Wireless PHY: Modulation and Channels

Y. Richard Yang

09/6/2012

2

Outline

Recap Frequency domain examples Introduction to modulation

3

Frequency Domain Analysis Examples Using GNURadio

spectrum_2sin_plus Audio FFT Sink Scope Sink Noise

4

Frequency Domain Analysis Examples Using GNURadio

spectrum_1sin_rawfft Raw FFT

5

Frequency Domain Analysis Examples Using GNURadio

spectrum_2sin_multiply_complex Multiplication of a sine first by

• a real sine and then by • a complex sine to observe spectrum

6

Takeaway of the Example

Advantages of I/Q representation

7

Quadrature Mixing

spectrum of complexsignal x(t)

spectrum of complexsignal x(t)ej2f0t

spectrum of complexsignal x(t)e-j2f0t

8

Basic Question: Why Not Send Digital Signal in Wireless Communications?

Signals at undesirable frequencies suppose digital frame length T, then signal decomposes into frequencies at 1/T, 2/T, 3/T, …

let T = 1 ms, generates radio waves at frequencies of 1 KHz, 2 KHz, 3 KHz, …

1

0

digital signal

t

9

Frequencies are Assigned and Regulated

Europe USA Japan

Cellular Phones

GSM 450 - 457, 479 -486/460 - 467,489 -496, 890 - 915/935 -960, 1710 - 1785/1805 -1880 UMTS (FDD) 1920 -1980, 2110 - 2190 UMTS (TDD) 1900 -1920, 2020 - 2025

AMPS , TDMA , CDMA 824 - 849, 869 -894 TDMA , CDMA , GSM 1850 - 1910, 1930 - 1990

PDC 810- 826, 940-956, 1429 - 1465, 1477 - 1513

Cordless Phones

CT1+ 885 - 887, 930 -932 CT2 864-868 DECT 1880 - 1900

PACS 1850 - 1910, 1930 -1990 PACS -UB 1910 - 1930

PHS 1895 - 1918 JCT 254-380

Wireless LANs

IEEE 802.11 2400 - 2483 HIPERLAN 2 5150 - 5350, 5470 -5725

902-928 I EEE 802.11 2400 - 2483 5150 - 5350, 5725 - 5825

IEEE 802.11 2471 - 2497 5150 - 5250

Others RF- Control 27, 128, 418, 433,

868

RF- Control 315, 915

RF- Control 426, 868

10

Spectrum and Bandwidth: Shannon Channel Capacity The maximum number of bits that can be transmitted per second by a physical channel is:

where W is the frequency range of the channel, and S/N is the signal noise ratio, assuming Gaussian noise

)1(log2 NSW

11

Frequencies for Communications

VLF = Very Low Frequency UHF = Ultra High FrequencyLF = Low Frequency SHF = Super High FrequencyMF = Medium Frequency EHF = Extra High Frequency

HF = High Frequency UV = Ultraviolet LightVHF = Very High Frequency

Frequency and wave length:

= c/f wave length , speed of light c 3x108m/s, frequency f

1 Mm300 Hz

10 km30 kHz

100 m3 MHz

1 m300 MHz

10 mm30 GHz

100 m3 THz

1 m300 THz

visible lightVLF LF MF HF VHF UHF SHF EHF infrared UV

optical transmissioncoax cabletwisted pair

12

Why Not Send Digital Signal in Wireless Communications?

voice Transmitter

20-20KHzAntenna:

size ~ wavelength

At 3 KHz,

Antenna too large!Use modulation to transfer to higher

frequency

13

Outline

Recap Frequency domain examples Basic concepts of modulation

14

The information source Typically a low frequency signal Referred to as baseband signal

Carrier A higher frequency sinusoid Example cos(2π10000t)

Modulated signal Some parameter of the carrier (amplitude, frequency, phase) is varied in accordance with the baseband signal

Basic Concepts of Modulation

15

Types of Modulation

Analog modulation Amplitude modulation (AM) Frequency modulation (FM) Double and signal sideband: DSB, SSB

Digital modulation Amplitude shift keying (ASK) Frequency shift keying: FSK Phase shift keying: BPSK, QPSK, MSK Quadrature amplitude modulation (QAM)

16

Outline

Recap Frequency domain examples Basic concepts of modulation Amplitude modulation

17

Example: Amplitude Modulation (AM) Block diagram

Time domain

Frequency domain

18

Example: am_modulation Example

Setting Audio source (sample 32K) Signal source (300K, sample 800K) Multiply

Two Scopes

FFT Sink

19

Example AM Frequency Domain

Note: There is always the negative freq. in the freq. domain.

20

Problem: How to Demodulate AM Signal?

21

Outline

Recap Frequency domain examples Basic concepts of modulation Amplitude modulation Amplitude demodulation

22

Design Option 1

Step 1: Multiply signal by e-jfct

Implication: Need to do complex multiple multiplication

23

Design Option 1 (After Step 1)

-2fc

24

Design Option 1 (Step 2)

Apply a Low Pass Filter to remove the extra frequencies at -2fc

-2fc

25

Design Option 1 (Step 1 Analysis)

How many complex multiplications do we need for Step 1 (Multiply by e-jfct)?

26

Design Option 2: Quadrature Sampling

27

Quadrature Sampling: Upper Path (cos)

28

Quadrature Sampling: Upper Path (cos)

29

Quadrature Sampling: Upper Path (cos)

30

Quadrature Sampling: Lower Path (sin)

31

Quadrature Sampling: Lower Path (sin)

32

Quadrature Sampling: Lower Path (sin)

33

Quarature Sampling: Putting Together

34

Exercise: SpyWork

Setting: a scanner scans 128KHz blocks of AM radio and save each block to a file (see am_rcv.py).

SpyWork: Scan the block in a saved file to find radio stations and tune to each station (each AM station has 10 KHz)

35

Remaining Hole: Designing LPF

Frequency domain view

freqB-B

freqB-B

36

Design Option 1

freqB-B

freqB-B

compute freq

zeroing outnot want freq

compute timesignal

Problem of Design Option 1?

37

Impulse Response Filters

GNU software radio implements filtering using Finite Impulse Response (FIR) filters Infinite Impulse Response (IIR) Filters

FIR filters are more commonly used

Filtering is common in networks/communications (and AI and …)

38

FIR Filter

An N-th order FIR filter h is defined by an array of N+1 numbers:

Assume input sequence x0, x1, …,

39

Implementing a 3-rd Order FIR Filter

An array of size N+1 for h

xnxn-1xn-2xn-3

h0h1h2h3

****

xn+1

compute y[n]

40

Implementing a 3-rd Order FIR Filter

An array of size N+1 for h

xnxn-1xn-2xn-3

h0h1h2h3

****

xn+1

compute y[n+1]

41

FIR Filter

is also called convolution between x (as a vector) and h (as a vector), denoted as

Key Question: How to Determine h?

g*h in the Continuous Time Domain

42

Remember that we consider x as samples of time domain function g(t) on [0, 1] and (repeat in other intervals)

We also consider h as samples of time domain function h(t) on [0, 1] (and repeat in other intervals)for (i = 0; i< N; i++)

y[t] += h[i] * g[t-i];

Visualizing g*h

43

g(t)

h(t)

time

Visualizing g*h

44

g(t)

h(t)

timet

Fourier Series of y=g*h

45

Fubini’s Theorem

In English, you can integrate first along y and then along x first along x and then along y at (x, y) gridThey give the same result

46

See http://en.wikipedia.org/wiki/Fubini's_theorem

Fourier Series of y=g*h

47

Summary of Progress So Far

48

y = g * h => Y[k] = G[k] H[k]

is called the Convolution Theorem, an important theorem.

Applying Convolution Theorem to Design LPF

49

Choose h() so that H() is close to a rectangle shape h() has a low order (why?)

Applying Convolution Theorem to Design LPF

50

Choose h() so that H() is close to a rectangle shape h() has a low order (why?)

Sinc Function

51

The h() is often related with the sinc(t)=sin(t)/t function

f1/2-1/2

1

FIR Design in Practice

52

Compute h MATLAB or other design software GNU Software radio: optfir (optimal filter design)

GNU Software radio: firdes (using a method called windowing method)

Implement filter with given h freq_xlating_fir_filter_ccf or fir_filter_ccf

LPF Design Example

53

Design a LPF to pass signal at 1 KHz and block at 2 KHz

LPF Design Example

54

#create the channel filter # coefficients chan_taps = optfir.low_pass( 1.0, #Filter gain 48000, #Sample Rate 1500, #one sided mod BW (passband edge) 1800, #one sided channel BW (stopband edge) 0.1, #Passband ripple 60) #Stopband Attenuation in dB print "Channel filter taps:", len(chan_taps) #creates the channel filter with the coef foundchan = gr.freq_xlating_fir_filter_ccf( 1 , # Decimation rate chan_taps, #coefficients 0, #Offset frequency - could be used to shift 48e3) #incoming sample rate

55

Outline

Recap Frequency domain examples Basic concepts of modulation Amplitude modulation Amplitude demodulation Digital modulation

56

Modulation of digital signals also known as Shift Keying

Amplitude Shift Keying (ASK): vary carrier amp. according to bit value

Frequency Shift Keying (FSK)o pick carrier freq according to bit value

Phase Shift Keying (PSK):

1 0 1

t

1 0 1

t

1 0 1

t

Modulation

57

BPSK (Binary Phase Shift Keying): bit value 0: sine wave bit value 1: inverted sine wave very simple PSK

Properties robust, used e.g. in satellite

systems

Q

I01

Phase Shift Keying: BPSK

58

Phase Shift Keying: QPSK

11 10 00 01

Q

I

11

01

10

00

A

t

QPSK (Quadrature Phase Shift Keying): 2 bits coded as one symbol symbol determines shift of

sine wave often also transmission of

relative, not absolute phase shift: DQPSK - Differential QPSK

59

Quadrature Amplitude Modulation (QAM): combines amplitude and phase modulation

It is possible to code n bits using one symbol 2n discrete levels

0000

0001

0011

1000

Q

I

0010

φ

a

Quadrature Amplitude Modulation

Example: 16-QAM (4 bits = 1 symbol)

Symbols 0011 and 0001 have the same phase φ, but different amplitude a. 0000 and 1000 have same amplitude but different phase

Exercise

Suppose fc = 1 GHz(fc1 = 1 GHz, fc0 = 900 GHzfor FSK)

Bit rate is 1 Mbps Encode one bit at a time Bit seq: 1 0 0 1 0 1

Q: How does the wave look like for?

60

11 10 00 01

Q

I

11

01

10

00

A

t

Generic Representation of Digital Keying (Modulation) Sender sends symbols one-by-one Each symbol has a corresponding signaling function g1(t), g2(t), …, gM(t), each has a duration of symbol time T

Exercise: What is the setting for BPSK? for QPSK?

61

Checking Relationship Among gi()

62

BPSK 1: g1(t) = -sin(2πfct) t in [0, T]

0: g0(t) = sin(2πfct) t in [0, T]

Are the two signaling functions independent? Hint: think of the samples forming a vector, if it helps, in linear algebra

Ans: No. g1(t) = -g0(t)

Checking Relationship Among gi()

63

QPSK 11: sin(2πfct + π/4) t in [0, T]

10: sin(2πfct + 3π/4) t in [0, T]

00: sin(2πfct - 3π/4) t in [0, T]

01: sin(2πfct - π/4) t in [0, T]

Are the four signaling functions independent? Ans: No. They are all linear combinations of sin(2πfct) and cos(2πfct).

We call sin(2πfct) and cos(2πfct) the bases. They are orthogonal because the integral of their product is 0.

Discussion: How does the Receiver Detect Which gi() is Sent?

64

Assume synchronized (i.e., the receiver knows the symbol boundary). This is also called coherent detection

Example: Matched Filter Detection

65

Basic idea consider each gm[0,T] as a point (with coordinates) in a space

compute the coordinate of the received signal s[0,T]

check the distance between gm[0,T] and the received signal s[0,T]

pick m* that gives the lowest distance value

Computing Coordinates

66

Pick orthogonal bases {f1(t), f2(t), …, fN(t)} for {g1(t), g2(t), …, gM(t)}

Compute the coordinate of gm[0,T] as cm = [cm1, cm2, …, cmN], where

Compute the coordinate of the received signal r[0,T] as r = [r1, r2, …, rN]

Compute the distance between r and cm every cm and pick m* that gives the lowest distance value

Example: Matched Filter => Correlation Detector

67

receivedsignal

68

Spectral Density of BPSK

b

Rb =Bb = 1/Tbb

fc : freq. of carrier

fc

Spectral Density =

bit rate-------------------

width of spectrum used

69

Phase Shift Keying: Comparison

BPSK

QPSK

fc: carrier freq.Rb: freq. of data10dB = 10; 20dB =100

11 10 00 01

A

t

Question

70

Why would any one use BPSK, given higher QAM?

Signal Propagation

72

Isotropic radiator: a single point equal radiation in all directions (three dimensional)

only a theoretical reference antenna

Radiation pattern: measurement of radiation around an antenna

zy

x

z

y x idealisotropicradiator

Antennas: Isotropic Radiator

Q: how does power level decrease as a function of d, the distancefrom the transmitter to the receiver?

73

Free-Space Isotropic Signal Propagation

In free space, receiving power proportional to 1/d² (d = distance between transmitter and receiver)

Suppose transmitted signal is cos(2ft), the received signal is

2

4

dGG

P

Ptr

t

r

Pr: received power

Pt: transmitted power

Gr, Gt: receiver and transmitter antenna gain

(=c/f): wave length

Sometime we write path loss in log scale: Lp = 10 log(Pt) – 10log(Pr)

d

cdtftfEd

)]/(2cos[),(

74

Real Antennas

Real antennas are not isotropic radiators Some simple antennas: quarter wave /4 on car

roofs or half wave dipole /2 size of antenna proportional to wavelength for better transmission/receiving

/4/2

Q: Assume frequency 1 Ghz, = ?

Why Not Digital Signal (revisited) Not good for spectrum usage/sharing

The wavelength can be extremely large to build portal devices e.g., T = 1 us -> f=1/T = 1MHz -> wavelength = 3x108/106 = 300m

75

76

Figure for Thought: Real Measurements

77

Receiving power additionally influenced by shadowing (e.g., through a wall or a door)

refraction depending on the density of a medium

reflection at large obstacles scattering at small obstacles diffraction at edges

reflection

scattering

diffraction

shadow fadingrefraction

Signal Propagation

78

Signal Propagation: Scenarios

Details of signal propagation are very complicated

We want to understand the key characteristics that are important to our understanding

79

Shadowing

Signal strength loss after passing through obstacles

Same distance, but different levels of shadowing: It is a random, large-scale effect depending on the environment

Example Shadowing Effects

80

i.e. reduces to ¼ of signal10 log(1/4) = -6.02

81

JTC Indoor Model for PCS: Path Loss

)(10 nLdBLogAL fA: an environment dependent fixed loss factor (dB)

B: the distance dependent loss coefficient,d : separation distance between the base station and mobile terminal, in meters

Lf : a floor penetration loss factor (dB)

n: the number of floors between base station and mobile terminal

Shadowing path loss follows a log-normal distribution (i.e. L is normal distribution) with mean:

82

JTC Model at 1.8 GHz

)(10 nLdBLogAL f

83

Signal can take many different paths between sender and receiver due to reflection, scattering, diffraction

Multipath

84

Example: reflection from the ground or building

Multipath Example: Outdoor

ground

85

Multipath Effect (A Simple Example)

d1d2

1

11 ][2cos

d

tfc

d

ft2cos

2121 22)(2 21dd

c

ddfff c

dcd

2

22 ][2cos

d

tfc

d

phase difference:

Assume transmitter sends out signal cos(2 fc t)

Multipath Effect (A Simple Example)

Suppose at d1-d2 the two waves totally destruct. (what does it mean?)

Q: where are places the two waves construct?

86

integer2121

dd

c

ddf

2121 22

dd

c

ddf

Option 1: Change Location If receiver moves to the right by

/4: d1’ = d1 + /4; d2’ = d2 - /4;

->

87

21

21

21

2

)4/(4/22

''2

dd

dd

dd

By moving a quarter of wavelength, destructiveturns into constructive.Assume f = 1G, how far do we move?

Option 2: Change Frequency

88

Change frequency:

212

1'

dd

cff

2121 22

dd

c

ddf

89

Multipath Delay SpreadRMS: root-mean-square

90

Multipath Effect(moving receiver)

d1d2

1

11 ][2cos

d

tfc

d

ft2cos

example

2

22 ][2cos

d

tfc

d

Suppose d1=r0+vt

d2=2d-r0-vtd1d2

d

Derivation

91

])[sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

])[2sin(])[2sin(2

)sin()sin(2

])[2cos(])[2cos(

0

0

0

0000

020020

00

2

2)2(

22

2

][2][2

2

][2][2

2

cvrd

cvf

cd

cdvtr

cd

cdvtr

cd

cvtrdvtr

cvtrdvtr

tftftftf

cvtrd

cvtr

ttf

ftf

ftf

ftf

tftf

cvtrd

cvtr

cvtrd

cvtr

See http://www.sosmath.com/trig/Trig5/trig5/trig5.html for cos(u)-cos(v)

92

Waveform

v = 65 miles/h, fc = 1 GHz: fc v/c =

10 ms

deep fade

Q: How far does a car drive in ½ of a cycle?

])[sin(])[2sin(2 02cv

rdcvf

cd ttf

109 * 30 / 3x108 = 100 Hz

93

Multipath with Mobility

94

Effect of Small-Scale Fading

no small-scalefading

small-scalefading

95

signal at sender

Multipath Can Spread Delay

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

Time dispersion: signal is dispersed over time

96

JTC Model: Delay Spread

Residential Buildings

97

signal at sender

Multipath Can Cause ISI

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI)

Assume 300 meters delay spread, the arrival time difference is 300/3x108 = 1 ns if symbol rate > 1 Ms/sec, we will have serious ISI

In practice, fractional ISI can already substantially increase loss rate

98

Channel characteristics change over location, time, and frequency

small-scale fading

Large-scalefading

time

power

Summary: Wireless Channels

path loss

log (distance)

Received Signal Power (dB)

frequency

99

Representation of Wireless Channels

Received signal at time m is y[m], hl[m] is the strength of the l-th tap, w[m] is the background noise:

When inter-symbol interference is small:

(also called flat fading channel)

100

Preview: Challenges and Techniques of Wireless Design

Performance affected

Mitigation techniques

Shadow fading(large-scale fading)

Fast fading(small-scale, flat fading)

Delay spread (small-scale fading)

received signal

strength

bit/packet error rate at

deep fade

ISI

use fade margin—increase power or reduce distance

diversity

equalization; spread-spectrum; OFDM; directional

antenna

Backup Slides

101

Received Signal

102

2

2

1

1 )]/(2cos[)]/(2cos[),(

d

cdtf

d

cdtftfEd

c

fd

c

fd 12 22diff phase

d2

d1 receiver

c

ddf )(2 12

103

Multipath Fading with Mobility: A Simple Two-path Example

r(t) = r0 + v t, assume transmitter sends out signal cos(2 fc t)

r0

104

Received Waveform

v = 65 miles/h, fc = 1 GHz: fc v/c = 109 * 30 / 3x108 = 100 Hz

10 ms

Why is fast multipath fading bad?

deep fade

105

Small-Scale Fading

106

signal at sender

Multipath Can Spread Delay

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

Time dispersion: signal is dispersed over time

107

Delay SpreadRMS: root-mean-square

108

signal at sender

Multipath Can Cause ISI

signal at receiver

LOS pulsemultipathpulses

LOS: Line Of Sight

dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI)

Assume 300 meters delay spread, the arrival time difference is 300/3x108 = 1 msif symbol rate > 1 Ms/sec, we will have serious ISI

In practice, fractional ISI can already substantially increase loss rate

109

Channel characteristics change over location, time, and frequency

small-scale fading

Large-scalefading

time

power

Summary: Wireless Channels

path loss

log (distance)

Received Signal Power (dB)

frequency

110

Dipole: Radiation Pattern of a Dipole

http://www.tpub.com/content/neets/14182/index.htmhttp://en.wikipedia.org/wiki/Dipole_antenna

Free Space Signal Propagation

111

1 0 1

t

1 0 1

t

1 0 1

t

at distance d

?

112

Fourier Series: An Alternative Representation

A problem of the expression

contains both cos() and sin(). Using Euler’s formula:

113

Implementing Wireless: From Hardware to Software

114

Making Sense of the Transform

115

Relating the Two Representations