Multipath fading and reflections

1
Multipath fading and reflections
The signal takes many paths to the destination.
The propagation delay along each path is
different. How many meters difference gives you
0.00001 seconds of delay difference?
2
Effects of Multipath Fading/Reflection

• Ghost on TV.
• GPS incorrect position calculation.
• Frequency Selective Fading.
• Intersymbol interference.

3
Intersymbol Interference
Suppose that there are two paths. The shorter
path has length d1, the longer path has length
d2. What is the difference in propagation delay
between the two paths?
2
Symbols received over the shorter path
3
1
0
How big does ? have to be to so that the 3 of the
longer path arrives exactly when the 0 arrives on
the shorter path? How big must the difference in
paths be for this to happen?
2
3
Symbols received over the longer path
?
1
0
Received signal a combination of the two signals
4
Intersymbol Interference
Suppose we use differential phase shift keying to
transmit 3 2 1 0
3
2
1
0
?
5
Intersymbol Interference
6
Phasor addition of sine waves with the same
frequency
x
a
?
?
b
x (b cos(?)acos(?) , b sin(?)asin(?))

M
A
7
(No Transcript)
8
zero amplitude!
9
Intersymbol Interference

• ISI can be avoided by making the baud rate small.
• If the baud rate is 11MHz (802.11b), how much
  delay will cause complete ISI interference?
• How much path length difference will cause
  complete ISI interference?
• In suburban areas, multiple signals arrive with
  timing differences up to 25microsec.
• Indoors, timing differences up to 300ns.
• What is the max baud rate so that complete ISI
  occurs

10
Frequency Selective Fading
The received signal is made up of many different,
slightly delayed, versions of the same signal.
What is going on at these frequencies?
11
Frequency Selective Fading
Phase is ok, but zero amplitude!
For what values of T/R does this happen?
12
Frequency Selective Fading
Indoor impulse responds
13
Frequency Selective Fading
delay 1/(2fc)
Suppose fc 2.4GHz. Delay 0.2 ns Distance
0.2ns 0.3m/ns 0.06m (6cm)!!!!

• So very small differences in path length cause
  very big changes in signal.
• Frequency selective fading is be mitigated by
• Using spread spectrum. Thus multiple frequencies
  are simultaneously used. If a few frequencies
  suffer attenuation the others might not. (Used in
  802.11b)
• Channel estimation and adaptation (used in GSM
  cell phones)
• Use many narrow band frequencies. Then the good
  ones should work (like spread spectrum). Used in
  802.11a

14
Frequency Selective Fading
Now suppose that there are many paths, each with
a different delay. Then the received signal is
Q
The I component is modeled as a normally
distributed random variable. The Q component is
modeled as a normally distributed random
variable. Both have zero mean and the same
variance. Then, the amplitude is a Raleigh
random variable and the phase is uniform between
0 and 2?. This is called a Raleigh channel.
I
received signal
Hence, the result is that the amplitude and phase
are random. If they vary slowly, then the
channel is called a slowly fading channel
(indoors). If the channel varies quickly, it is a
fast fading channel (driving with cell phone). If
the channel changes too fast, then changes in
phase and amplitude cannot be detected.
15
Effect of Movement
If the receiver or transmitter are moving, then
the channel will vary. Hence, the I and Q
components will vary with time.
Here is a plot of the magnitude of fading as a
function of time and frequency. In this case,
the channel does not change much over time. It is
a slowly fading channel.
16
Effect of Movement
If the receiver or transmitter are moving, then
the channel will vary. Hence, the I and Q
components will vary with time.
Here is a plot of the magnitude of fading as a
function of time and frequency. In this case,
the channel does not vary with frequency, it only
varies over time.
17
Effect of Movement
If the receiver or transmitter are moving, then
the channel will vary. Hence, the I and Q
components will vary with time.
Here is a plot of the magnitude of fading as a
function of time and frequency. In this case,
the channel varies both in time and frequency.
18
Doppler Effect

• When the receiver or transmitter are moving, the
  frequency is shifted by ?f v/? cos(?), v is
  velocity and ? is wave length

?
c is the speed of light.
If the the signal is sent at fc and passed
through a fading channel, the spectrum of the
received signal is
Thus, not only one frequency is received, but
many.
19
Doppler Effect

• To mitigate the Doppler effect
• Use low frequencies
• Transmit in bursts so the channel is constant
  during the burst.
• Include training sequences on each frame so the
  channel can be re-estimated for each
  transmission.
• Do move indoor use only

20
Rician Channel Model

• A Raleigh channel assumes that all the paths
  arrive with random amplitude.
• A Rician channel assumes that there is a line of
  sight component that has much larger amplitude.