2020/7/18
10
the time varying discrete-time impulse response model for a multipath radio channel
2020/7/18
11
N 1
hb (t,t ) ai (t,t ) exp[ ji (t,t )] (t ti (t)) i0
Local area: no greater than 6m outdoor Local area: no greater than 2m indoor
2020/7/18
14
Parameters of Mobile Multipath Channels
• Time Dispersion Parameters • Coherent bandwidth • Doppler Spread • Coherence Time
•We need a few major parameters for easy –Compare different channels (delay, bandwidth, spectrum, etc) –Develop design guide lines for wireless signals
-If the vehicle is moving directly towards the transmitter
f 26.82 165Hz 0.162
-If the vehicle is moving perpendicular to the angle of arrival of
the transmitted signal
t : time variation due to motion/Doppler shift
t: multipath delay (time-dispersion)
2020/7/18
9
Impulse response of wireless channels (con’t)
• The impulse response of the time-variant multipath channel is a random process
y(t) h(t,t ) x(t) h(t,t )x(t t )dt
or y(t) x(t) h(t,t ) x(t )h(t,t t )dt
2020/7/18
8
h(t, t ) complex passband channel hb (t, t ) complex baseband equivalent channel
•So far, we have channel model –Good: it gives every detail about the channel –Bad: it is hard to see any essential characteristics of channels, such as what signal can pass, what signal can not pass
Are measured by channel sounding techniques Plots of relative received power as a function of excess delay They are found by averaging instantenous power delay measurements over a local area
f 0
2020/7/18
5
Coherence Bandwidth&Coherence Time
2020/7/18
6
Characteristics of Radio Channel
• (Large path loss) • Multipath (reflection, scattering) • Time-variant (time-varying, a consequence of the
(0.1)(1)2
(0.1)(2)2
(0.01)(0)2
21.07s2
[0.010.10.11]
t 21.07(4.38)2 1.37s
2020/7/18
17
Coherence Bandwidth
• Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be consider “flat”(i.e. , a channel which passes all spectral components with approximately equal gain and linear phase)
• Fading[path loss, slow fading, fast fading] (multipath and time-variant)
• Time spread (multipath) • Frequency spread (time-variant)
2020/7/18
7
Impulse response of wireless channels
Where t RMS delay spread
Bc
1
5 t
RMS delay spread (time dispersion parameters) and coherence bandwidth are parameters which describe multipath nature of the radio
surroundings • signals wider than coherence bandwidth of radio
channel
2020/7/18
3
Time-variant multipath channel
2020/7/18
4
Doppler Shift
Example
-Carrier frequency fc = 1850 MHz (i.e. = 16.2 cm) -Vehicle speed v = 60 mph = 26.82 m/s
• The impulse response h(t,t) completely characterizes the channel and is a function of both t and t
• The received signal can be expressed as a convolution of the channel impulse response h(t,t) with the transmitted signal x(t)
• The signal passed through a time-variant multipath channel is a random process
• describe multipath delay as the excess delay, relative to the first arriving multipath component with excess delay t0 = 0
• The mobile channel can be modeled as a linear, time varying filter with impulse response h(t,t), where t is the channel multipath delay for a fixed t.
area
|
hb (t
)
|2
E
N 1
aie ji (t
ti )
2
i0
–It is a function: power~ delay, i.e., the average received power with some delay.
2020/7/18
13
Power Delay Profiles
• Two frequencies separated greater than Bc have different channel response
• If the coherence bandwidth is defined as the bandwidth over which the frequency correlation function is above 0.5, then the coherence bandwidth is approximately
2020/7/18
12
•Such parameters can be derived from channel model
–Specifically, from “power delay profile” of the channel
–Power delay profile is the spatial/time average over a local
Mobile Radio Propagation: Small-Scale Fading and Multipath
2020/7/18
1
2020/7/18
2
Small-Scale fading
Fading (small-scale) is a more rapid fluctuation of signals
2 k
t 2 k ak 2 k P(t k )
k
k
2020/7/18
16
Example
1.37 µs
0 dB
-10 dB
-20 dB
-30 dB 012
t 5 (µs)