Communications Systems, Signals, and Modulation

1
Communications Systems, Signals, and Modulation

• Session 3
• Nilesh Jha

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About Channel Capacity

• Impairments, such as noise, limit data rate that
  can be achieved
• Channel Capacity the maximum rate at which data
  can be transmitted over a given communication
  path, or channel, under given conditions

3
Transmission Impairments

• Signal received may differ from signal
  transmitted
• Analog - degradation of signal quality
• Digital - bit errors
• Caused by
• Attenuation and attenuation distortion
• Delay distortion
• Noise

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Attenuation

• Signal strength falls off with distance
• Depends on medium
• Received signal strength
• must be enough to be detected
• must be sufficiently higher than noise to be
  received without error
• Attenuation is an increasing function of
  frequency

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Noise (1)

• Additional EM energy and signals on the receiver
• Thermal -- usually inserted by receiver circuits
• Due to thermal agitation of electrons
• Uniformly distributed
• White noise
• Intermodulation
• Signals that are the sum and difference of
  original frequencies sharing a medium, and
  falling within the desired signals passband

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Noise (2)

• Crosstalk
• A signal from one line or channel is picked up by
  another
• Impulse
• Irregular pulses or spikes
• e.g. External electromagnetic interference
• Short duration
• High amplitude
• Multipath
• See in later Sessions, causes distortions

7
Signal-to-Noise Ratio

• Ratio of the power in a signal to the power
  contained in the noise thats present at a
  particular point in the transmission
• Typically measured at a receiver
• Signal-to-noise ratio (SNR, or S/N)
• A high SNR means a high-quality signal, low
  number of required intermediate repeaters
• SNR sets upper bound on achievable data rate

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Signals and Noise
High SNR
Lower SNR
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Concepts Related to Channel Capacity

• Data rate - rate at which data can be
  communicated (bps)
• Bandwidth - the bandwidth of the transmitted
  signal as constrained by the transmitter and the
  nature of the transmission medium (Hertz)
• Noise - average level of noise over the
  communications path
• Error rate - rate at which errors occur
• Error transmit 1 and receive 0 transmit 0 and
  receive 1

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Nyquist Bandwidth

• For binary signals (two voltage levels)
• C 2B
• With multilevel signaling
• C 2B log2 M
• M number of discrete signal or voltage levels

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Shannon Capacity Formula

• Equation
• Represents theoretical maximum that can be
  achieved
• In practice, somewhat lower rates achieved
• Formula assumes white noise (thermal noise)
• Worse when other forms of noise are included
• Impulse noise
• Attenuation distortion or delay distortion
• Interference

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Example of Nyquist and Shannon Formulations

• Spectrum of a channel between 3 MHz and 4 MHz
  SNRdB 24 dB
• Using Shannons formula

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Example of Nyquist and Shannon Formulations

• How many signaling levels are required?

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Multiplexing

• Capacity of transmission medium usually exceeds
  capacity required for transmission of a single
  signal
• Multiplexing - carrying multiple signals on a
  single medium
• More efficient use of transmission medium

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Multiplexing
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Reasons for Widespread Use of Multiplexing

• Cost per kbps of transmission facility declines
  with an increase in the data rate
• Cost of transmission and receiving equipment
  declines with increased data rate
• Most individual data communicating devices
  require relatively modest data rate support

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Multiplexing Techniques

• Frequency-division multiplexing (FDM)
• Takes advantage of the fact that the useful
  bandwidth of the medium exceeds the required
  bandwidth of a given signal --- different users
  at different frequency bands or subbands
• Time-division multiplexing (TDM)
• Takes advantage of the fact that the achievable
  bit rate of the medium exceeds the required data
  rate of a digital signal --- different users at
  different time slots

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Frequency-division Multiplexing
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Time-division Multiplexing
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Multiplexing and Multiple Access

• Both refer to the sharing of a communications
  resource, usually a channel
• Multiplexing usually refers to sharing some
  resource by doing something at one site --- eg,
  at the multiplexer
• Often a static or pseudo-static allocation of
  fractions of the multiplexed channel, eg, a T1
  line. Often refers to sharing one resource. The
  division of the resource can be made on
  frequency, or time, or other physical feature
• Multiple Access shares an asset in a distributed
  domain
• ie, multiple users at different places sharing an
  overall media, and using a scheme where it is
  divided into channels based on frequency, or time
  or another physical feature
• Usually dynamic

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Factors Used to CompareModulation and Encoding
Schemes

• Signal spectrum
• With fewer higher frequency components, less
  bandwidth required --- Spectrum Efficiency
• For wired comms with no DC component, AC
  coupling via transformer possible --- DC
  components cause problems
• Transfer function of a channel is worse near band
  edges -- always better to constrain signal
  spectrum well inside the spectrum available
• Synchronization and Clocking
• Determining when 0 phase occurs -- carrier synch
• Determining beginning and end of each bit
  position -- bit sync
• Determining frame sync --- usually layer above
  physical

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Signal Modulation/Encoding Criteria
Demodulating/Decoding Accurately

• What determines how successful a receiver will be
  in interpreting an incoming signal?
• Signal-to-noise ratio SNR
• signal power/noise power
• Note power energy per unit time
• Data rate (R)
• Bandwidth (BW)
• An increase in data rate increases bit error rate
• An increase in SNR decreases bit error rate
• An increase in bandwidth allows an increase in
  data rate

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Factors Used to CompareModulation/Encoding
Schemes

• Signal interference and noise immunity ---
• Performance in the presence of interference and
  noise
• For a given signal power level, the effect of
  noise and interference is then labeled the Power
  Efficiency
• For digital modulation, Prob. Of Bit Error
  function (SNR) where N includes the interference
  terms
• More exactly, Prob. Bit Error function (Energy
  per bit/Noise power density, with noise including
  interference and other noise like terms) --- see
  next chart
• Cost and complexity
• Usually the higher the signal and data rates
  require a higher complexity and greater the cost

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A Figure of Merit in CommunicationsNoise
Immunity

• For digital modulation one bottom line Figure of
  Merit (FOM) is Probability of Bit Error (Psub e)
  -- Lowest for Most Accurate Decoding of Bit
  Stream
• Prob. Bit Error function of (Eb/Nsub 0)
• Many functions for many different modulation and
  coding types have been computed - usually
  decreases with increasing Eb/Nsub 0
• Ebenergy per bit
• Nsub 0noise spectral density Noise Power N
  (Nsub 0) BW
• Note Includes Interference and Intermodulation
  and Crosstalk
• (Eb/Nsub 0) is a critically important number for
  digital comms
• Eb/Nsub0(SNR)(BW/R) ---- important formula --
  derive it
• SNR is signal to noise ratio, a ratio of power
  levels
• BW is signal bandwidth, R is data rate in
  bits/sec
• For analog modulation the FOM is SNR
• Signal quality given by subjective statistical
  scores -- voice 1-5 (high)
• FM requires a lower SNR than AM for the same
  signal quality

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Basic Modulation/Encoding Techniques

• Digital data to analog signal --- Digital
  Modulation
• Amplitude-shift keying (ASK)
• Amplitude difference of carrier frequency
• Frequency-shift keying (FSK)
• Frequency difference near carrier frequency
• Phase-shift keying (PSK)
• Phase of carrier signal shifted

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Basic Encoding Techniques
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Amplitude-Shift Keying

• One binary digit represented by presence of
  carrier, at constant amplitude
• Other binary digit represented by absence of
  carrier
• where the carrier signal is Acos(2pfct)

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Amplitude-Shift Keying

• Susceptible to sudden gain changes
• Inefficient modulation technique
• On voice-grade lines, used up to 1200 bps
• Used to transmit digital data over optical fiber

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Binary Frequency-Shift Keying (BFSK)

• Two binary digits represented by two different
  frequencies near the carrier frequency
• where f1 and f2 are offset from carrier frequency
  fc by equal but opposite amounts

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Binary Frequency-Shift Keying (BFSK)

• Less susceptible to error than ASK
• On voice-grade lines, used up to 1200bps
• Used for high-frequency (3 to 30 MHz) radio
  transmission
• Can be used at higher frequencies on LANs that
  use coaxial cable

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Multiple Frequency-Shift Keying (MFSK)

• More than two frequencies are used
• More bandwidth efficient but more susceptible to
  error
• f i f c (2i 1 M)f d
• f c the carrier frequency
• f d the difference frequency
• M number of different signal elements 2 L
• L number of bits per signal element

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Multiple Frequency-Shift Keying (MFSK)

• To match data rate of input bit stream, each
  output signal element is held for
• TsLT seconds
• where T is the bit period (data rate 1/T)
• So, one signal element encodes L bits

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Multiple Frequency-Shift Keying (MFSK)

• Total bandwidth required
• 2Mfd
• Minimum frequency separation required 2fd1/Ts
• Therefore, modulator requires a bandwidth of
• Wd2L/LTM/Ts

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Multiple Frequency-Shift Keying (MFSK)
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Phase Shift Keying (PSK)

• The signal carrier is shifted in phase according
  to the input data stream
• 2 level PSK, also called binary PSK or BPSK or
  2-PSK, uses 2 phase possibilities over which the
  phase can vary, typically 0 and 180 degrees --
  each phase represents 1 bit
• can also have n-PSK -- 4-PSK often is 0, 90, 180
  and 270 degrees --- each phase then represents 2
  bits
• Each phase called a symbol
• Each bit or groups of bits can be represented by
  a phase value (eg, 0 degrees, or 180 degrees), or
  bits can be based on whether or not phase changes
  (differential keying, eg, no phase change is a 0,
  a phase change is a 1) --- DPSK

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Phase-Shift Keying (PSK)

• Two-level PSK (BPSK)
• Uses two phases to represent binary digits

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Phase-Shift Keying (PSK)

• Differential PSK (DPSK)
• Phase shift with reference to previous bit
• Binary 0 signal burst of same phase as previous
  signal burst
• Binary 1 signal burst of opposite phase to
  previous signal burst

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Phase-Shift Keying (PSK)

• Four-level PSK (QPSK)
• Each element represents more than one bit

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Quadrature PSK

• More efficient use by each signal element (or
  symbol) representing more than one bit
• e.g. shifts of ?/2 (90o)
• In QPSK each element or symbol represents two
  bits
• Can use 8 phase angles and have more than one
  amplitude -- then becomes QAM then (combining PSK
  and ASK)
• QPSK used in different forms in a many cellular
  digital systems
• Offset-QPSK O-QPSK The I (0 and 180 degrees)
  and Q (90 and 270 degrees) quadrature bits are
  offset from each other by half a bit --- becomes
  a more efficient modulation, with phase changes
  not so abrupt so better spectrally, and more
  linear
• Pi/4-QPSK is a similar approach to O-QPSK, also
  used

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Multilevel Phase-Shift Keying (MPSK)

• Multilevel PSK
• Using multiple phase angles multiple signals
  elements can be achieved
• D modulation rate, baud
• R data rate, bps
• M number of different signal elements or
  symbols 2L
• L number of bits per signal element or symbol
• eg, 4-PSK is QPSK, 8-PSK, etc

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Quadrature Amplitude Modulation

• QAM is a combination of ASK and PSK
• Two different signals sent simultaneously on the
  same carrier frequency

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Quadrature Amplitude Modulation
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Quadrature Amplitude Modulation (QAM)

• The most common method for quad (4) bit transfer
• Combination of 8 different angles in phase
  modulation and two amplitudes of signal
• Provides 16 different signals (or symbols),
  each of which can represent 4 bits (there are 16
  possible 4 bit combinations)

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Quadrature Amplitude Modulation Illustration --
example of Constellation Diagram
90
135
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Notice that there are 16 circles or nodes,
each represents a possible amplitude and phase,
and each represents 4 bits Obviously there are
many such constellation diagrams possible --- the
technical issue winds up being that as the nodes
get closer to each other any noise can lead to
the receiver confusing them, and making a bit
error
amplitude 1
0
180
amplitude 2
225
315
270
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Performance of Digital Modulation Schemes

• Bandwidth or Spectral Efficiency
• ASK and PSK bandwidth directly related to bit
  rate
• FSK bandwidth related to data rate for lower
  frequencies, but to offset of modulated frequency
  from carrier at high frequencies
• Determined by C/BW ie bps/Hz
• Noise Immunity or Power Efficiency In the
  presence of noise, bit error rate of PSK and QPSK
  are about 3dB superior to ASK and FSK ---- ie, x2
  less power for same performance
• Determined by BER as function of Eb/Nsub0

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Spectral Performance

• Bandwidth of modulated signal (BT)
• ASK, PSK BT(1r)R
• FSK BT2DF(1r)R
• R bit rate
• 0 lt r lt 1 related to how signal is filtered
• DF f2-fcfc-f1

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SPECTRAL Performance

• Bandwidth of modulated signal (BT)
• MPSK
• MFSK
• L number of bits encoded per signal element
• M number of different signal elements

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In Stallings
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In Stallings
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Power-Bandwidth Efficiency Plane
By Sklar, from Gibson
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Analog Modulation Techniques

• Analog data to analog signal
• Also called analog modulation
• Amplitude modulation (AM)
• Angle modulation
• Frequency modulation (FM)
• Phase modulation (PM)

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AM MODULATION
Top left source (baseband) signal to be
modulated bottom left modulated signal, carrier
lines inside white right demodulated after it
is transmitted and received (note after 1.e-3
similarity except for attenuation)
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Input Voice and Received Voice after Transmission
and Reception, Using FM --- Only a Little Noise
-- Notice Similarity
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Input Voice and Received Voice after Transmission
and Reception, Using FM --- Lots More Noise in
Channel -- Notice that Received Signal is NOT
What Was Transmitted
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Amplitude Modulation

• Amplitude Modulation
• cos2?fct carrier
• x(t) input signal
• na modulation index
• Ratio of amplitude of input signal to carrier
• a.k.a double sideband transmitted carrier (DSBTC)

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Spectrum of AM signal
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Amplitude Modulation

• Transmitted power
• Pt total transmitted power in s(t)
• Pc transmitted power in carrier

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Single Sideband (SSB)

• Variant of AM is single sideband (SSB)
• Sends only one sideband
• Eliminates other sideband and carrier
• Advantages
• Only half the bandwidth is required
• Less power is required
• Disadvantages
• Suppressed carrier cant be used for
  synchronization purposes

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Angle Modulation

• Angle modulation
• Phase modulation
• Phase is proportional to modulating signal
• np phase modulation index

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Angle Modulation

• Frequency modulation
• Derivative of the phase is proportional to
  modulating signal
• nf frequency modulation index

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Angle Modulation

• Compared to AM, FM and PM result in a signal
  whose bandwidth
• is also centered at fc
• but has a magnitude that is much different
• Angle modulation includes cos(? (t)) which
  produces a wide range of frequencies
• Thus, FM and PM require greater bandwidth than AM

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Angle Modulation

• Carsons rule
• where
• The formula for FM becomes

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Coding

• Encoding sometimes is used to refer to the way in
  which analog data is converted to digital signals
• eg, A/Ds, PCM or DM
• Source Coding refers to the way in which basic
  digitized analog data can be compressed to lower
  data rates without loosing any or to much
  information -- eg, voice, video, fax, graphics,
  etc.
• Channel coding refers to signal transformations
  used to improve the signals ability to withstand
  the channel propagation impairments --- two types
• waveform coding --- transforms signals
  (waveforms) into better ones --- able to
  withstand propagation errors better --- this
  refers to different modulation schemes, Mary
  signaling, spread spectrum
• Sequence coding, also generally labelled error
  coding or FEC, transforms data bits sequences
  into ones less error prone, by inserting
  redundant bits in a smart way -- eg, block and
  convolutional codes

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Basic Encoding Techniques

• Analog data to digital signal
• Used for digitization of analog sources
• Pulse code modulation (PCM)
• Delta modulation (DM)
• After the above, usually additional processing
  done to compress signal to achieve similar signal
  quality with fewer bits --- called source coding

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Analog to Digital Conversion

• Once analog data have been converted to digital
  signals, the digital data
• can be transmitted using NRZ-L
• can be encoded as a digital signal using a code
  other than NRZ-L
• can be modulated to an analog signal for wireless
  transmission, using previously discussed
  techniques

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Pulse Code Modulation

• Based on the sampling theorem
• Each analog sample is assigned a binary code
• Analog samples are referred to as pulse amplitude
  modulation (PAM) samples
• The digital signal consists of block of n bits,
  where each n-bit number is the amplitude of a PCM
  pulse

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Pulse Code Modulation
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Pulse Code Modulation

• By quantizing the PAM pulse, original signal is
  only approximated
• Leads to quantizing noise
• Signal-to-noise ratio for quantizing noise
• Thus, each additional bit increases SNR by 6 dB,
  or a factor of 4

69
Delta Modulation

• Analog input is approximated by staircase
  function
• Moves up or down by one quantization level (?) at
  each sampling interval
• The bit stream approximates derivative of analog
  signal (rather than amplitude)
• 1 is generated if function goes up
• 0 otherwise

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Delta Modulation
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Delta Modulation

• Two important parameters
• Size of step assigned to each binary digit (?)
• Sampling rate
• Accuracy improved by increasing sampling rate
• However, this increases the data rate
• Advantage of DM over PCM is the simplicity of its
  implementation

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Source Coding

• Voice or Speech or Audio
• Basic PCM yields 4 KHz2 samples/Hz8
  bits/sample64 Kbps -- music/etc up to 768 Kbps
• Coding can exploit redundancies in the speech
  waveform -- one way is LPC, linear predictive
  coding --- predicts whats next, sends only the
  changes expected
• RPE and CELP (Code Excited LPC) used in cell
  phones, using LPC, at rates of 4 to 9.6 to 13
  kbps
• Graphics and Video eg, JPEG or GIF, MPEG

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Reasons for Growth of Digital Modulation and
Transmission

• Growth in popularity of digital techniques for
  sending analog or digital source data
• Cheaper components used in creating the
  modulations and doing the encoding, and similarly
  on the receivers
• Best performance in terms of immunity to noise
  and in terms of spectral efficiency --- improved
  digital modulation and channel coding techniques
  
• Great improvements in digital voice and video
  compression
• Voice to about 8 Kbps at good quality, video
  varies to below 1 Mbps provide increased capacity
  in terms of numbers of users in given BW
• Dynamic and efficient multiple access and
  multiplexing techniques using TDM, TDMA and CDMA,
  even when some larger scale Frequency Allocations
  (FDMA) -- labeled as combinations
• Easier and simpler implementation interfaces to
  the digital landline networks and IP

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Duplex Modes

• Duplex modes refer to the ways in which two way
  traffic is arranged
• One way vs two way
• simplex (one way only), half duplex (both ways,
  but only one way at a time), duplex (two ways at
  the same time)
• If duplex, question is then how one separates the
  two ways
• In wired systems, it could be in different wires
  (or cables, fibers, etc)
• Both wired and wireless one way is to separate
  the two paths in frequency --- FDD, frequency
  division duplex
• If two frequencies, or frequency bands, are
  separate enough, no cross interference
• Cellular systems are all FDD
• Its clean and easy to do, good performance, but
  it limits channel assignments and is not best for
  asymmetric traffic
• TDD is time division duplex, same frequencies are
  used both ways, but time slots are assigned one
  way or the other
• Good for asymmetrical traffic, allows more
  control through time slot reassignments
• But strong transmissions one way could interfere
  with other users
• Mostly not used in cellular, but 3G has one such
  protocol, and low tier portables also