Chapter 2 Wireless Communication

Technology(Part Two in textbook)

Outline

- 2.1Antennas and Propagation(?????)
- 2.2 Signal Encoding Techniques(??????)
- 2.3 Spread Spectrum(??)
- 2.4 Coding and Error Control(????)

2.1Antennas and Propagation

Reading material 1Antenna

Tutorial2Chapter 5 in textbook

2.1.1 Classifications of Transmission Media (2.4

in textbook)

- Transmission Medium(????)
- Physical path between transmitter and receiver
- Guided Media(????)
- Waves are guided along a solid medium
- E.g., copper twisted pair, copper coaxial cable,

optical fiber - Unguided Media
- Provides means of transmission but does not guide

electromagnetic signals - Usually referred to as wireless transmission
- E.g., atmosphere, outer space

Unguided Media

- Transmission and reception are achieved by means

of an antenna - Configurations for wireless transmission
- Directional
- Omnidirectional

?????????

General Frequency Ranges

- Microwave frequency range
- 1 GHz to 40 GHz
- Directional beams possible
- Suitable for point-to-point transmission
- Used for satellite communications
- Radio frequency range
- 30 MHz to 1 GHz
- Suitable for omnidirectional applications
- Infrared frequency range
- Roughly, 3x1011 to 2x1014 Hz
- Useful in local point-to-point multipoint

applications within confined areas

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???????

ISM

???(1)

???(2)

???(3)

???????

- ??--LF (Low Frequency)
- ????--?????,?????
- ???????????????,?????????????????,???? ?
- ????????????,??? ,???? ,???? ,????
- ??????????

Broadcast Radio

- Description of broadcast radio antennas
- Omnidirectional
- Antennas not required to be dish-shaped
- Antennas need not be rigidly mounted to a precise

alignment - Applications
- Broadcast radio
- VHF and part of the UHF band 30 MHZ to 1GHz
- Covers FM radio and UHF and VHF television

Microwave

Microwave System

Terrestrial Microwave

- Description of common microwave antenna
- Parabolic "dish", 3 m in diameter
- Fixed rigidly and focuses a narrow beam
- Achieves line-of-sight transmission to receiving

antenna - Located at substantial heights above ground level

- Applications
- Long haul telecommunications service
- Short point-to-point links between buildings

Satellite Microwave

- Description of communication satellite
- Microwave relay station
- Used to link two or more ground-based microwave

transmitter/receivers - Receives transmissions on one frequency band

(uplink), amplifies or repeats the signal, and

transmits it on another frequency (downlink) - Applications
- Television distribution
- Long-distance telephone transmission
- Private business networks

???

??????(Multiplexing)(1)

??????(2)

??????(3)

??????(4)

??????(5)

??????(6)

2.1.2 Introduction to Antennas

- ?????????????????(An antenna is an electrical

conductor or system of conductors) - Transmission - radiates electromagnetic energy

into space - Reception - collects electromagnetic energy from

space - ???????????????????????(In two-way communication,

the same antenna can be used for transmission and

reception)

????(Radiation Patterns)

- ?????????????,?????????????????????????????????
- ????(Radiation pattern)
- ?????????????
- ?????????????????(cross section)
- ???????????
- ??????(????)?????
- ????(Reception pattern)
- Receiving antennas equivalent to radiation

pattern

????(Radiation Patterns)

??????(????) ????

????(Types of Antennas)

- ??????? (idealized)
- Radiates power equally in all directions
- ????(Dipole antennas)
- ?????? (or ????)
- 1/4????? (or ?????)??????????????????
- ??????

????(Dipole antennas)

- ??????????????????????????8????????

????????????????????

????(Dipole antennas)

- ??????????
- ????????
- ????????????

??????(parabolic reflective)

- ?????? ?????????,???????????
- ?????????????????????????????????????????(focus),?

??????(directrix)

??????WL-ANT150????

- ???

??????WL-ANT150????

- ????

??????WL-ANT168????

- ????

??????WL-ANT168????

- ??????

????????

????(Antenna Gain)

- ?????????????
- ????????????????????
- ???????????????????????????
- ???????????????????????,???????????
- ????Effective area
- Related to physical size and shape of antenna

????(Antenna Gain)

- ?????????
- G antenna gain
- Ae effective area
- f carrier frequency
- c speed of light ( 3 108 m/s)
- ? carrier wavelength

????(Antenna Gain)

- ??????2m???????,?????12GHz,???????????????
- ???????0.56A,A?????????
- ?
- Api, Ae 0.56A, ??0.025m
- G7pi/(0.0250.025)35186
- Gdbl0lg3518645.46db

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2.1.3 Propagation Modes

- Ground-wave propagation
- Sky-wave propagation
- Line-of-sight propagation

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Ground Wave Propagation

Ground Wave Propagation

- Follows contour of the earth
- Can Propagate considerable distances
- Frequencies up to 2 MHz
- Example
- AM radio

Sky Wave Propagation

Sky Wave Propagation

- Signal reflected from ionized layer of atmosphere

back down to earth - Signal can travel a number of hops, back and

forth between ionosphere and earths surface - Reflection effect caused by refraction
- Examples
- Amateur radio
- CB radio

Line-of-Sight Propagation

Line-of-Sight Propagation

- Transmitting and receiving antennas must be

within line of sight - Satellite communication signal above 30 MHz not

reflected by ionosphere - Ground communication antennas within effective

line of site due to refraction - Refraction bending of microwaves by the

atmosphere - Velocity of electromagnetic wave is a function of

the density of the medium - When wave changes medium, speed changes
- Wave bends at the boundary between mediums

Line-of-Sight Equations

- Optical line of sight
- Effective, or radio, line of sight
- d distance between antenna and horizon (km)
- h antenna height (m)
- K adjustment factor to account for refraction,

rule of thumb K 4/3

Line-of-Sight Equations

- Maximum distance between two antennas for LOS

propagation - h1 height of antenna one
- h2 height of antenna two

2.1.4 LOS Wireless Transmission Impairments

- ?????(Attenuation and attenuation distortion)
- ??????(Free space loss)
- ??(Noise)
- ????(Atmospheric absorption)
- ??(Multipath)
- ??(Refraction)
- ???(Thermal noise)

??(Attenuation)

- ????????????????????????
- ??????????????,????????????????
- ?????????????
- ?????,??????????????????????
- ??????????,??????

??????(Free Space Loss)

- ????????,?????????,??,????????????????,???????????

- ??????????,???????????????????????????????????????

?? - ??????????????????????????

??????(Free Space Loss)

- ??????(?????????)
- Pt signal power at transmitting antenna
- Pr signal power at receiving antenna
- ? carrier wavelength
- d propagation distance between antennas
- c speed of light ( 3 10 8 m/s)
- where d and ? are in the same units (e.g., meters)

Free Space Loss

- Free space loss equation can be recast

??????(Free Space Loss)

- ??????(???????)
- Gt gain of transmitting antenna
- Gr gain of receiving antenna
- At effective area of transmitting antenna
- Ar effective area of receiving antenna

Free Space Loss

- Free space loss accounting for gain of other

antennas can be recast as

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????(Categories of Noise)

- ???(Thermal Noise)
- ????(Intermodulation noise)
- ??(Crosstalk)
- ????(Impulse Noise)

???(Thermal Noise)

- ????????????????.?????????????????,

?????????.??????????????,???????. - ?????
- ????????????????,??????????????????.

???(Thermal Noise)

- ?????????1Hz????????
- N0 noise power density in watts per 1 Hz of

bandwidth - k Boltzmann's constant 1.3803 10-23 J/K
- T ??,?????(????)??

??T17 ?290K????,?????? No 1.3803 10-23

290410-21(W/Hz) -240(dbw/hz)

???(Thermal Noise)

- ????????
- ?B???????????????????
- or, ?????

Noise Terminology

- ??????????????????????,??????????? f1, f2 ,

f1f2, f1-f2 - ?? ?????????
- ????????????????????,???ISM???,????????
- ???? ???????????????
- ??????,????,??????????
- ??????,??????????

Expression Eb/N0

- Ratio of signal energy per bit to noise power

density per Hertz - The bit error rate for digital data is a function

of Eb/N0 - Given a value for Eb/N0 to achieve a desired

error rate, parameters of this formula can be

selected - As bit rate R increases, transmitted signal power

must increase to maintain required Eb/N0

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Other Impairments

- Atmospheric absorption water vapor and oxygen

contribute to attenuation - Multipath obstacles reflect signals so that

multiple copies with varying delays are received - Refraction bending of radio waves as they

propagate through the atmosphere

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2.1.5 Fading

- Fading refers to the time variation of received

signal power caused by changes in the

transmission medium or path (s).

Multipath Propagation

- ??(Reflection) - occurs when signal encounters a

surface that is large relative to the wavelength

of the signal - ??(Diffraction) - occurs at the edge of an

impenetrable body that is large compared to

wavelength of radio wave - ??(Scattering) occurs when incoming signal hits

an object whose size in the order of the

wavelength of the signal or less

??

??

??

Multipath Propagation

The Effects of Multipath Propagation

- Multiple copies of a signal may arrive at

different phases - If phases add destructively, the signal level

relative to noise declines, making detection more

difficult - Intersymbol interference (ISI)
- One or more delayed copies of a pulse may arrive

at the same time as the primary pulse for a

subsequent bit

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???????????????????????,????????????????????????.

???????,???????????????????????

Types of Fading

- Fast fading
- Slow fading
- Flat fading
- Selective fading
- Rayleigh fading
- Rician fading

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??????(Error Compensation Mechanisms)

- ????(Forward error correction)
- ?????(Adaptive equalization)
- ????(Diversity techniques)

????(Forward Error Correction)

- ???????????????????????????????????
- ???????????????????????????????
- Transmitter adds error-correcting code to data

block - Code is a function of the data bits
- Receiver calculates error-correcting code from

incoming data bits - If calculated code matches incoming code, no

error occurred - If error-correcting codes dont match, receiver

attempts to determine bits in error and correct

????(Forward Error Correction)

- ????????????????
- ????????,??????????????????23??
- ?????,????????????????????

?????( Adaptive Equalization)

- Can be applied to transmissions that carry analog

or digital information - Analog voice or video
- Digital data, digitized voice or video
- Used to combat intersymbol interference
- Involves gathering dispersed symbol energy back

into its original time interval - Techniques
- Lumped analog circuits
- Sophisticated digital signal processing algorithms

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????( Diversity Techniques)

- Diversity is based on the fact that individual

channels experience independent fading events - Space diversity techniques involving physical

transmission path - Frequency diversity techniques where the signal

is spread out over a larger frequency bandwidth

or carried on multiple frequency carriers - Time diversity techniques aimed at spreading

the data out over time

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2.2 Signal Encoding Techniques

Reading material 1Chapter 6 in textbook

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Reasons for Choosing Encoding Techniques

- Digital data, digital signal
- Equipment less complex and expensive than

digital-to-analog modulation equipment - Analog data, digital signal
- Permits use of modern digital transmission and

switching equipment

Reasons for Choosing Encoding Techniques

- Digital data, analog signal
- Some transmission media will only propagate

analog signals - E.g., optical fiber and unguided media
- Analog data, analog signal
- Analog data in electrical form can be transmitted

easily and cheaply - Done with voice transmission over voice-grade

lines

2.2.1 Signal Encoding Criteria

- What determines how successful a receiver will be

in interpreting an incoming signal? - Signal-to-noise ratio
- Data rate
- Bandwidth
- 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 CompareEncoding Schemes

- Signal spectrum
- With lack of high-frequency components, less

bandwidth required - With no dc component, ac coupling via transformer

possible - Transfer function of a channel is worse near band

edges - Clocking
- Ease of determining beginning and end of each bit

position

Factors Used to CompareEncoding Schemes

- Signal interference and noise immunity
- Performance in the presence of noise
- Cost and complexity
- The higher the signal rate to achieve a given

data rate, the greater the cost

2.2.2 Digital data, analog signals

Basic Encoding Techniques

- Digital data to analog signal
- 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 Techniques

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)

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

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

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

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

Multiple Frequency-Shift Keying (MFSK)

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

Multiple Frequency-Shift Keying (MFSK)

Phase-Shift Keying (PSK)

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

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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Phase-Shift Keying (PSK)

- Multilevel PSK
- Using multiple phase angles with each angle

having more than one amplitude, multiple signals

elements can be achieved - D modulation rate, baud
- R data rate, bps
- M number of different signal elements 2L
- L number of bits per signal element

Performance

- Bandwidth of modulated signal (BT)
- ASK, PSK BT(1r)R
- FSK BT2?F(1r)R
- R bit rate
- 0 lt r lt 1 related to how signal is filtered
- ?F f2-fcfc-f1

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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Quadrature Amplitude Modulation

- QAM is a combination of ASK and PSK
- Two different signals sent simultaneously on the

same carrier frequency

Quadrature Amplitude Modulation

2.2.3 Analog data, analog signals

Reasons for Analog Modulation

- Modulation of digital signals
- When only analog transmission facilities are

available, digital to analog conversion required - Modulation of analog signals
- A higher frequency may be needed for effective

transmission - Modulation permits frequency division multiplexing

Basic Encoding Techniques

- Analog data to analog signal
- Amplitude modulation (AM)
- Angle modulation
- Frequency modulation (FM)
- Phase modulation (PM)

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 (also known as) double sideband transmitted

carrier (DSBTC)

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Spectrum of AM signal

Amplitude Modulation

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

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

Angle Modulation

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

Angle Modulation

- Frequency modulation
- Derivative of the phase is proportional to

modulating signal - nf frequency modulation index

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

Angle Modulation

- Carsons rule
- where
- The formula for FM becomes

2.2.4 Analog data, digital signals

Basic Encoding Techniques

- Analog data to digital signal
- Pulse code modulation (PCM)
- Delta modulation (DM)

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Analog Data to Digital Signal

- 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 converted to an analog signal, using

previously discussed techniques

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

Pulse Code Modulation

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

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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

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

Reasons for Growth of Digital Techniques

- Growth in popularity of digital techniques for

sending analog data - Repeaters are used instead of amplifiers
- No additive noise
- TDM is used instead of FDM
- No intermodulation noise
- Conversion to digital signaling allows use of

more efficient digital switching techniques

2.3 Spread Spectrum

Reading material 1Chapter 7 in textbook

2.3.1 The Concept of Spread Spectrum

??????

Spread Spectrum

- Input is fed into a channel encoder
- Produces analog signal with narrow bandwidth
- Signal is further modulated using sequence of

digits - Spreading code or spreading sequence
- Generated by pseudonoise, or pseudo-random number

generator - Effect of modulation is to increase bandwidth of

signal to be transmitted

Spread Spectrum

- On receiving end, digit sequence is used to

demodulate the spread spectrum signal - Signal is fed into a channel decoder to recover

data

Spread Spectrum

Spread Spectrum

- What can be gained from apparent waste of

spectrum? - Immunity from various kinds of noise and

multipath distortion - Can be used for hiding and encrypting signals
- Several users can independently use the same

higher bandwidth with very little interference

?????????(1)

- ?????????????1941????????Hedy Lamarr ????George

Antheil???? - 1949????????????????????????,Derosa?Rogoff????????

???????????????,??????New Jersey?California???????

?? - 1950?Basore?????????????NOMACS(Noise Modulation

and Correlation Detection System)?????????????? - 1951???,??????????MIT???????????NOMACS??,?????????

???????????????????MIT??????? - 1952??????????P9D?NOMACS ??,???????

?????????(2)

- 1955??????????????,??????????????????,???????Phat

om(??,??)? Hush-Up(??),???????Blades(??),????

????????? - 1976??????????????Spread Spectrum Systems???
- 1978??????????????????(CCIR)??????????????

?????????(3)

- 1982??????????????????????????????,???????????????

???,????????????? - ???????????????Coherent Spread Spectrum ???
- 1985??????????????
- ?????,??????????????????,??????????????????????

2.3.2 Frequency Hopping Spread Spectrum

Frequency Hoping Spread Spectrum (FHSS)

- Signal is broadcast over seemingly random series

of radio frequencies - A number of channels allocated for the FH signal
- Width of each channel corresponds to bandwidth of

input signal - Signal hops from frequency to frequency at fixed

intervals - Transmitter operates in one channel at a time
- Bits are transmitted using some encoding scheme
- At each successive interval, a new carrier

frequency is selected

Frequency Hoping Spread Spectrum

- Channel sequence dictated by spreading code
- Receiver, hopping between frequencies in

synchronization with transmitter, picks up

message - Advantages
- Eavesdroppers hear only unintelligible blips
- Attempts to jam signal on one frequency succeed

only at knocking out a few bits

Frequency Hoping Spread Spectrum

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FHSS Using MFSK

- MFSK signal is translated to a new frequency

every Tc seconds by modulating the MFSK signal

with the FHSS carrier signal - For data rate of R
- duration of a bit T 1/R seconds
- duration of signal element Ts LT seconds
- Tc ? Ts - slow-frequency-hop spread spectrum
- Tc lt Ts - fast-frequency-hop spread spectrum

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FHSS Performance Considerations

- Large number of frequencies used
- Results in a system that is quite resistant to

jamming - Jammer must jam all frequencies
- With fixed power, this reduces the jamming power

in any one frequency band

2.3.3 Direct Sequence Spread Spectrum

Direct Sequence Spread Spectrum (DSSS)

- Each bit in original signal is represented by

multiple bits in the transmitted signal - Spreading code spreads signal across a wider

frequency band - Spread is in direct proportion to number of bits

used - One technique combines digital information stream

with the spreading code bit stream using

exclusive-OR (Figure 7.6)

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DSSS Using BPSK

- Multiply BPSK signal,
- sd(t) A d(t) cos(2? fct)
- by c(t) takes values 1, -1 to get
- s(t) A d(t)c(t) cos(2? fct)
- A amplitude of signal
- fc carrier frequency
- d(t) discrete function 1, -1
- At receiver, incoming signal multiplied by c(t)
- Since, c(t) x c(t) 1, incoming signal is

recovered

DSSS Using BPSK

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2.3.4 Code Division Multiple Access

Code-Division Multiple Access (CDMA)

- Basic Principles of CDMA
- D rate of data signal
- Break each bit into k chips
- Chips are a user-specific fixed pattern
- Chip data rate of new channel kD

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CDMA Example

- If k6 and code is a sequence of 1s and -1s
- For a 1 bit, A sends code as chip pattern
- ltc1, c2, c3, c4, c5, c6gt
- For a 0 bit, A sends complement of code
- lt-c1, -c2, -c3, -c4, -c5, -c6gt
- Receiver knows senders code and performs

electronic decode function - ltd1, d2, d3, d4, d5, d6gt received chip pattern
- ltc1, c2, c3, c4, c5, c6gt senders code

CDMA Example

- User A code lt1, 1, 1, 1, 1, 1gt
- To send a 1 bit lt1, 1, 1, 1, 1, 1gt
- To send a 0 bit lt1, 1, 1, 1, 1, 1gt
- User B code lt1, 1, 1, 1, 1, 1gt
- To send a 1 bit lt1, 1, 1, 1, 1, 1gt
- Receiver receiving with As code
- (As code) x (received chip pattern)
- User A 1 bit 6 -gt 1
- User A 0 bit -6 -gt 0
- User B 1 bit 0 -gt unwanted signal ignored

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CDMA for Direct Sequence Spread Spectrum

2.3.5 Generation of Spreading Sequences

Categories of Spreading Sequences

- Spreading Sequence Categories
- PN sequences
- Orthogonal codes
- For FHSS systems
- PN sequences most common
- For DSSS systems not employing CDMA
- PN sequences most common
- For DSSS CDMA systems
- PN sequences
- Orthogonal codes

PN Sequences

- PN generator produces periodic sequence that

appears to be random - PN Sequences
- Generated by an algorithm using initial seed
- Sequence isnt statistically random but will pass

many test of randomness - Sequences referred to as pseudorandom numbers or

pseudonoise sequences - Unless algorithm and seed are known, the sequence

is impractical to predict

Important PN Properties

- Randomness
- Uniform distribution
- Balance property
- Run property
- Independence
- Correlation property
- Unpredictability

Linear Feedback Shift Register Implementation

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Properties of M-Sequences

- Property 1
- Has 2n-1 ones and 2n-1-1 zeros
- Property 2
- For a window of length n slid along output for N

(2n-1) shifts, each n-tuple appears once, except

for the all zeros sequence - Property 3
- Sequence contains one run of ones, length n
- One run of zeros, length n-1
- One run of ones and one run of zeros, length n-2
- Two runs of ones and two runs of zeros, length

n-3 - 2n-3 runs of ones and 2n-3 runs of zeros, length 1

Properties of M-Sequences

- Property 4
- The periodic autocorrelation of a 1

m-sequence is

Definitions

- Correlation
- The concept of determining how much similarity

one set of data has with another - Range between 1 and 1
- 1 The second sequence matches the first sequence
- 0 There is no relation at all between the two

sequences - -1 The two sequences are mirror images
- Cross correlation
- The comparison between two sequences from

different sources rather than a shifted copy of a

sequence with itself

Advantages of Cross Correlation

- The cross correlation between an m-sequence and

noise is low - This property is useful to the receiver in

filtering out noise - The cross correlation between two different

m-sequences is low - This property is useful for CDMA applications
- Enables a receiver to discriminate among spread

spectrum signals generated by different

m-sequences

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Gold Sequences

- Gold sequences constructed by the XOR of two

m-sequences with the same clocking - Codes have well-defined cross correlation

properties - Only simple circuitry needed to generate large

number of unique codes - In following example (Figure 7.16a) two shift

registers generate the two m-sequences and these

are then bitwise XORed

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Orthogonal Codes

- Orthogonal codes
- All pairwise cross correlations are zero
- Fixed- and variable-length codes used in CDMA

systems - For CDMA application, each mobile user uses one

sequence in the set as a spreading code - Provides zero cross correlation among all users
- Types
- Welsh codes
- Variable-Length Orthogonal codes

Walsh Codes

- Set of Walsh codes of length n consists of the n

rows of an n n Walsh matrix - W1 (0)
- n dimension of the matrix
- Every row is orthogonal to every other row and to

the logical not of every other row - Requires tight synchronization
- Cross correlation between different shifts of

Walsh sequences is not zero

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Typical Multiple Spreading Approach

- Spread data rate by an orthogonal code

(channelization code) - Provides mutual orthogonality among all users in

the same cell - Further spread result by a PN sequence

(scrambling code) - Provides mutual randomness (low cross

correlation) between users in different cells

2.4 Coding and Error Control

Coping with Data Transmission Errors

- Error detection codes
- Detects the presence of an error
- Automatic repeat request (ARQ) protocols
- Block of data with error is discarded
- Transmitter retransmits that block of data
- Error correction codes, or forward correction

codes (FEC) - Designed to detect and correct errors

2.4.1 Error Detection

Error Detection Probabilities

- Definitions
- Pb Probability of single bit error (BER)
- P1 Probability that a frame arrives with no bit

errors - P2 While using error detection, the probability

that a frame arrives with one or more undetected

errors - P3 While using error detection, the probability

that a frame arrives with one or more detected

bit errors but no undetected bit errors

Error Detection Probabilities

- With no error detection
- F Number of bits per frame

Error Detection Process

- Transmitter
- For a given frame, an error-detecting code (check

bits) is calculated from data bits - Check bits are appended to data bits
- Receiver
- Separates incoming frame into data bits and check

bits - Calculates check bits from received data bits
- Compares calculated check bits against received

check bits - Detected error occurs if mismatch

Error Detection Process

Parity Check

- Parity bit appended to a block of data
- Even parity
- Added bit ensures an even number of 1s
- Odd parity
- Added bit ensures an odd number of 1s
- Example, 7-bit character 1110001
- Even parity 11100010
- Odd parity 11100011

Cyclic Redundancy Check (CRC)

- Transmitter
- For a k-bit block, transmitter generates an

(n-k)-bit frame check sequence (FCS) - Resulting frame of n bits is exactly divisible by

predetermined number - Receiver
- Divides incoming frame by predetermined number
- If no remainder, assumes no error

CRC using Modulo 2 Arithmetic

- Exclusive-OR (XOR) operation
- Parameters
- T n-bit frame to be transmitted
- D k-bit block of data the first k bits of T
- F (n k)-bit FCS the last (n k) bits of T
- P pattern of nk1 bits this is the

predetermined divisor - Q Quotient
- R Remainder

CRC using Modulo 2 Arithmetic

- For T/P to have no remainder, start with
- Divide 2n-kD by P gives quotient and remainder
- Use remainder as FCS

CRC using Modulo 2 Arithmetic

- Does R cause T/P have no remainder?
- Substituting,
- No remainder, so T is exactly divisible by P

CRC using Polynomials

- All values expressed as polynomials
- Dummy variable X with binary coefficients

CRC using Polynomials

- Widely used versions of P(X)
- CRC12
- X12 X11 X3 X2 X 1
- CRC16
- X16 X15 X2 1
- CRC CCITT
- X16 X12 X5 1
- CRC 32
- X32 X26 X23 X22 X16 X12 X11 X10

X8 X7 X5 X4 X2 X 1

CRC using Digital Logic

- Dividing circuit consisting of
- XOR gates
- Up to n k XOR gates
- Presence of a gate corresponds to the presence of

a term in the divisor polynomial P(X) - A shift register
- String of 1-bit storage devices
- Register contains n k bits, equal to the length

of the FCS

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Digital Logic CRC

2.4.2 Block Error Correction Codes

Wireless Transmission Errors

- Error detection requires retransmission
- Detection inadequate for wireless applications
- Error rate on wireless link can be high, results

in a large number of retransmissions - Long propagation delay compared to transmission

time

Block Error Correction Codes

- Transmitter
- Forward error correction (FEC) encoder maps each

k-bit block into an n-bit block codeword - Codeword is transmitted analog for wireless

transmission - Receiver
- Incoming signal is demodulated
- Block passed through an FEC decoder

Forward Error Correction Process

FEC Decoder Outcomes

- No errors present
- Codeword produced by decoder matches original

codeword - Decoder detects and corrects bit errors
- Decoder detects but cannot correct bit errors

reports uncorrectable error - Decoder detects no bit errors, though errors are

present

Block Code Principles

- Hamming distance for 2 n-bit binary sequences,

the number of different bits - E.g., v1011011 v2110001 d(v1, v2)3
- Redundancy ratio of redundant bits to data bits
- Code rate ratio of data bits to total bits
- Coding gain the reduction in the required Eb/N0

to achieve a specified BER of an error-correcting

coded system

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Hamming Code

- Designed to correct single bit errors
- Family of (n, k) block error-correcting codes

with parameters - Block length n 2m 1
- Number of data bits k 2m m 1
- Number of check bits n k m
- Minimum distance dmin 3
- Single-error-correcting (SEC) code
- SEC double-error-detecting (SEC-DED) code

Hamming Code Process

- Encoding k data bits (n -k) check bits
- Decoding compares received (n -k) bits with

calculated (n -k) bits using XOR - Resulting (n -k) bits called syndrome word
- Syndrome range is between 0 and 2(n-k)-1
- Each bit of syndrome indicates a match (0) or

conflict (1) in that bit position

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Cyclic Codes

- Can be encoded and decoded using linear feedback

shift registers (LFSRs) - For cyclic codes, a valid codeword (c0, c1, ,

cn-1), shifted right one bit, is also a valid

codeword (cn-1, c0, , cn-2) - Takes fixed-length input (k) and produces

fixed-length check code (n-k) - In contrast, CRC error-detecting code accepts

arbitrary length input for fixed-length check code

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BCH Codes

- For positive pair of integers m and t, a (n, k)

BCH code has parameters - Block length n 2m 1
- Number of check bits n k mt
- Minimum distancedmin 2t 1
- Correct combinations of t or fewer errors
- Flexibility in choice of parameters
- Block length, code rate

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Reed-Solomon Codes

- Subclass of nonbinary BCH codes
- Data processed in chunks of m bits, called

symbols - An (n, k) RS code has parameters
- Symbol length m bits per symbol
- Block length n 2m 1 symbols m(2m 1) bits
- Data length k symbols
- Size of check code n k 2t symbols m(2t)

bits - Minimum distance dmin 2t 1 symbols

Block Interleaving

- Data written to and read from memory in different

orders - Data bits and corresponding check bits are

interspersed with bits from other blocks - At receiver, data are deinterleaved to recover

original order - A burst error that may occur is spread out over a

number of blocks, making error correction possible

Block Interleaving

2.4.3 Convolutional Codes

Convolutional Codes

- Generates redundant bits continuously
- Error checking and correcting carried out

continuously - (n, k, K) code
- Input processes k bits at a time
- Output produces n bits for every k input bits
- K constraint factor
- k and n generally very small
- n-bit output of (n, k, K) code depends on
- Current block of k input bits
- Previous K-1 blocks of k input bits

Convolutional Encoder

Decoding

- Trellis diagram expanded encoder diagram
- Viterbi code error correction algorithm
- Compares received sequence with all possible

transmitted sequences - Algorithm chooses path through trellis whose

coded sequence differs from received sequence in

the fewest number of places - Once a valid path is selected as the correct

path, the decoder can recover the input data bits

from the output code bits

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2.4.4 Automatic Repeat Request

Automatic Repeat Request

- Mechanism used in data link control and transport

protocols - Relies on use of an error detection code (such as

CRC) - Flow Control
- Error Control

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Flow Control

- Assures that transmitting entity does not

overwhelm a receiving entity with data - Protocols with flow control mechanism allow

multiple PDUs in transit at the same time - PDUs arrive in same order theyre sent
- Sliding-window flow control
- Transmitter maintains list (window) of sequence

numbers allowed to send - Receiver maintains list allowed to receive

Flow Control

- Reasons for breaking up a block of data before

transmitting - Limited buffer size of receiver
- Retransmission of PDU due to error requires

smaller amounts of data to be retransmitted - On shared medium, larger PDUs occupy medium for

extended period, causing delays at other sending

stations

Flow Control

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Error Control

- Mechanisms to detect and correct transmission

errors - Types of errors
- Lost PDU a PDU fails to arrive
- Damaged PDU PDU arrives with errors

Error Control Requirements

- Error detection
- Receiver detects errors and discards PDUs
- Positive acknowledgement
- Destination returns acknowledgment of received,

error-free PDUs - Retransmission after timeout
- Source retransmits unacknowledged PDU
- Negative acknowledgement and retransmission
- Destination returns negative acknowledgment to

PDUs in error

Go-back-N ARQ

- Acknowledgments
- RR receive ready (no errors occur)
- REJ reject (error detected)
- Contingencies
- Damaged PDU
- Damaged RR
- Damaged REJ

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