog carrier radian frequency
- in the above (5.5-1), modulating signal vm(t) is

a normalized binary waveform, where 1V logic 1

and -1V logic 0.

5.5.1 Amplitude Shift Keying

- for a logic 1 input, vm(t) 1V, and (5.5-1)

reduces to - and for logic 0 input, vm(t) -1V, and (5.5-1)

reduces to - so the modulated wave vask(t), is either

Acos(?ct) or 0, means the carrier is either on

or off. ASK is sometimes referred as on-off

keying (OOK).

5.5.1 Amplitude Shift Keying

5.5.2 Frequency Shift Keying

- general expression for FSK
- (5.5-2)
- where vfsk(t) binary FSK waveform
- Vc peak analog carrier amplitude
- fc analog carrier center frequency (Hz)
- vm(t) binary input (modulating signal)
- ?f peak change (shift) in the analog

carrier frequency - from (5.5-2), the peak shift in the carrier

frequency (?f) is proportional to the amplitude

of the binary input signal vm(t). - the direction of the shift is determined by the

polarity of signal ( 1 or 0 ). - the modulating signal vm(t) is a normalized

binary waveform where a logic 1 1V and a logic

0 -1V.

5.5.2 Frequency Shift Keying

- for logic 1 input, vm(t) 1, equation (5.5-2)

becomes - for logic 0 input, vm(t) -1, equation (5.5-2)

becomes - the carrier center frequency fc is shifted

(deviated) up and down in the frequency domain by

the binary input signal as shown below.

5.5.2 Frequency Shift Keying

5.5.2 Frequency Shift Keying

- mark (fm) logic 1 frequency
- space (fs) logic 0 frequency

5.5.3 Phase Shift Keying

- modulation technique that alters the phase of the

carrier. - in a binary phase-shift keying (BPSK), where N

(number of bits) 1, M (number of output phases)

2, one phase represents a logic 1 and another

phase represents a logic 0. - as the input digital signal changes state (i.e.

from 1 to 0 or 0 to 1), the phase of the output

carrier shifts between two angles that are

separated by 180º.

5.5.3 Phase Shift Keying