1. Wireless Networks (PHY): Design for Diversity
Y. Richard Yang
9/18/2012

2. Admin
Assignment 1 questions
Assignment 1 office hours

3. Recap: Demodulation of Digital Modulation
Setting
Sender uses M signaling functions g1(t), g2(t), …, gM(t), each has a duration of symbol time T
Each value of a symbol has a corresponding signaling function
The received x maybe corrupted by additive noise
Maximum likelihood demodulation
picks the m with the highest P{x|gm}
For Gaussian noise,

4. Recap: Matched Filter Demodulation/Decoding
Project (by matching filter/correlation) each signaling function to bases
Project received signal x to bases
Compute Euclidean distance
sin(2πfct)
cos(2πfct)
[a01,b01]
[a10,b10]
[a00,b00]
[a11,b11]
[ax,bx]

5. Recap: Wireless Channels
Non-additive effect of distance d on received signaling function
free space
Fluctuations at the same distance

6. Reasons Shadowing Multipath
Same distance, but different levels of shadowing by large objects
It is a random, large-scale effect depending on the environment
Multipath
Signal of same symbol taking multiple paths may interfere constructively and destructively at the receiver
also called small-scale fading

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

8. Multipath Effect (A Simple Example)
Suppose at d1-d2 the two waves totally destruct, i.e.,
if receiver moves to the right by /4:
d1’ = d1 + /4; d2’ = d2 - /4;
constructive
Discussion: how far is /4? What are implications?

9. Multipath Effect (A Simple Example): Change Frequency
Suppose at f the two waves totally destruct, i.e.
If we look at a different frequency f’:
the two waves construct
(d1-d2)/c is called delay spread.
Discussion: how far is ½ c/(d1-d2)?

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

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

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

13. Waveform v = 65 miles/h, fc = 1 GHz: fc v/c =
109 * 30 / 3x108 = 100 Hz
10 ms
deep fade
Q: how far does the car move between two deep fade?

14. Multipath with Mobility

15. Outline Admin and recap Wireless channels Intro Shadowing Multipath
space, frequency, time deep fade
delay spread

16. 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

17. JTC Model: Delay Spread
Residential Buildings

18. 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

19. 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

20. 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)

21. 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
today
bit/packet error rate at deep fade
diversity
equalization; spread-spectrum; OFDM; directional antenna
ISI

22. Outline Recap Wireless channels Physical layer design
design for flat fading
how bad is flat fading?

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

24. Baseline: Previous Additive Gaussian Noise

25. Baseline: Additive Gaussian Noise

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

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

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

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

30. Comparison
flat fading channel
static channel

31. Outline Recap Wireless channels Physical layer design
design for flat fading
how bad is flat fading?
diversity to handle flat fading

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 exploit the added diversity in an efficient manner

33. Diversity
Time: when signal is bad at time t, it may not be bad at t+t
Space: when one position (with d1 and d2) is in deep fade, another position (with d’1 and d’2) 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 channels Physical layer 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
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 !

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

38. Performance

39. 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

40. Outline Recap Wireless channels Physical layer design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
time
space

41. Space Diversity: Antenna
Receive
Transmit
Both

42. 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

43. Outline Recap Wireless channels Physical layer design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
time
space
frequency

44. 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

45. 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

46. FHSS: Advantages
Frequency selective fading and interference limited to short period
Simple implementation
Uses only small portion of spectrum at any time
explores frequency sequentially

47. Direct Sequence Spread Spectrum (DSSS)
One symbol is spread to multiple chips
the number of chips is called the expansion factor
examples
802.11: 11 Mcps; 1 Msps
how may chips per symbol?
IS-95 CDMA: 1.25 Mcps; 4,800 sps
WCDMA: 3.84 Mcps; suppose 7,500 symbols/s
how many chips per symbol?

48. Direct Sequence Spread Spectrum (DSSS)
The increased rate provides frequency diversity (explores frequency in parallel)

49. DSSS
Wider spectrum to reduce frequency selective fading and interference
Provides frequency diversity
un-spread signal
spread signal Bb Bs
: num. of bits in the chip * Bb
dP/df f
sender
dP/df f

50. 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

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

52. DSSS Encoding tb: bit period tc: chip period tb user data d(t) 1 -1 X
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

53. 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

54. 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

55. DSSS Decoding (BPSK): Another View
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

56. Outline Recap Wireless channels Physical layer design
design for flat fading
how bad is flat fading?
diversity to handle flat fading
time
space
frequency
DSSS: why it works?

57. 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

58. 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)

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

60. DSSS/BPSK Decoding

61. 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

62. Backup Slides