1. CS434/534: Topics in Networked (Networking) Systems Wireless Foundation: Diversity Design for Flat fading Yang (Richard) Yang Computer Science Department Yale University 208A Watson

2. Admin
Start to schedule meetings w/ me on potential projects.

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

4. Recap: QAM as an Example
Quadrature Amplitude Modulation (QAM): combines amplitude and phase modulation, e.g., 16-QAM (4 bits = 1 symbol)
0000
0001
0011
1000 Q I
0010 φ a

5. Reality Check

6. Recap:: How does the Receiver Detect Which gi() is Sent?
Assume synchronized (i.e., the receiver knows the symbol boundary).

7. Recap: General Matched Filter Detection: Implementation for Multiple Sig Func.
Basic idea
consider each gm[0,T] as a point (with coordinates) in a space
compute the coordinate of the received signal x[0,T]
check the distance between gm[0,T] and the received signal x[0,T]
pick m* that gives the lowest distance value

8. Recap: 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

9. Recap: Wireless Channel: Multipath Effect (A Simple Example)
Assume transmitter sends out signal cos(2 fc t) d1 d2
phase difference:
receiver moves to the right by /4, phase diff changes by pi.

10. Recap: Wireless Channel: Multipath Effect (Mover)
example d d1 d2
Suppose d1=r0+vt
d2=2d-r0-vt
d1d2

11. Waveform v = 65 miles/h, fc = 1 GHz: fc v/c =
109 * 30 / 3x108 = 100 Hz
10 ms
deep fade

12. Multipath with Mobility

13. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Basic concepts
Amplitude modulation/demodulation
Digital modulation of additive noise channel
Wireless channels
intro
shadowing
multipath
space, frequency, time deep fade
delay spread

14. Multipath Can Disperse Signal
signal at sender
LOS pulse
Time dispersion: signal is dispersed over time
multipath
pulses
signal at receiver
LOS: Line Of Sight

15. JTC Model: Delay Spread
Residential Buildings

16. Dispersed Signal -> 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 us
if symbol rate > 1 Ms/sec, we will have 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

17. Summary of Progress: 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

18. Roadmap: 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

19. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless design
design for flat fading
how bad is flat fading
diversity to handle flat fading

20. Offline Slides (Begin)

21. Background
For standard Gaussian white noise N(0, 1), Prob. density function:

22. Background

23. Baseline: Additive Gaussian Noise

24. Baseline: Additive Gaussian Noise

25. Baseline: Additive Gaussian Noise
Conditional probability density of y(T), given sender sends 1:
Conditional probability density of y(T), given sender sends 0:

26. Baseline: Additive Gaussian Noise
Demodulation error probability:
assume equal 0 or 1

27. Baseline: Error Probability
Error probability decays exponentially with signal-noise-ratio (SNR).
See A.2.1:

28. Assume h is Gaussian random:
Flat Fading Channel
Assume h is Gaussian random:
BPSK:
For fixed h,
Averaged out over h,
at high SNR.

29. Offline Slides (End)

30. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
design for flat fading

31. Flat Fading Effects
flat fading channel
static channel

32. Main Storyline Today
Communication over a flat fading channel has poor performance due to significant probability that channel is in a deep fade
Reliability is increased by providing more resolvable signal paths that fade independently
Name of the game is how to find and efficiently exploit the paths

33. Where to Find Diversity?
Time: when signal is bad at time t, it may not be bad at t+t
Space: when one position is in deep fade, another position may be not
Frequency: when one frequency is in deep fade (or has large interference), another frequency may be in good shape

34. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
time

35. Time Diversity
Time diversity can be obtained by interleaving and coding over symbols across different coherent time periods
coherence
time
interleave

36. Example: GSM Time Structure
MHz
124 channels (200 kHz)
downlink
frequency
MHz
124 channels (200 kHz)
uplink
time
GSM TDMA frame 1 2 3 4 5 6 7 8
4.615 ms
GSM time-slot (normal burst)
guard
space
guard
space
tail
user data S
Training S
user data
tail
3 bits
57 bits 1
26 bits 1
57 bits 3
546.5 µs
577 µs
S: indicates data or control

37. Example: GSM Bit Assignments
Amount of time diversity limited by delay constraint and how fast channel varies
In GSM, delay constraint is 40 ms (voice)
To get better diversity, needs faster moving vehicles !

38. Simplest Code: Repetition
After interleaving over L coherence time periods,

39. Performance

40. Beyond Repetition Coding
Repetition coding gets full diversity, but sends only one symbol every L symbol times
We can use other codes, e.g. Reed-Solomon code

41. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
Time
space

42. Space Diversity: Antenna
Receive
Transmit
Both

43. User Diversity: Cooperative Diversity
Different users can form a distributed antenna array to help each other in increasing diversity
Interesting characteristics:
users have to exchange information and this consumes bandwidth
broadcast nature of the wireless medium can be exploited
we will revisit the issue later in the course

44. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
Time
Space
frequency

45. Sequential Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum)
Discrete changes of carrier frequency
sequence of frequency changes determined via pseudo random number sequence
used in , GSM, etc
Co-inventor: Hedy Lamarr
patent# 2,292,387 issued on August 11, 1942
intended to make radio-guided torpedoes harder for enemies to detect or jam
used a piano roll to change between 88 frequencies

46. Sequential Frequency Diversity: FHSS (Frequency Hopping Spread Spectrum)
Two versions
slow hopping: several user bits per frequency
fast hopping: several frequencies per user bit tb
user data 1 1 1 t f f1 f2 f3 td
slow
hopping
(3 bits/hop) t td f f1 f2 f3
fast
hopping
(3 hops/bit) t
tb: bit period td: dwell time

47. FHSS: Advantages
Frequency selective fading and interference limited to short period
Simple implementation
what is a major issue in design?
Uses only small portion of spectrum at any time
explores frequency sequentially
used in simple devices such Bluetooth

48. Bluetooth Design Objective
Design objective: a cable replacement technology
1 Mb/s
range 10+ meters
single chip radio + baseband (means digital part)
low power
low price point (target price $5 or lower)

49. Bluetooth Architecture

50. Bluetooth Radio Link Bluetooth shares the same freq. range as 802.11
Radio link is the most expensive part of a communication chip and hence chose simpler FHSS
2.402 GHz + k MHz, k=0, …, 78
1,600 hops per second
A type of FSK modulation
1 Mb/s symbol rate
transmit power: 1mW

51. Bluetooth Physical Layer
Nodes form piconet: one master and upto 7 slaves
Each radio can function as a master or a slave
The slaves follow the pseudorandom jumping sequence of the master
A piconet

52. Piconet Formation
Master hopes at a universal frequency hopping sequence (32 frequencies)
announce the master and sends Inquiry msg
Joining slave:
jump at a much lower speed
after receiving an Inquiry message, wait for a random time, then send a request to the master
The master sends a paging message to the slave to join it

53. Outline Recap Wireless background Frequency domain
Modulation and demodulation
Wireless channels
Wireless PHY design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
Time
Space
Frequency sequential parallel

54. Direct Sequence Spread Spectrum (DSSS)
Basic idea: increase signaling function alternating rate to expand frequency spectrum (explores frequency in parallel)
fc: carrier freq. Rb: freq. of data
10dB = 10; 20dB =100

55. Direct Sequence Spread Spectrum (DSSS)
Approach: One symbol is spread to multiple chips
the number of chips is called the expansion factor tb
user data d(t) 1 -1 X tc
chipping
sequence c(t) -1 1 1 -1 1 -1 1 -1 1 1 -1 1 -1 1 =
resulting
signal -1 1 1 -1 1 -1 1 1 -1 -1 1 -1 1 -1
tb: bit period
tc: chip period

56. DSSS Encoding
chip: -1 1
Data: [ ] -1 1 1 -1

57. DSSS in Real Life 802.11: 11 Mcps; 1 Msps
how may chips per symbol?
WCDMA: 3.84 Mcps; suppose 7,500 sps
how many chips per symbol?

58. Effects of Spreading dP/df f sender dP/df f un-spread signalBb Bs
: num. of bits in the chip * Bb

59. DSSS Encoding/Decoding: An Operating View
spread
spectrum
signal
transmit
signal
user data X
modulator
chipping
sequence
radio
carrier
transmitter
correlator
sampled
sums
products
received
signal
data
demodulator X
low pass
decision
radio
carrier
chipping
sequence
receiver

60. DSSS Decoding chip: Data: [1 -1] inner product: 6 -6 decision: 1 -1 -1
Trans
chips -1 1 1 -1
decoded
chips -1 1 1 -1
Chip seq: -1 1 -1 1
inner product: 6 -6
decision: 1 -1

61. DSSS Decoding with noise
chip: -1 1
Data: [ ]
Trans
chips -1 1 1 -1
decoded
chips -1 -1 1 -1 1 -1 1 -1 -1 -1 1 1
Chip seq: -1 1 -1 1
inner product: 4 -2
decision: 1 -1

62. Assume no DSSS Consider narrowband interference
Consider BPSK with carrier frequency fc
A “worst-case” scenario
data to be sent x(t) = 1
channel fades completely at fc (or a jam signal at fc)
then no data can be recovered

63. Why Does DSSS Work: A Decoding Perspective
Assume BPSK modulation using carrier frequency f :
A: amplitude of signal
f: carrier frequency
x(t): data [+1, -1]
c(t): chipping [+1, -1]
y(t) = A x(t)c(t) cos(2 ft)

64. Add Noise/Jamming/Channel Loss
Assume noise at carrier frequency f:
Received signal: y(t) + w(t)

65. DSSS Decoding (BPSK): Matched Filter
compute correlation for each bit time
bit time
y: received signal
take N samples of a bit time
sum = 0;
for i =0; { sum += y[i] * c[i] * s[i] }
if sum >= 0
return 1;
else
return -1;
c: chipping seq.
s: modulating sinoid

66. DSSS/BPSK Decoding
Properties of chipping sequence to help?

67. Why Does DSSS Work: A Spectrum Perspective
sender
dP/df
dP/df f
ii)
user signal
broadband interference
narrowband interference i) f
receiver
dP/df
dP/df
dP/df
iii)
iv) v) f f f
i) → ii): multiply data x(t) by chipping sequence c(t) spreads the spectrum
ii) → iii): received signal: x(t) c(t) + w(t), where w(t) is noise
iii) → iv): (x(t) c(t) + w(t)) c(t) = x(t) + w(t) c(t)
iv) → v) : low pass filtering

68. Reality Check

69. Backup Slides

70. Inquiry Hopping

71. The Bluetooth Link Establishment Protocol
FS: Frequency Synchronization
The Bluetooth Link Establishment Protocol
DAC: Device Access Code
IAC: Inquiry Access Code

72. Bluetooth Links

73. Bluetooth Packet Format
Header

74. Multiple-Slot Packet