1. Wireless PHY: Frequency-Domain Analysis
Y. Richard Yang
09/4/2012

2. Outline
Recap
Frequency domain analysis
Introduction to modulation

3. Recap: Wireless and Mobile Computing
Driven by infrastructure and device technology
global infrastructures
device miniaturization and capabilities
software development platforms
Challenges:
wireless channel: unreliable, open access
mobility
portability
changing environment
heterogeneity

4. Overview of Wireless Physical Layer
source coding
bit
stream
channel coding
analog
signal
sender
modulation
receiver
bit
stream
source decoding
channel decoding
demodulation

5. Wireless Physical Layer Example: Wireless: 802.11

6. Our Objective
Understand key issues and techniques in the design of wireless physical layer
Key approach: identify the problem and then the solution(s).

7. Outline Recap Frequency domain analysis Modulation
Characteristic of wireless channels and potential impacts

8. Fourier Series: Decomposing into a Collection of Harmonics
A periodic real function g(t) on [-π, π] can be decomposed as a set of harmonics (cos, sin):
Time domain 1 1 t t
decomposition
periodical signal
set bk = 0

9. Fourier Analysis

10. Fourier Analysis

11. Fourier Analysis: Example

12. Fourier Series: An Alternative Representation
A problem of the expression
It contains both cos() and sin(), and hence is somehow complex to manipulate.

13. Fourier Series: Using Euler’s formula
Applying Euler’s formula
We have

14. Fourier Series: Using Euler’s formula

15. Making Sense of Complex Numbers
What is the effect of multiplying c by ejπ/2?
What is the effect of multiplying c by j?

16. Making Sense of Complex Numbers

17. Making Sense of Complex Numbers: Conjugate

18. Summary of Progress: Fourier Analysis of Real Function on [-π, π]

19. Defining Decomposition in a General Interval
A periodic function g(t) on [a, a+T] can be decomposed as:

20. Defining Decomsition on [0, 1]

21. ej2πft Making Sense of ej2πft

22. Making Sense of ej2πft G[f]e-j2πft ej2πft ϕ=2πft ϕ=-2πft e-j2πft

23. Two Domain Representations
See examples: spectrum_2in.m
Two representations: time domain; frequency domain
Knowing one can recover the other

24. Example: Frequency Analysis of sine and cosine
See examples: spectrum_2in.m

25. Example: Frequency Analysis of sine and cosine

26. Example: Frequency Domain’s View of Euler’s Formula

27. From Integral to Computation

28. Discrete Domain Analysis
Transforming a sequence of numbers x0, x1, …, xN-1 to another sequence of numbers X0, X1, …, XN-1
Inverse DFFT

30. Frequency Analysis Examples Using GNURadio
spectrum_2sin_plus
FFT Scope
spectrum_1sin_rawfft
Raw FFT
spectrum_2sin_multiply_complex
Multiplication of 2 sines
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

31. Quadrature Mixing spectrum of complex signal x(t)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
spectrum of complex signal x(t)
spectrum of complex signal x(t)ej2f0t
spectrum of complex signal x(t)e-j2f0t

32. Signals at undesirable frequencies
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, …
$22 billion: Amount operators paid the U.S. government over the past ten years for spectrum. Source Burton Group. 1
digital signal t

33. 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
(TDD) 1900
1920, 2020
2025
AMPS ,
TDMA
CDMA
824
849,
869
894
1850
1910,
1930
1990
PDC
810
826,
940
956,
1429
1465,
1477
1513
Cordless
CT1+
885
887, 930
932
CT2
864
868
DECT
1900
PACS
1910, 1930 UB
1910
PHS
1895
1918
JCT
254
380
Wireless
LANs
IEEE
2400
2483
HIPERLAN 2
5150
5350, 5470
5725
902
928 I
EEE
5350, 5725
5825
2471
2497
5250
Others RF
Control
27, 128, 418, 433,
315, 915
426, 868

34. 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

35. Frequencies for Communications
twisted pair
coax cable
optical transmission
1 Mm
300 Hz
10 km
30 kHz
100 m
3 MHz
1 m
300 MHz
10 mm
30 GHz
100 m
3 THz
1 m
300 THz
VLF LF MF HF
VHF
UHF
SHF
EHF
infrared
visible light UV
VLF = Very Low Frequency UHF = Ultra High Frequency
LF = Low Frequency SHF = Super High Frequency
MF = Medium Frequency EHF = Extra High Frequency
HF = High Frequency UV = Ultraviolet Light
VHF = Very High Frequency
Frequency and wave length:
 = c/f
wave length , speed of light c  3x108m/s, frequency f

36. Why Not Send Digital Signal in Wireless Communications?
Transmitter
voice
Antenna: size ~ wavelength
20-20KHz
At 3 KHz,
$22 billion: Amount operators paid the U.S. government over the past ten years for spectrum. Source Burton Group.
Antenna too large!
Use modulation to transfer to higher frequency

37. Basic Concept of Modulation
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

38. Types of Modulation Analog modulation Digital 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)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

39. Example: Amplitude Modulation (AM)
Block diagram
Time domain
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.
Frequency domain

40. Problem: How to Demodulate AM Signal?
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

41. Quadrature Sampling (Software Radio Foundation)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

42. Quadrature Sampling: Upper Path (cos)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

43. Quadrature Sampling: Upper Path (cos)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

44. Quadrature Sampling: Upper Path (cos)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

45. Quadrature Sampling: Lower Path (sin)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

46. Quadrature Sampling: Lower Path (sin)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

47. Quadrature Sampling: Lower Path (sin)
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

48. Quarature Sampling: Putting Together
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

49. Software AM Radio Receiver
Relationship between FFT size N, and sample rate Ns. FFT Xk is for frequency at k * frequency of the N samples N/Ns.

50. Modulation Modulation of digital signals known as Shift Keying
Amplitude Shift Keying (ASK):
Frequency Shift Keying (FSK):
Phase Shift Keying (PSK): 1 t

51. Phase Shift Keying: BPSK
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 I 1

52. Phase Shift Keying: QPSK11 10 00 01 Q I 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

53. Quadrature Amplitude Modulation
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
Example: 16-QAM (4 bits = 1 symbol)
Symbols 0011 and 0001 have the same phase φ, but different amplitude a and 1000 have same amplitude but different phase

54. Exercise Suppose fc = 1 GHz (fc1 = 1 GHz, fc0 = 900 GHz for FSK)
Bit rate is 1 Mbps
Encode one bit at a time
Bit seq:
Q: How does the wave look like for? 11 10 00 01 Q I A t

55. Spectral Density of BPSK
Spectral Density = bit rate width of spectrum used b
fc : freq. of carrier
Rb =Bb = 1/Tb b fc

56. Phase Shift Keying: Comparison
fc: carrier freq.
Rb: freq. of data
10dB = 10; 20dB =100
BPSK A
QPSK t 11 10 00 01

57. Question
Why would any one use BPSK, given higher QAM?

58. Signal Propagation

59. Antennas: Isotropic Radiator
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 z y z
ideal
isotropic
radiator y x x
Q: how does power level decrease as a function of d, the distance
from the transmitter to the receiver?

60. 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(2ft), the received signal is
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)

61. Real Antennas Q: Assume frequency 1 Ghz,  = ?
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,  = ?

62. 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

63. Figure for Thought: Real Measurements

64. Signal Propagation 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
diffraction
reflection
refraction
scattering
shadow fading

65. Signal Propagation: Scenarios
Details of signal propagation are very complicated
We want to understand the key characteristics that are important to our understanding

66. 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

67. Example Shadowing Effects
i.e. reduces to ¼ of signal 10 log(1/4) = -6.02

68. JTC Indoor Model for PCS: Path Loss
Shadowing path loss follows a log-normal distribution (i.e. L is normal distribution) with mean:
A: 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

69. JTC Model at 1.8 GHz

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

71. Multipath Example: Outdoor
Example: reflection from the ground or building
ground

72. Multipath Effect (A Simple Example)
Assume transmitter sends out signal cos(2 fc t) d1 d2
phase difference:

73. 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?

74. Option 1: Change Location
If receiver moves to the right by /4: d1’ = d1 + /4; d2’ = d2 - /4;
->
By moving a quarter of wavelength, destructive turns into constructive.
Assume f = 1G, how far do we move?

75. Option 2: Change Frequency

76. Multipath Delay Spread
RMS: root-mean-square

77. Multipath Effect (moving receiver)
example d d1 d2
Suppose d1=r0+vt
d2=2d-r0-vt
d1d2

78. Derivation
See for cos(u)-cos(v)

79. Waveform v = 65 miles/h, fc = 1 GHz: fc v/c =
109 * 30 / 3x108 = 100 Hz
10 ms
deep fade
Q: How far does a car drive in ½ of a cycle?

80. Multipath with Mobility

81. Effect of Small-Scale Fading
no small-scale
fading

82. Multipath Can Spread Delay
signal at sender
LOS pulse
Time dispersion: signal is dispersed over time
multipath
pulses
signal at receiver
LOS: Line Of Sight

83. JTC Model: Delay Spread
Residential Buildings

84. Multipath Can Cause ISI
Dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI)
Assume 300 meters delay spread, the arrival time difference is /3x108 = 1 ns
if symbol rate > 1 Ms/sec, we will have serious ISI
In practice, fractional ISI can already substantially increase loss rate
signal at sender
LOS pulse
multipath
pulses
signal at receiver
LOS: Line Of Sight

85. Summary: Wireless Channels
Channel characteristics change over location, time, and frequency
Received
Signal
Large-scale
fading
Power
power
(dB)
path loss
log (distance)
time
small-scale fading
signal at receiver
LOS pulse
multipath
pulses
frequency

86. 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)

87. 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
use fade margin—increase power or reduce distance
bit/packet error rate at deep fade
diversity
equalization; spread-spectrum; OFDM; directional antenna
ISI

88. Backup Slides

89. Received Signal d2 d1
receiver

90. Multipath Fading with Mobility: A Simple Two-path Example
r(t) = r0 + v t, assume transmitter sends out signal cos(2 fc t) r0
More detail see page 16 Eqn. (2.13):

91. Received Waveform v = 65 miles/h, fc = 1 GHz:
10 ms
deep fade
v = 65 miles/h, fc = 1 GHz:
fc v/c = 109 * 30 / 3x108 = 100 Hz
Why is fast multipath fading bad?

92. Small-Scale Fading

93. Multipath Can Spread Delay
signal at sender
LOS pulse
Time dispersion: signal is dispersed over time
multipath
pulses
signal at receiver
LOS: Line Of Sight

94. RMS: root-mean-square
Delay Spread
RMS: root-mean-square

95. Multipath Can Cause ISI
dispersed signal can cause interference between “neighbor” symbols, Inter Symbol Interference (ISI)
Assume 300 meters delay spread, the arrival time difference is /3x108 = 1 ms
if symbol rate > 1 Ms/sec, we will have serious ISI
In practice, fractional ISI can already substantially increase loss rate
signal at sender
LOS pulse
multipath
pulses
signal at receiver
LOS: Line Of Sight

96. Summary: Wireless Channels
Channel characteristics change over location, time, and frequency
Received
Signal
Large-scale
fading
Power
power
(dB)
path loss
log (distance)
time
small-scale fading
frequency

97. Dipole: Radiation Pattern of a Dipole

98. Free Space Signal Propagation1 t
at distance d ?

99. Fourier Series: An Alternative Representation
A problem of the expression
contains both cos() and sin().
Using Euler’s formula:

100. Implementing Wireless: From Hardware to Software

101. Making Sense of the Transform

102. Relating the Two Representations