introduction to mobile communications tcom 552, lecture #3 hung nguyen, ph.d. 18 september, 2006
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Introduction to Mobile Introduction to Mobile CommunicationsCommunications
TCOM 552, Lecture #3Hung Nguyen, Ph.D.18 September, 2006
09/18/2006Hung Nguyen, TCOM 552, Fall 20062
OutlineOutline
Channel Capacity Signal-to-Noise Ratio (SNR) Multiplexing Digital Modulation Analog Modulation Coding Simplex and Duplex Transission
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About Channel CapacityAbout 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
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Transmission ImpairmentsTransmission 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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AttenuationAttenuation
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)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 signal’s passband
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Noise (2)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
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Signal-to-Noise RatioSignal-to-Noise Ratio
Ratio of the power in a signal to the power contained in the noise that’s 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
power noise
power signallog10)( 10dB SNR
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High SNR
Lower SNR
Signals and NoiseSignals and Noise
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Concepts Related to Channel CapacityConcepts 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 BandwidthNyquist 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 FormulaShannon 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
SNR1log2 BC
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Example of Nyquist and Shannon Example of Nyquist and Shannon FormulationsFormulations
Spectrum of a channel between 3 MHz and 4 MHz ; SNRdB = 24 dB
Using Shannon’s formula
251SNR
SNRlog10dB 24SNR
MHz 1MHz 3MHz 4
10dB
B
Mbps88102511log10 62
6 C
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Example of Nyquist and Shannon Example of Nyquist and Shannon FormulationsFormulations
How many signaling levels are required?
16
log4
log102108
log2
2
266
2
M
M
M
MBC
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MultiplexingMultiplexing
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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MultiplexingMultiplexing
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Reasons for Widespread Use of Reasons for Widespread Use of MultiplexingMultiplexing
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 TechniquesMultiplexing 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 MultiplexingFrequency-division Multiplexing
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Time-division MultiplexingTime-division Multiplexing
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Multiplexing and Multiple Access 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 --- e.g., at the multiplexer– Often a static or pseudo-static allocation of fractions of the
multiplexed channel, e.g., 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– i.e., 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 CompareFactors Used to CompareModulation and Encoding SchemesModulation 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
09/18/2006Hung Nguyen, TCOM 552, Fall 200623
Signal Modulation/Encoding Criteria: Signal Modulation/Encoding Criteria: Demodulating/Decoding AccuratelyDemodulating/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 CompareFactors Used to CompareModulation/Encoding SchemesModulation/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 Communications:A Figure of Merit in Communications:Noise ImmunityNoise Immunity
For digital modulation one bottom line Figure of Merit (FOM) is Probability of Bit Error (Pe) -- Lowest for Most Accurate Decoding of Bit Stream– Prob. Bit Error= function of (Eb/N0)
Many functions for many different modulation and coding types have been computed - usually decreases with increasing Eb/N0
Eb = energy per bit N0 = noise spectral density; Noise Power N = (N0)* BW
– Note: Includes Interference and Intermodulation and Crosstalk (Eb/N0) is a critically important number for digital comms Eb/N0 =(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 TechniquesBasic 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 TechniquesBasic Encoding Techniques
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Amplitude-Shift KeyingAmplitude-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 A*cos(2πfct)
0
ts tfA c2cos 1binary
0binary
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Amplitude-Shift KeyingAmplitude-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)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
tfA 12cos
ts tfA 22cos 1binary 0binary
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Binary Frequency-Shift Keying (BFSK)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)Multiple Frequency-Shift Keying (MFSK)
More than two frequencies are used More bandwidth efficient but more
susceptible to error
fi = fc + (2i – 1 – M)fd
fc = the carrier frequency
fd = the difference frequency M = number of different signal elements = 2 L L = number of bits per signal element
tfAts ii 2cos Mi 1
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Multiple Frequency-Shift Keying (MFSK)Multiple Frequency-Shift Keying (MFSK)
To match data rate of input bit stream, each output signal element is held for:– Ts = LT 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)Multiple Frequency-Shift Keying (MFSK)
Total bandwidth required – 2Mfd
Minimum frequency separation required 2fd = 1/Ts
Therefore, modulator requires a bandwidth of– Wd = 2L/LT = M/Ts
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Multiple Frequency-Shift Keying (MFSK)Multiple Frequency-Shift Keying (MFSK)
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Phase Shift Keying (PSK)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 (e.g., 0 degrees, or 180 degrees), or bits can be based on whether or not phase changes (differential keying, e.g., no phase change is a 0, a phase change is a 1) --- DPSK
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Phase-Shift Keying (PSK)Phase-Shift Keying (PSK)
Two-level PSK (BPSK)– Uses two phases to represent binary digits
tfA c2cos
ts tfA c2cos1binary 0binary
tfA c2cos
tfA c2cos1binary 0binary
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Phase-Shift Keying (PSK)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)Phase-Shift Keying (PSK)
Four-level PSK (QPSK)– Each element represents more than one bit
ts
42cos
tfA c 11
4
32cos
tfA c
4
32cos
tfA c
42cos
tfA c
01
00
10
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Quadrature PSKQuadrature 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: OQPSK: 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
/4-QPSK is a similar approach to OQPSK, also used
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Multilevel Phase-Shift Keying (MPSK)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
– e.g., 4-PSK is QPSK, 8-PSK, etc
M
R
L
RD
2log
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Quadrature Amplitude ModulationQuadrature Amplitude Modulation
QAM is a combination of ASK and PSK– Two different signals sent simultaneously on the
same carrier frequency
tftdtftdts cc 2sin2cos 21
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Quadrature Amplitude ModulationQuadrature Amplitude Modulation
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Quadrature Amplitude Modulation Quadrature Amplitude Modulation (QAM)(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 Quadrature Amplitude Modulation Illustration -- Example of Constellation Diagram-- Example of Constellation Diagram
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
90
45
0
135
180
225
270
315
amplitude 1
amplitude 2
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Performance of Digital Modulation Performance of Digital Modulation SchemesSchemes
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 i.e. 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 ---- i.e., x2 less power for same performance– Determined by BER as function of Eb/N0
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Spectral PerformanceSpectral Performance
Bandwidth of modulated signal (BT)– ASK, PSK BT = (1+r)R
– FSK BT = 2F+(1+r)R
R = bit rate 0 < r < 1; related to how signal is filtered F = f2fc = fcf1
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SPECTRAL PerformanceSPECTRAL Performance
Bandwidth of modulated signal (BT)
– MPSK
– MFSK
L = number of bits encoded per signal element M = number of different signal elements
RM
rR
L
rBT
2log
11
R
M
MrBT
2log
1
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In Stallings
BER vs.. EBER vs.. Ebb/N/N00
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In Stallings
BER vs.. EBER vs.. Ebb/N/N00 (cont’d) (cont’d)
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From Bernard Sklar
Power-Bandwidth Efficiency PlanePower-Bandwidth Efficiency Plane
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Analog Modulation TechniquesAnalog 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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•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)
AM Modulation & DemodulationAM Modulation & Demodulation
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Input Voice and Received Voice after Transmission and Reception, Using FM --- Only a Little Noise -- Notice Similarity
FM Modulation & DemodulationFM Modulation & Demodulation
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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 ModulationAmplitude Modulation
Amplitude Modulation
cos2fct = carrier x(t) = input signal na = modulation index
– Ratio of amplitude of input signal to carrier
– a.k.a double sideband transmitted carrier (DSBTC)
tftxnts ca 2cos1
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Spectrum of AM signalSpectrum of AM signal
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Amplitude ModulationAmplitude Modulation
Transmitted power
Pt = total transmitted power in s(t) Pc = transmitted power in carrier
21
2a
ct
nPP
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Single Sideband (SSB)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 can’t be used for
synchronization purposes
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Angle ModulationAngle Modulation
Angle modulation
Phase modulation– Phase is proportional to modulating signal
np = phase modulation index
ttfAts cc 2cos
tmnt p
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Angle ModulationAngle Modulation
Frequency modulation– Derivative of the phase is proportional to
modulating signal
nf = frequency modulation index
tmnt f'
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Angle ModulationAngle 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 ModulationAngle Modulation
Carson’s rule
– where
The formula for FM becomes
BBT 12
BFBT 22
FMfor
PMfor
2
B
An
B
F
An
mf
mp
09/18/2006Hung Nguyen, TCOM 552, Fall 200664
CodingCoding
Encoding sometimes is used to refer to the way in which analog data is converted to digital signals– e.g., A/D’s, 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 -- e.g., voice, video, fax, graphics, etc.
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Coding (cont’d)Coding (cont’d)
Channel coding refers to signal transformations used to improve the signal’s 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, M-ary signaling, spread spectrum
– Forward Error coding (FEC), also called Sequence coding, transforms data bits sequences into those that are less error prone, by inserting redundant bits in a smart way -- e.g., block and convolutional codes
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Basic Encoding TechniquesBasic 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 ConversionAnalog 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 ModulationPulse 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 ModulationPulse Code Modulation
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Pulse Code ModulationPulse 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
dB 76.102.6dB 76.12log20SNR dB nn
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Delta ModulationDelta 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 ModulationDelta Modulation
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Delta ModulationDelta 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 CodingSource Coding
Voice or Speech or Audio– Basic PCM yields 4 KHz*2 samples/Hz*8
bits/sample=64 Kbps -- music/etc up to 768 Kbps– Coding can exploit redundancies in the speech
waveform -- one way is LPC, linear predictive coding --- predicts what’s 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: e.g., JPEG or GIF, MPEG
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Reasons for Growth of Digital Reasons for Growth of Digital Modulation and TransmissionModulation and Transmission
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 ModesDuplex 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)
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Duplex Modes (cont’d)Duplex Modes (cont’d)
FDD, frequency division duplex. Both wired and wireless one way is to separate the two paths in frequency. If two frequencies, or frequency bands, are separate enough, no cross interference
Cellular systems are all FDD It’s 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
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