Transcript partIV-p2

Mobile Communications
Part IV- Propagation Characteristics
Multi-path Propagation - Fading
Professor Z Ghassemlooy
School of Computing, Engineering and
Information Sciences, University of Northumbria
U.K.
http://soe.unn.ac.uk/ocr
Z. Ghassemlooy
Contents




Fading
Doppler Shift
Dispersion
Summary
Z. Ghassemlooy
Fading
Is due to multipath propagation.
With respect to a stationary base station, multipath
propagation creates a stochastic standing wave pattern,
through which the mobile station moves.
Caused by shadowing:
when the propagation environment is changing
significantly, but this fading is typically much slower than
the multipath fading.
Modem design is affected mainly by the faster
multipath fading, which can be normally assumed to
be locally wide-sense stationary (WSS).
Z. Ghassemlooy
Multipath Propagation - Fading
a
b
Diffracted
wave
a
b
Antenna
y=a+b
a & b are in phase
Z. Ghassemlooy
No direct path
Reflected
wave
a
b
Antenna
y=0
a & b are out of phase by 
Complete fading when
2d/ = n, d is the path difference
Multipath Propagation - contd.
• For a stationary mobile unit with no direct path, the
received signal can be expressed as a sum of delayed
components or in terms of phasor notation:
N
Pulse train
S r t    ai Pt  ti 
i 1
N
A single pulse
S r (t )   ai cos(2f c  i )
i 1
Where: ai is the amplitude of the scattered signal,
p(t) is the transmitted signal (pulse) shape,
ti is the time taken by the pulse to reach the receiver,
N is the number of different paths
fc is the carrier frequency
Z. Ghassemlooy
Fading - Types
Signal strength relative to 1uV (db)
• Slow (Long) Term
•Fast (Short) Term (Also known as Rayleigh fading)
30
Fast fading
20
10
Slow fading
0
0
5
10
15
20
25 Distance ()
Exact representation of fading characteristics is not possible,
because of infinite number of situation.
Z. Ghassemlooy
Fading - Slow (Long) Term
 Slower variation in mean signal strength (distance 12 km)
 Produced by movement over much longer distances
 Caused by:
- Terrain configuration (hill, flat area etc.):
Results in local mean (long term fading) attenuation
and fluctuation.
- The built environment (rural and urban areas etc.),
between base station and the mobile unit:
Results in local mean attenuation
Z. Ghassemlooy
Fading - Slow (Long) Term
Receiver
tn,2
tn,3
path n
Sr(t)
tn,1
tk,4
Transmitter
tk,1
tk,2
one
subpath
tk,3
path k
Number of path
N
S r t    ai P0 t  ti 
i 1
path attenuation factor
for the ith path
Z. Ghassemlooy
C. D. Charalambous et al
Fading- Fast (Short) Term
 Describes the constant amplitude fluctuations in the received
signal as the mobile moves.
 Caused by
- multipath reflection of transmitted signal by local scatters
(houses, building etc.)
- random fluctuations in the received power
 Observed over distances = /2
 Signal variation up to 30 dB.
 Is a frequency selective phenomenon.
 Can be described using
- Rayleigh statistics, (no line of sight).
- Rician statistics, (line of sight).
Z. Ghassemlooy
Fading- Fast (Short) Term - contd.
A received signal amplitude is given as the sum of delayed
components. In terms of phasor notation it is given as:
N
S r (t )   ai cos(2f c  i )
i 1
Or
N
N
i 1
i 1
S r (t )  cos(2f ct )  ai cos(i )  sin(2f ct )  ai sin(i )
In-phase
Z. Ghassemlooy
Quadrature
Fading- Fast (Short) Term - contd.
The phase i can be assumed to be uniformly distributed in
the range (0, 2), provided the locations of buildings etc. are
completely random.
For a large N, the amplitude of the received signal is:
Sr (t )  X cos(2f ct )  Y sin(2f ct )
where
N
N
i 1
i 1
X   ai cos(i ), Y   ai sin(i )
X and Y are independent, identically distributed Gaussian random
variables.
Z. Ghassemlooy
Fading- Fast (Short) Term - contd.
The envelope of the received signal is:
A  (X Y )
2
2 0.5
Which will be Rayleigh distributed:
Assuming all components received
have approximately the same power
and that all are resulting from scattering.
Rayleigh
Probability
density
function
Exponential
A or power P
Z. Ghassemlooy
æ r2 ö
÷
pr   2 exp çç 
2 ÷
s
è 2s ø
r
Where 0< r < , s2 is
variance of A (the total received
power in the multipath signal).
Ricean Fading
If there is one direct component in addition to scattered
components, the envelope received multipath is Ricean,
where the impulse response has a non zero mean.
Ricean distribution = Rayleigh signal + direct line of sight
signal. The distribution is:
æ r 2  s 2 ö æ rs ö
÷I
pr   2 exp çç 
2 ÷ 0ç
2 ÷
s
è 2s ø è s ø
r
s2 is the power of the line of sight signal and I0 is a Bessel function of
the first kind
Z. Ghassemlooy
Fading- Fast (Short) Term - contd.
 The probability that the realization of the random
variable has a value smaller than x is defined by
the cumulative distribution function:
cdf (r )   pdf (u )du
 Applying it to the Rayleigh distribution
cdf (r )  1  exp (r 2 / 2s2 )
 For small r
cdf (r ) ~ r 2 / 2s2
Z. Ghassemlooy
Fast Fading – Cases 1: Stationary Mobile
6
v
1
t6
t2
Stationary
2
t4
t3
3
Z. Ghassemlooy
4
v
t5
Field strength
t1
5
t
Fast Fading – Cases 1
 The number of fading depends on:
– Traffic flow
– Distance between the mobile and moving cars
 The received signal at the MU is:
N
S r t    ai P0 t  ti 
i 1
ti  t ti
Z. Ghassemlooy
Fast Fading – Cases 1
where 
ti
and
Thus
envelope
Z. Ghassemlooy
is additional relative delay (positive or negative)
1
t
N
N
t
i 1
i
Sr t   x(t  t) e
 
j 2 f c t  t  jo
N
 j 2 f c ti 
xt   ao  ai e

 i 1

Fast Fading – Cases 2
T1 = d1/c
T2 = d2/c
t1(t1)
t2(t2)
S t   xt exp  jc exp  jct 
N
xt    ac ai t  exp  jc ti t 
i 1
18
No scattered signals

V
Field strength
Fast Fading – Cases 3: Non-stationary
Mobile
Signal level
t
The received signal at the mobile is:
sr (t )  aoe
j ( 2 f c o x cos )
Amplitude
Wave number =2/
Transmitting frequency
Z. Ghassemlooy
x = Vt
Fast Fading – Cases 3: Doppler Frequency
A moving object causes the frequency of a received wave to
change
Substituting for  and x, the expression for the received signal is
sr (t )  aoe
The Doppler
frequency
The received
signal frequency
Z. Ghassemlooy
fD
V
j 2 ( f c  cos ) t

V
 cos   f m cos 

f r  f c  f m cos
Fast Fading – Cases 3: Doppler Frequency
• When  = 0o (mobile moving away from the transmitter)
fr  fc  fm
• When  = 90o (I.e. mobile circling around)
fr  fc
• When  = 180o (mobile moving towards the transmitter)
fr  fc  fm
Z. Ghassemlooy
Fast Fading – Cases 4: Moving MU +
Stationary Scatterer
Voltage
Standing Wave Pattern
x(t)
so(t)
MU
t=0
Z. Ghassemlooy
V
so(t)
t = round trip time
Fast Fading – Cases 4
Received signal at the MU:
sr (t )  ao e
j  2 f c t  o Vt cos  
and for q = 0
sr (t )  ao e
j  2 f c t  o Vt 
 ao e
Incident signal
j  2 f c t  o Vt  2 f c t 
Reflected signal
2f c t ö j 2 f ct o f c t 
æ
sr (t )   j 2ao sin ç Vt 
÷e
2 ø
è
Fading with zero amplitude occurs when
Z. Ghassemlooy
Vt  n  f c t
Fast Fading – Cases 5: Moving MU and
Scatterers
The resultant received signal is the sum of all the scattered
waves from different angles qi depending upon the momentary
attitude of the various scatterers.
N
sr (t )   ao ai e
i 1
Z. Ghassemlooy
j  2 f c t  o Vt cos i  i 
Channel Fading Effects
Transmitting a short pulse over a
(i) frequency-selective (time-spread) fading channel:
Transmitted
Received
t
Tp
t
Tp + dt
(ii) time-selective (Doppler-spread) fading channel:
Transmitted
Received
t
Tp
Z. Ghassemlooy
t
Tp
Effects of Doppler shifts
 Bandwidth of the signal could increase or decrease leading to
poor and/or missed reception.
 The effect in time is coherence time variation and signal
distortion
– Coherence time: Time duration over which channel impulse response is
invariant, and in which two signals have strong potential for amplitude
correlation
– Coherence time is expressed by:
9
Tc 
2
16f D-max
– where fD-max is the maximum Doppler shift, which occurs when  = 0 degrees
 To avoid distortion due to motion in the channel, the symbol
rate must be greater than the inverse of coherence time.
Z. Ghassemlooy
Coherence Distance
 Coherence distance is the minimum distance
between points in space for which the signals are
mostly uncorrelated.
 This distance is usually grater than 0.5
wavelengths, depending on antenna beamwidth
and angle of arrival distribution.
 At the BTS, it is common practice to use spacing
of about 10 and 20 wavelengths for low-medium
and high antenna heights, respectively (120o
sector antennas).
Z. Ghassemlooy
Coherence Bandwidth (Bc)
 Range of frequency over which channel is “flat”
 It is the bandwidth over which two frequencies have a
strong potential for amplitude correlation
Power
Signal bandwidth Bs
Describes frequency selective
phenomenon of fast fading
Coherence
Bandwidth Bc
Freq.
Effect of frequency selective fading on the received signal spectrum
Z. Ghassemlooy
Estimation of Coherence Bandwidth
Coherence bandwidth is estimated using the value of delay
spread of the channel, st
Bc 
For correlation > 0.9
For correlation > 0.5
Bc 
0.2
tt
0.02
tt
Delay spread figures
Delay in
at 900 MHz
microseconds
Urban
1.3
Urban, worst-case
10 - 25
spreads for various types
Suburban, typical
0.2 - 0.31
Suburban, extreme
1.96 - 2.11
of terrain:
Indoor, maximum
0.27
Typical values of delay
Delay Spread at 1900 MHz
Buildings, average
0.07 - 0.094
Buildings, worst -
1.47
case
Z. Ghassemlooy
Channel Classification
Based on Time-Spreading
Flat Fading
Frequency Selective
1. BS < BC  Tm < Ts
2. Rayleigh, Ricean distrib.
3. Spectral chara. of transmitted
signal preserved
1. BS > BC  Tm > Ts
2. Intersymbol Interference
3. Spectral chara. of transmitted
signal not preserved
4. Multipath components resolved
Channel
Channel
Signal
Signal
BC
Z. Ghassemlooy
BS
freq.
BS
BC
freq.
C. D. Charalambous et al
Fading in Digital Mobile Communications
• If Bs>> Bc, then a notch appears in the spectrum. Thus
resulting in inter-symbol interference (ISI).
- To overcome this, an adaptive equaliser (AE) with
inverse response may be used at the receiver.
Training sequences are transmitted to update AE.
• If Bs<< Bc, then flat fading occurs, resulting in a
burst of error.
- Error correction coding is used to overcome this
problem.
Z. Ghassemlooy
Multipath Delay Spread
 First-arrival delay (τA)
 Mean excess delay
Z. Ghassemlooy
t e   (t  t A ) P (t )dt
Multipath Delay Spread
 The standard deviation of the distribution of multipath signal
amplitudes is called delay spread. For directive antenna is
characterized by the rms delay spread of the entire delay
profile, which is defined as:
2
t rms
  Pjt 2j  (t avg )2
j
where
tavg = Σj Pj t j ,
t j is the delay of the j th delay component of the profile
Pj = (power in the j th delay component) / (total power in all components
• Delay spread varies with the terrain with typical values for rural, urban and
suburban areas:
 3.0 ms urban 
 0.5ms suburban 
 0.2 ms rural 
Z. Ghassemlooy
Multipath Delay Spread - Dispersion
 The delay spread limits the maximum data rate:
– No new impulses should arrive at the receiver before the last
replica of the pervious impulse has perished.
– Otherwise symbol spreads (dispersion) into its adjacent slot, thus
resulting in Inter Symbol Interference (ISI)
Transmitted
symbols
Received
symbols
 The signal arrived at the receiver directly and phase shifted
– Distorted signal depending on the phases of the different parts
Z. Ghassemlooy
Mitigation Techniques for the Multipath
Fading Channel
 Space diversity –
– Signals at the same frequency using two or three antennas located
several wavelengths a part.
– Antennas are connected to two or three radio receivers.
– The receiver will the strongest signal is elected
– Disadvantage: Uses two or more antennas, therefore the
need for a large site.
 Frequency diversity –
– Signals at different frequencies received by the same antenna
very rarely fade simultaneously. Thus the use of several carrier
frequencies or the use of a wideband signal to combat fading.
– A single aerial connected to a number receiver, each tuned to a
different frequency, whose outputs are connected in parallel.
The receiver with the strongest instantaneous signal will provide
the output.
– Disadvantage: Uses two or more frequencies to transmit
the same signal.
Z. Ghassemlooy
Mitigation Techniques for the Multipath
Fading Channel
 Time diversity – Spread out the effects of errors
through interleaving and coding
 Multipath diversity
– Consider the tapped delay line model of a channel
shown previously
– If multipaths can be put together coherently at the
receiver, diversity improvement results
– This is what the RAKE receiver does (see next
viewgraph)
Z. Ghassemlooy
RAKE Multipath Signal Processing
R.E. Ziemer 2002
Z. Ghassemlooy
System Design and Performance
Prediction
 Base station placement dependent on
–
–
–
–
–
Propagation environment
Anticipated geographic distribution of users
Economic considerations (minimize number of base stations)
Political and public opinion considerations
Traffic types (3G)
 Performance figure of merit
– Spectrum efficiency for voice: ηv voice circuits/MHz/base station
– Spectrum efficiency for information: ηi bps/MHz/base station
– Dropped call rate – fraction of calls ended prematurely
Z. Ghassemlooy
Summary
• The random fluctuations in the received power are due to
fading.
• If there is a relative motion between transmitter and receiver
(mobile) the result is Doppler shift
• If maximum Doppler shift is less than the data rate, there
is “slow” fading channel.
• If maximum Doppler shift is larger than the data rate, there
is “fast” fading channel.
Z. Ghassemlooy
Questions and Answers
 Tell me what you think about this lecture
– [email protected]
 Next lecture: Modulation Techniques
Z. Ghassemlooy