1. Wireless PHY: Modulation and Demodulation
Y. Richard Yang
09/6/2012

2. Outline Admin and recap Frequency domain examples
Basic concepts of modulation
Amplitude modulation
Amplitude demodulation
Digital modulation

3. Admin
First assignment to be posted by this weekend

4. Recap: Why Not Send Digital Signal in Wireless Communications?
Frequency assignment/allocation
Match to antenna characteristics

5. Recap: Modulation Basic concepts the information source (baseband)
carrier
modulated signal

6. Recap: Amplitude Modulation (AM)
Block diagram
Time domain
Frequency domain

7. Recap: Demod of AM
Design option 1: multiply modulated signal by e-jfct
Design option 2: quadrature sampling

8. 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.

9. 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)

10. Remaining Hole: Designing LPF
Frequency domain view
freq B -B
freq B -B

11. zeroing out not want freq
Design Option 1
compute freq
freq B -B
zeroing out not want freq
compute time signal
freq B -B
Problem of Design Option 1?

12. 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 …)

13. FIR Filter
An N-th order FIR filter h is defined by an array of N+1 numbers:
Assume input sequence x0, x1, …,

14. Implementing a 3-rd Order FIR Filter
An array of size N+1 for h
compute y[n]
xn-3
xn-2
xn-1 xn
xn+1 * * * * h3 h2 h1 h0

15. Implementing a 3-rd Order FIR Filter
An array of size N+1 for h
compute y[n+1]
xn-3
xn-2
xn-1 xn
xn+1 * * * * h3 h2 h1 h0

16. Key Question: How to Determine h?
FIR Filter
is also called convolution between x (as a vector) and h (as a vector), denoted as
Key Question: How to Determine h?

17. g*h in the Continuous Time Domain
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];

18. Visualizing g*h
g(t)
time
h(t)

19. Visualizing g*h
g(t)
time t
h(t)

20. Fourier Series of y=g*h

21. In English, you can integrate
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) grid
They give the same result
See

22. Fourier Series of y=g*h

23. Summary of Progress So Far
y = g * h => Y[k] = G[k] H[k] is called the Convolution Theorem, an important theorem.

24. Applying Convolution Theorem to Design LPF
Choose h() so that
H() is close to a rectangle shape
h() has a low order (why?)

25. Applying Convolution Theorem to Design LPF
Choose h() so that
H() is close to a rectangle shape
h() has a low order (why?)

26. Sinc Function
The h() is often related with the sinc(t)=sin(t)/t function f
1/2
-1/2 1

27. Implement filter with given h
FIR Design in Practice
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

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

29. LPF Design Example
#create the channel filter # coefficients chan_taps = optfir.low_pass(
1.0, #Filter gain , #Sample Rate , #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 found chan = gr.freq_xlating_fir_filter_ccf(
1 , # Decimation rate
chan_taps, #coefficients 0, #Offset frequency - could be used to shift
48e3) #incoming sample rate

30. Outline Recap Amplitude demodulation Digital modulation
frequency shifting
low pass filter
Digital modulation

31. Modulation Modulation of digital signals also known as Shift Keying
Amplitude Shift Keying (ASK):
vary carrier amp. according to bit value
Frequency Shift Keying (FSK)
pick carrier freq according to bit value
Phase Shift Keying (PSK): 1 t

32. 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

33. 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

34. 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

35. 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

36. 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?

37. Checking Relationship Among gi()
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)

38. Checking Relationship Among gi()
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.

39. Discussion: How does the Receiver Detect Which gi() is Sent?
Assume synchronized (i.e., the receiver knows the symbol boundary).
This is also called coherent detection

40. Example: Matched Filter Detection
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

41. Computing Coordinates
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

42. Example: Matched Filter => Correlation Detector
received signal

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

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

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

46. Signal Propagation

47. 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?

48. 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)

49. 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,  = ?

50. 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

51. Figure for Thought: Real Measurements

52. 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

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

54. 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

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

56. 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

57. JTC Model at 1.8 GHz

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

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

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

61. 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?

62. 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?

63. Option 2: Change Frequency

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

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

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

67. 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?

68. Multipath with Mobility

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

70. 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

71. JTC Model: Delay Spread
Residential Buildings

72. 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

73. 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

74. 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)

75. 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

76. Backup Slides

77. Received Signal d2 d1
receiver

78. 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):

79. 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?

80. Small-Scale Fading

81. 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

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

83. 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

84. 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

85. Dipole: Radiation Pattern of a Dipole

86. Free Space Signal Propagation1 t
at distance d ?