Chapter 5 : Digital Communication Systems Chapter contents

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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

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5.1 Overview

• Digital communications is the transfer of
  information (voice, data etc) in digital form.
• Basic diagram of digital/data communications

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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.

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5.1 Overview

• Transmission schemes for analog and digital
  signals

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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
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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.

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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)

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5.3 Pulse Code Modulation (PCM)

• Block diagram of a single channel, simplex PCM
  transmission channel

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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.

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5.3.1 PCM Sampling

Natural sampling
Flat-top sampling
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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

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5.3.2 Sampling Rate

• If fs is less than 2 times fm(max) an impairment
  called as alias or fold-over distortion occurs.

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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.

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5.3.3 Quantization

• Ex

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5.3.3 Quantization

• Ex (continue)

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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).

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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

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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

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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

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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 !

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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

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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

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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

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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 !

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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

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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

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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).

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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.

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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.

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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).

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5.5.1 Amplitude Shift Keying
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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.

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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.

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5.5.2 Frequency Shift Keying

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5.5.2 Frequency Shift Keying

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

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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.

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5.5.3 Phase Shift Keying