ii-1-PHY

Taekyoung Kwon

Data vs. signal• Digital data vs. analog data• Digital signal vs. analog signal• Data are symbols like bits that have some info. • A signal refers to physical representation of data,

electrically or electromagnetically

signal• A signal is a time-varying value (electric or electromagnetic

representation) or event that conveys information from a transmitter to a receiver

• A function of time and location• parameters of periodic signals:

period T, frequency f=1/T, amplitude A, phase shift – E.g., sinewave is expressed as

s(t) = At sin(2 ft t + t)

: phi [fee]

signal• Different representations of signals

– Amplitude over time (time domain)– frequency spectrum (frequency domain)

– phase state diagram (amplitude M and phase in polar coordinates)

f [Hz]

A [V]

I= M cos

Q = M sin

A [V]

t[s]

signal

f=1/T

min

Nyquist bandwidth• Ideally, we need only B=n/2 bandwidth to represent

the original digital signal of bit rate n• In reality, we need more due to noise, interference,…

– For bit rate n, n/2 ≤ B ≤ n– B = n/2 * (1 + α) 0 ≤ α ≤ 1

• The most naïve case will be when B is equal to n

: roll-off factor

What is ?

Pulse shaping• Original rectangle pulses require infinite BW• We need to change the binary inputs to BW-limited signals• Nyquist BW makes a binary input into a sinc function

t

0 bT2 bT bT 3 bT2 bT3 bT

( )p t

f

( )P f

1

bT

1

2ob

WT

1

2 bT 0

sin( ) sinc

1 decays as (slowly decaying)

e

tt T

h ttTT

t

Inter symbol interference (ISI)

• Consecutive bits or symbols interfere each other

Sampling instants

No ISI

Theoretically adjacent pulsesgo to zero hence no ISI

Tb

Pulse shaping issues Two practical difficulties

• If we use a sinc function, minimum BW is required, but physically unrealizable

• If clocks are perfectly synchronized, then there is no ISI => which is impossible

• Timing errors, delay jitters

senstive to timing errors

t

Roll-off• How to mitigate ISI despite timing errors and delay jitters?• To make a sinc realizable, we begin by smoothing the edges of its

squared-off spectrum• This process is called “roll-off”• We can smooth the sinc spectrum by the smoothing parameter. The

cost is increased BW

f

=0.5=0

=1

Rb/2 Rb

0r 0.5r

1r

(b)

As increases

• The pulse (a function of time) after its symbol time decreases more sharply

Baseband signal vs. bandpass signal• We use B bandwidth to represent the original digital signal

of bit rate n• This analog signal occupying 0B Hz is called baseband

signal– Used for PSTN local loop and Ethernet

• In wireless, we cannot use baseband signal– Shared medium– A long antenna will be required (at least half or quarter of

wavelength)– Not suitable for propagation

• That’s why we need bandpass signals

Bandpass signal• Using carriers to shift the frequency spectrum

– Called (analog) modulation– different radio bands can be used for different

communications– wireless communications– multiplexing techniques become applicable– However, it occupies twice bandwidth

Bandpass signal: twice BW• Consider a single frequency component cos(mt) from within

the baseband spectrum (0 – B Hz) • perform the mathematical multiplication with the carrier

cos(ct)

• The modulated signal becomes:– cos(ct) . cos(mt) = 0.5 cos (c - m)t + 0.5 cos (c + m)t

– two identical components symmetric about the carrier frequency

= 2f

VASK(t) =Vd(t) * Vc(t)

Summary of modulation • digital modulation is a process of transforming a digital signal (or

data) into a baseband signal– A digital signal: a series of bits– A baseband signal: an analog signal of [0 B Hz] bandwidth– n bps corresponds to B bandwidth (n/2 ≤ B ≤ n)

• For wireless communications, we have to use a bandpass signal, which requires 2B bandwidth– A process of changing baseband to bandpass is called analog modulation

Modulation and demodulation

synchronizationdecision

digitaldataanalog

demodulation

radiocarrier

analogbasebandsignal

101101001radio receiver

digitalmodulation

digitaldata analog

modulation

radiocarrier

analogbasebandsignal

101101001 radio transmitter

Spread Spectrum (SS) and CDMA• Basic idea: Use a wider bandwidth than needed to transmit the signal• Why??

– Don’t put all your eggs in one basket!– Resistance to jamming and interference

• If one sub-channel is blocked, you still have the others• Good for military• Minimize impact of a “bad” frequency

– Pseudo-encryption• Have to know what frequencies it will use

• Two techniques for spread spectrumSo far, we have assumed that BW is precious and should be minimized. What if we don’t know which portion of frequency spectrum is used by a particular technology.

Spread spectrum technology is to address this problem; it uses much wider BW to transmit a signalSpread spectrum distributes the energy of a signal over a wider BW to make the system robust to interferenceEven if some portion of BW (sub-channel) is erroneous, the other parts may be able to get over that interference.

This situation happens in ISM band. 900MHz, 2.4GHz, 5GHz.As it is license-free, there are many technologies crowded in that band

Frequency Hopping (FH) SS• Pick a set of frequencies within a band• At each time slot, pick a new frequency

– Each frequency has the bandwidth of the original signal• Dwell time is the time spent using one frequency• Spreading code determines the hopping sequence

– Must be shared by sender and receiver (e.g. standardized)– Usually frequency determined by a pseudorandom generator

function with a shared seed

Time

Frequency

In FH technique, there are multiple subchannels, and the TX selects a particular subchannel at each interval by a given hopping sequence

The hopping sequence is determined by a seed to pseudorandom generator and the seed should be shared by TX and RX

Direct Sequence SS (DSSS)• Each bit represented by multiple chips using spreading code• Spreading code spreads signal across wider frequency band

– In proportion to number of bits used– 10 chip spreading code spreads signal across 10 times bandwidth

of 1 bit code (of original message)• One method:

– Combine input with spreading code using XOR– Data rate becomes multiplied by the length of spreading code

The 2nd technique, DSSS is more popular. Here, we have a chip sequence or spreading code. The spreading code is a fixed number of chips (they are similar to bits)

We multiply or XOR two streams: original bit stream and spreading codeE.g. if the input bit of data is 1, we invert the spreading code and do not invert the spreading code otherwise

Suppose the spreading code is a 10 chip sequence. If data rate is n bps, the DSSS transmits 10*n chips per second instead of n bits per sec

This illustrates how DSSS works when the spreading code is a 8 chip sequence, -1-1-11-1111 (from right to left in the figure)

In the circle, what happens is multiplication, so the 1st data bit leaves the spreading code intact while the 2nd bit inverts the spreading code

the binary digital signal is often formulated by (1,-1) pair instead of (1,0) pair. However, there is no essential difference and I will explain in terms of (1,-1) in this slide

On the receipt of the chip sequence, the RX just again multiplies it with the spreading code again. Then the original bit stream is restored

DSSS Properties• Since each bit is sent as multiple chips, you need more

bps bandwidth to send the signal– Number of chips per bit is called the spreading ratio

• We need more spectral bandwidth to do this– Spreading the signal over the spectrum

• Advantage is that transmission is more resilient– DSSS signal will look like noise in a narrow band– Can lose some chips in a word and recover easily

• Multiple users can share bandwidth (easily)– Use a different chipping sequence– CDMA

In the previous slide, the spreading code is a 8 bit chip sequence.If we use X bandwidth for original data of n bps, now we need 8*X BW for 8*n chips per secondBy spreading its energy over 8*X BW, even if there is some error, we may be able to restore the original bit streamIf every user can have a different and orthogonal spreading code, they can transmit individually at the same time over the same frequency band, so-called CDMA

SS Discussion• Spread spectrum is very widely used

– Effectively resilient against noise and multipath– Multiple transmitters can use the same frequency range

• FCC requires the use of SS in ISM band– If signal is above a certain power level

• Is also used in some 802.11 versions

In FH and DS techniques, we achieve a trade-off between bandwidth and robustness: using more BW and getting over noise and interference

SS is especially required for communication environments where TX power should be limited.

A number of wireless comm. technologies are sharing the ISM band.

To lower the interference level of communications, FCC mandates SS for wireless comm. in ISM band and the maximum TX power.

Bit rate vs. BW in 802.11• The original 802.11 has two date rates: 1 and 2 Mbps• We will consider 1 Mbps first• 1 Mbps bit stream requires a baseband signal of B bandwidth between 0.5

MHz and 1MHz• 802.11 adopts a naïve approach: 1MHz• Wireless requires a bandpass signal, which occupies 2MHz• Then there comes spread spectrum technique

– 11 chip Barker sequence

• Eventually, 22MHz bandwidth is needed for each channel for IEEE 802.11

Original 802.11 standardized in 1997 offers two bit rates: 1 and 2 Mbps

For simplicity, let’s see how much BW is used for 1Mbps case

In 802.11, the baseband signal for 1Mbps uses ample BW, 1MHz

There are 11 channels in 802.11, each of which has its own carrier frequency. The bandpass signal for each channel occupies 2MHzOwing to SS technique, we need to transmit 11Mchips per sec instead of 1Mbps, which increases BW 11 timesFinally, each channel uses 22MHz

802.11 DSSS: how 1Mbps is spread

X

=

“symbol”

“Barker” sequence

Result of multiplication

Symbol time ts

“1” “0”

Chip time tc

• Due to the multiplication of a symbol with Barker code, the “rate-of-change” increases with a factor 11

• This means that cycle rate increases from 1 MHz to 11 MHz

• In terms of spectrum, this means that after RF modulation the signal is spread from 2 MHz bandwidth to 22 MHz bandwidth

2 Mhz 22 Mhz

This slide how a symbol (which is 1 bit with BPSK) is spread by 11 chip Barker sequence. Note that all the stations use the same Barker code, not CDMAThe rate of change (BW) is multiplied 11 times due to DSSS

Note that the power distribution around carrier freq. is quite flattened

*Barker Code: 10110111000

Channel Allocation

There are 11 channels in USA, which are depicted in the slide Each channel occupies 22MHz BW, and there are three non-overlapping channels: 1, 6, 11

Symbol in communications• The original 802.11 has two date rates: 1 and 2 Mbps• What about 2Mbps?• There is another notion of symbol between a bit and BW

• If there are M kinds of symbols, a symbol can represent log2M bits

• Chips were transmitted using BPSK modulation.– Data rate was 1 Mbps (i.e. 11 Mchips/sec)

– Extended to 2 Mbps by using a QPSK modulation• Requires the detection of a ¼ phase shift

What I have explained so far has one missing part: the concept of symbol.The bit rate in the earlier slides is actually the symbol rate.

So if the symbol rate is n symbols per sec, the baseband signal requires from n/2 to n BW depending on the roll-off factor

One symbol can represent multiple bits.

BPSK has two symbols; so one symbol represents one bit, which is the 1Mbps in the previous slideQPSK has 4 symbols; so one symbol represents two bits, which is the 2Mbps case. It requires the same 22 MHz

SourceSource

EncoderChannelEncoder

Mod-ulator

UserSource

DecoderChannelDecoder

Demod-ulator

MessageSignal

Channel codeword

Estimate ofMessage

signalEstimate of

channel codeword

ReceivedSignal

Wireless

Channel

A Big Picture of wireless TX, RX

Source coding• Purpose of source coding: to transform the information in

the source into a digital form best suited for transmission• Often, seeks to minimize the number of bits required to

convey information– compression

• Voice, audio, video are primary targets

What is source coding?

If the original data is digital, we don’t need source coding

However, as voice and video data are inherently analog, we have to digitize the original analog data, which is called source coding

Typically, how to reduce the number of bits for the same analog data is of primary concern

Channel coding• Forward error correction (FEC)• add redundancy into the original info to protect them from

bit errors due to interference and noise in transmission • Input k bits Output n bits

– k/n code rate or (n,k) code rate

• Interleaving• E.g. Reed-solomon (RS) coding, convolutional coding

Source coding is important, but channel coding is even more important since it affects the effective bit rate of the wireless link

Channel coding is also called FEC since it adds redundant info to original info to make the signal more robust to errors

Normally, FEC is denoted by two parameters

Sometimes FEC is done in conjunction with interleaving since bit errors are often happening in a burst

Example of 802.11a bit rate• OFDM, 48 data subcarriers• 1 subcarrier: 250K symbol rate• 64QAM for each symbol in each subcarrier

– One symbol: 6 bits

• 3/4 convolutional coding (FEC)• 48 * 250K * 6 * 3/4 = 54Mbps

Let’s analyze the highest bit rate of 802.11a, 54Mbps

It employs OFDM, which uses multiple subcarriers

Multiple bit streams are TXed in parallel, each of which TXs 250K symbols per secUsing 64QAM modulation, one symbol represents 6 bits

Also, it uses ¾ FEC

Radio propagation vs Frequency• Surface wave

– Less than 3MHz

• Sky wave (ionospheric refraction) – 3 and 30 MHz

• Direct wave (line-of-sight)– Greater than 30Mhz– reflection is important

• Our main focus is on direct wave– UHF and SHF are subject to direct wave– Ultra High Frequency 300–3000 MHz– Super High Frequency 3–30 GHz

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c=λfc: speed of lightλ: wavelengthf: frequency

Radio propagation mechanisms: when direct wave is dominant

• Free space 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

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reflection scatteringdiffraction

Those lead to multi-path propagation• 4 mechanisms

– Free space propagation– Reflections– Scattering– Diffraction

• At receiver (RX)– These components arrive with different delays– These components are combined at RX – Sometimes they add up constructively or destructively

36

At RX• What happens is…

37

General propagation model• Path-loss + slow fading + fast fading• In free space, received power attenuates like 1/d2

38

Large scale fading• A large obstruction such as a hill or large building

obscures the main signal path between the transmitter and the receiver

• Aka, slow fading, shadowing• Relatively slow change in signal power

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Small scale fading• caused by the superposition or cancellation of multipath

propagation • Aka, fast fading, multipath fading• factors

– Multipath propagation.– Speed of the mobile.– Speed of the surrounding objects.– Transmission bandwidth of the signal

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Two main options in fast fading• Rician fading

– Dominant signal over the line-of-sight (LOS) path– K-factor is defined as the ratio of signal power in dominant

component over the (local-mean) scattered power

• Rayleigh fading– Most representative of fast fading– No dominant signal

41

More simplified model• Received signal strength is proportional to 1/dn • n: path-loss exponent

– Normally n is between 2 and 8– Often, n = 4 in simulation

42Rapapport, “wireless communications: principles and practice”

43

Signal Propagation Ranges

Distancefrom transmitter

sender

transmission

detection

interference

• Transmission range– communication possible– low error rate

• Detection range– detection of the signal

possible, but communication may not be possible

due to high error rate

• Interference range– signal may not be

detected – signal adds to the

background noise

Antennas• Electrical conductor (or system of..) used to radiate

electromagnetic energy or collect electromagnetic energy• Transmission

– RF signal energy from transmitter– Converted to electromagnetic (EM) energy– By antenna– Radiated into surrounding environment

• Reception– Electromagnetic energy impinging on antenna– Converted to radio frequency electrical energy– Fed to receiver

In wireless communications, an antenna is a key player

At TX, electric signal energy is transformed into EM energy

At RX, the reverse process is performed

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antennas• electromagnetic (EM) fields

– Tend to propagate– As waves– At speed of light

• EM waves can travel in empty space or can be confined (guided) by structures

• A transition structure between guided EM fields and free waves

• As a circuit: a transformer between terminals & free space radiation

To fully understand an antenna, we need to know EM field theory

When it is confined, there is an electric current in the circuit-type structure

45

At 2.4GHz, λ = 12.5cm by c=fλSo half-wave dipole antenna is 6.25cmDielectric constant can be a factor

Quarter-wave antennas are also popular, which requires ¼ length of wavelength.

Dipole antenna

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Radiation Pattern• Power radiated in all directions• Not same performance in all directions• Isotropic antenna is (theoretical) point in space

– Radiates in all directions equally– Gives spherical radiation pattern

Let’s see how EM waves are radiated from the antenna

In real antennas, the radiation pattern is not same for all directions

Suppose there is an ideal antenna, isotropic antenna.

An EM wave is radiated to all the possible directions of the sphere.

The isotropic antenna is often used as a reference.

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Antenna’s directivity• Isotropic• Omni-directional

– Radiation in every direction on azimuth/horizontal plane

• Directional– Narrower beamwidth, higher gain

In reality, every antenna has different level of radiation for each directionTo assess the directivity of an antenna, we measure the signal power of an antenna in all 3-D directions and compare with that of the isotropic antenna.The antennas in most of the low cost wireless devices are omni-directional

48

Omni vs directional

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Antenna (directed or sectorized)• E.g. 3 sectors per BS in cellular networks

side view (xy-plane)

x

y

side view (yz-plane)

z

y

top view (xz-plane)

x

z

top view, 3 sector

x

z

top view, 6 sector

x

z

directionalantenna

sectorizedantenna

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