4. mobile radio propagation. 4. Mobile Radio Propagation 4.1 Small Scale Multipath Propagation 4.2 Impulse Response on a Multipath Channel 4.3 Small Scale Path Measurements 4.3 Frequency Domain Channel Sounding 4.4 Multipath Channel Parameters 4.5 Types of Small Scale Fading
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4. Mobile Radio Propagation
4.1 Small Scale Multipath Propagation
4.2 Impulse Response on a Multipath Channel
4.3 Small Scale Path Measurements
4.3 Frequency Domain Channel Sounding
4.4 Multipath Channel Parameters
4.5 Types of Small Scale Fading
4.6 Rayleigh & Ricean Distributions
4.7 Statistical Models for Multipath Fading Channels
4. Mobile Radio Propagation – Small Scale Fading  Multipath
d1
d0
d2
t0 ≈t1 t2
Fading
Characteristics of Fading
High Mobility: receiver passes through several fades in a short time
Low Mobility: extended time in a deep fade possible
Doppler shift: relative mobility between TX & RX proportional
to direction & velocity
4.1.1: Four Factors of Fading
1
0
0.75

10
0.5
e
e
0.25

20
d
d
PSD (dB)
u
u
t
t
i
i
0
l
l
p
p
m
m
a
a

30

0.25

0.5

40

0.75

0.4

0.2
0
0.2
0.4
2.5
2.5
3.0
3.0
4.0
4.0
4.5
4.5
5.0
5.0
5.5
5.5
6.0
6.0
time
Frequency
0.23ns
1
0
0.75

10
0.5
4.4GHz
0.25

20
PSD (dB)
0

30

0.25

0.5

40

0.75

0.4

0.2
0
0.2
0.4
time
Frequency
(iv) bandwidth of transmitted signal
4.1.2 Doppler shift
S = signal source
v = velocity
d = distance YX on mobiles path of movement
t = d/v
l = dcos1= vtcos 1
if S is far away, assume 1≈ 2
S
l
1
2
X
Y
d
v
phase shift:
=
(4.1)
fd=
(4.2)
Doppler shift = relative frequency change during t
v
S
v
S
h(t)
x(t)
y(t)
4.2 Impulse Response on a Multipath Channel
Organization of 4.2:
(1) Mobile RF Channel Models
(2) Multipath Channels and Delay Spread
(3) Channel’s Power Delay Profile
4.2.1 Bandwidth vs Received Power
(1) wideband pulsed transmitted RF signal, x(t)
(2) Continuous Wave (CW) signal
(1) Mobile RF Channel Models
Channel Classification based only on h(t,) , noise is not considered
h(t,d)
y(d,t)
x(t)
then y(d,t) = x(t) h(d,t) =
(4.3)
if channel is causal (no output until input is applied) then for t < 0 h(d,t) = 0
and y(d,t) =
(4.4)
h(vt,t)
y(t)
x(t)
(4.7)
y(t) =
then y(vt,t) =
(4.6)
1.2 Assume constant v position at any time t is given by
d = vt (4.5)
since v is constant received signal y is just a function of t
y(t) = x(t) h(vt,t) = x(t) h(d,t)
channel model: linear timevarying channel that changes with t & d
y(t) = x(t) h(t,)
(4.8)
=
y(t) is the convolution of input signal & channel impulse
i. Bandpass Channel Impulse Response Model
h(t, )=Re{hb(t, ) exp(jwct)}
x(t)
y(t)
x(t) = channel input or transmitted signal
y(t) = channel output or received signal
h(t,) is equivalently described by its complex baseband impulse
responsehb(t,)
h(t, ) = Re{hb(t, ) exp(jwct) }
c(t) & r(t) are complex envelope representations of x(t) & y(t)
r(t) = c(t) ½ hb(t, )
(4.9)
x(t) = Re{c(t)exp(j2fct)} (4.10)
y(t) = Re{r(t)exp(j2fct)}(4.11)
c(t)
r(t)
½ hb(t, )
ii. Baseband Equivalent Channel Impulse Response Model
Average Power of bandpass signal, x(t) is given by (COU93)
0
1
2
3
4
0
1
2
3
4
All MPCs received in ith bin are represented as one Resolvable MPC with delayi
1
2
D
t
e.g. if = 1ns maximum signal bandwidth limited to 2GHz
hb(t, )
t1
t2
t3
0 1 2 3 4 5 6 7 8 9
t0
t0
t1
t2
t3
t
hb(t, )
t
t3
(t3)
t2
(t2)
t1
(t1)
t0
time
amplitude
(t0)
0 1 2 3 4 … N2 N1
delayedmultipath
components
hb(t,) =
(4.12)
Baseband Impulse Responseof multipath channel:
hb(t,) =
(4.13)
i =constant per excess delay bin
i= constant per excess delay bin
time invariant channel: i has constant amplitude
time variant channel: i has time varying amplitude
r(t) =
h()=
h()=
if
if
r(t)=
r(t)=
Pass Band Channel Models
(3) Channel’s Power Delay Profile(PDP) for smallscale channel model
p(t) (t ) (4.14)
P() k hb(t,)2(4.15)
Received Power Delay Profile (PDP) in a local area given by:
4.2.1 Bandwidth vs Received Power
(1)Wideband pulsed transmitted RF signal, x(t)
(2) Continuous Wave (CW) signal
Tbb
Max
TREP
wideband pulse p(t) will yield output hb(t,)
(1) Consider wideband pulsed transmitted RF signal, x(t)
for 0 t Tbb
p(t)=
p(t) = 0 elsewhere
r(t) =
r(t) =
For all excess delay, i, of interest, assume p(t) is a square pulse with
(4.16)
e.g. excess delay: let MAX = 40ns and Tbb = 10ns
then p(t)=
= 4 for 0 t Tbb,
2
40
/
10
= 0 elsewhere
and
=
=
r(t) =
(4.17)
r(t0)2 =
r(t0)2 =
= 0
and if i j
2.r(t0)2 =
=
=
(4.18)
E, [PWB]
(4.19)
hb(t,) =
r(t) =
(4.20)
r(t)2 =
(4.21)
(4.22)
E [PCW] =
E [PCW]
(4.23)
(4.24)
where rij= path amplitude correlation coefficient defined as:
rij = E[i, j]
(4.25)
average received power over a local area for CW signal is given by:
overbar denotes average CW measurements at a mobile receiver in a local area
In a Smallscale Region, if
and/or rij= 0 then
average received power of CW & wideband signals are equivalent
(1) Narrow Band CW Signal
=7.5cm
fc= 4GHz
10dB
(2) Wideband Pulse, Tbb = 10ns
5 1.25ns (0.375m)
(1/Tbb = 100MHz)
Relative Received Power
0.00 0.25 0.50 0.75 1.00
12 14 16
’s
0 50 100 150 200 250 Excess Delay (ns)
e.g. 4.2: discrete channel impulse response – used to model
(a) Width of Excess Delay Bin = MAX/N
(b) Maximum Bandwidth Accurately represented = 2/
v
1
2
i =
(i) instantaneous power given by:
r(t)2 =
(ii) phase: mobile moves  phase of 2 components changes in opposite
directions
r(t)2 =
spatial interval = v ·t
at t = 0 phase of both components, i= 0 and instantaneous
power given by:
instantaneous power,
r(t)2 =
the phase of each component given by 2vt/
at t = 0.1s
2 = 2(10m/s)(0.1s)/0.3 = 20.94rad = 120o
r(t)2 = 78pW
t
1
2
instantaneous power
r(t)2
phase
i =
0
0o
0o
291pW
0.1
120o
120o
78.2pW
0.2
240o
240o
81.5pW
instantaneous power
r(t)2 =
0.3
360o
360o
291pW
0.4
120o
120o
78.2pW
0.5
240o
240o
81.5pW
1 = 2(10m/s)(t)/0.3
2 = 2(10m/s)(t)/0.3
phase and instantaneous power over interval 0s  0.5s
Average Wideband Received Power
E, [PWB]
= 100pW + 50pW = 150pW