introduction to mobile communications tcom 552, lecture #3 hung nguyen, ph.d. 18 september, 2006

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


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


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


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


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


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


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


High SNR

Lower SNR

Signals and NoiseSignals and Noise


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


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


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


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


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


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


MultiplexingMultiplexing


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


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


Frequency-division MultiplexingFrequency-division Multiplexing


Time-division MultiplexingTime-division Multiplexing


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


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


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


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


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


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


Basic Encoding TechniquesBasic Encoding Techniques


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


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


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


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


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



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



Total bandwidth required – 2Mfd

Minimum frequency separation required 2fd = 1/Ts

Therefore, modulator requires a bandwidth of– Wd = 2L/LT = M/Ts


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


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



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



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


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


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


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


Quadrature Amplitude ModulationQuadrature Amplitude Modulation


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)


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


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


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


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


In Stallings

BER vs.. EBER vs.. Ebb/N/N00


In Stallings

BER vs.. EBER vs.. Ebb/N/N00 (cont’d) (cont’d)


From Bernard Sklar

Power-Bandwidth Efficiency PlanePower-Bandwidth Efficiency Plane


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)


•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


Input Voice and Received Voice after Transmission and Reception, Using FM --- Only a Little Noise -- Notice Similarity

FM Modulation & DemodulationFM Modulation & Demodulation


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


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


Spectrum of AM signalSpectrum of AM signal


Amplitude ModulationAmplitude Modulation

Transmitted power

Pt = total transmitted power in s(t) Pc = transmitted power in carrier

21

2a

ct

nPP


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


Angle ModulationAngle Modulation

Angle modulation

Phase modulation– Phase is proportional to modulating signal

np = phase modulation index

ttfAts cc 2cos

tmnt p



Frequency modulation– Derivative of the phase is proportional to

modulating signal

nf = frequency modulation index

tmnt f'



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



Carson’s rule

– where

The formula for FM becomes

BBT 12

BFBT 22

FMfor

PMfor

2

B

An

B

F

An

mf

mp


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.


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


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


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


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



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


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



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


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


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


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)


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

introduction to mobile communications tcom 552, lecture #3 hung nguyen, ph.d. 18 september, 2006

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