Wireless Networks (PHY): Design for Diversity
Y. Richard Yang
9/18/2012
2
Admin
Assignment 1 questions am_usrp_710.dat was sampled at 256K Rational Resampler not Rational Resampler
Base
Assignment 1 office hours Wed 11-12 @ AKW 307A Others to be announced later today
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,
3
Recap: Matched Filter Demodulation/Decoding
Project (by matching filter/correlation) each signaling function to bases
Project received signal x to bases
Compute Euclidean distance, and pick closest
4
sin(2πfct)
cos(2πfct)
[a01,b01]
[a10,b10]
[a00,b00]
[a11,b11]
[ax,bx]
Recap: Wireless Channels
Non-additive effect of distance d on received signaling function free space
Fluctuations at the same distance
5
d
cdtftfEd
)]/(2cos[),(
Recap: Reasons
Shadowing 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
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7
Multipath Effect (A Simple Example)
d1d2
1
11 ][2cos
d
tfcd
ft2cos
2121 22)(2 21dd
c
ddfff c
dcd
2
22 ][2cos
d
tfcd
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, i.e.,
if receiver moves to the right by /4: d1’ = d1 + /4; d2’ = d2 - /4;
8
integer2121
dd
c
ddf
2121 22
dd
c
ddf
constructive
Discussion: how far is /4? What are implications?
Multipath Effect (A Simple Example): Change Frequency
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Suppose at f the two waves totally destruct, i.e.
Smallest change to f for total construct:
(d1-d2)/c is called delay spread.
2121 22
dd
c
ddf
integer2121
dd
c
ddf
10
Multipath Delay SpreadRMS: root-mean-square
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Multipath Effect(moving receiver)
d1d2
1
11 ][2cos
d
tfcd
ft2cos
example
2
22 ][2cos
d
tfcd
Suppose d1=r0+vt
d2=2d-r0-vtd1d2
d
Derivation
12
])[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)
Derivation
13
])[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)
Derivation
14
])[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)
Derivation
15
])[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)
Derivation
16
])[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)
Derivation
17
])[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)
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Waveform
v = 65 miles/h, fc = 1 GHz: fc v/c =
10 ms
deep fade
])[sin(])[2sin(2 02cvrd
cvf
cd ttf
109 * 30 / 3x108 = 100 Hz
Q: how far does the car move between two deep fade?
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Multipath with Mobility
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Outline
Admin and recap Wireless channels
Intro Shadowing Multipath
• space, frequency, time deep fade• delay spread
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signal at sender
Multipath Can Disperse Signal
signal at receiver
LOS pulsemultipathpulses
LOS: Line Of Sight
Time dispersion: signal is dispersed over time
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JTC Model: Delay Spread
Residential Buildings
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signal at sender
Dispersed Signal -> 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 us if symbol rate > 1 Ms/sec, we will have ISI
In practice, fractional ISI can already substantially increase loss rate
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Channel characteristics change over location, time, and frequency
small-scale fading
Large-scalefading
time
power
Summary of Progress: Wireless Channels
path loss
log (distance)
Received Signal Power (dB)
frequency
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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)
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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
today
27
Outline
Recap Wireless channels Physical layer design
design for flat fading• how bad is flat fading?
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Background
For standard Gaussian white noise N(0, 1), Prob. density function: 2
2
21)(
w
ewf
2/2/121
22
)()1( xxx exQe
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Background
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Baseline: Additive Gaussian Noise
N(0, N0/2) =
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Baseline: Additive Gaussian Noise
Baseline: Additive Gaussian Noise
Conditional probability density of y(T), given sender sends 1:
Conditional probability density of y(T), given sender sends 0:
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Baseline: Additive Gaussian Noise
Demodulation error probability:
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assume equal 0 or 1
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Baseline: Error Probability
Error probability decays exponentially with signal-noise-ratio (SNR).
See A.2.1: http://www.eecs.berkeley.edu/~dtse/Chapters_PDF/Fundamentals_Wireless_Communication_AppendixA.pdf
2/2/121
22
)()1( xxx exQe
35
Flat Fading Channel
BPSK:
For fixed h,
Averaged out over h,
at high SNR.
Assume h is Gaussian random:
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Comparison
static channel
flat fading channel
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