✬ ✫ ✩ ✪ School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk, c L.-L. Yang 1/ 46 Wireless Channel Modeling - An Overview - Lie-Liang Yang Communications Research Group School of Electronics and Computer Science, University of Southampton, SO17 1BJ, UK. Tel: +44 23 8059 3364, Fax: +44 23 8059 4508 Email: [email protected]http://www-mobile.ecs.soton.ac.uk ✬ ✫ ✩ ✪ School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk, c L.-L. Yang 2/ 46 Summary ❐ Narrow-band wireless channels; ✓ Propagation path-loss; ✓ Shadowing slow fading; ✓ Fast fading; ✓ Power-budget design in wireless communications systems. ❐ Wideband (frequency-selective) fading channels; ❐ (Time-selective) fast fading channels; ❐ Wideband (time-frequency-selective) fast fading channels; ❐ Ultrawide bandwidth (UWB) channels. ✬ ✫ ✩ ✪ School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk, c L.-L. Yang 3/ 46 Factors Affecting Wireless Signal Transmission ✔ Propagation path-loss: The strength of radio wave decreases as the distance between the transmitter and receiver increases; ✔ Reflection: When a radio wave propagating in one medium impinges upon another medium having different electrical properties, the wave is partially reflected and partially transmitted; ✔ Diffraction : Radio wave bends when it passes around an edge or through a slit. This bending is called diffraction; ✔ Scattering: When a radio wave impinges on a rough surface, the reflected energy is spread out (diffused) in all directions due to scattering; ✔ Doppler effect: When radio wave travels between two objects, the wavelength changes if one or both of them are moving. The Doppler effect is observed whenever the source of waves is moving with respect to an observer. ✬ ✫ ✩ ✪ School of ECS, Univ. of Southampton, UK. http://www-mobile.ecs.soton.ac.uk, c L.-L. Yang 4/ 46 Propagation Path-Loss - Free Space Propagation ✔ The free space propagation model is usually used to predict received signal strength, when the transmitter and receiver have a clear, unobstructed line-of-sight (LoS) path between them. ✔ In free-space propagation environments the received signal power decays with the square of the propagation path length, and the received signal power can be expressed as P r (d) = 10 log 10 " P t G T G R λ 4πd 2 # dBm (dBW) (1) where P t ,P r (d): transmitted and received power, G T ,G R : antenna gains, d: distance between the transmitter and receiver, and λ: wavelength of the radio signal.
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Propagation path-loss: The strength of radio wave decreases as the distancebetween the transmitter and receiver increases;
Reflection: When a radio wave propagating in one medium impinges uponanother medium having different electrical properties, the wave is partiallyreflected and partially transmitted;
Diffraction : Radio wave bends when it passes around an edge or through aslit. This bending is called diffraction;
Scattering: When a radio wave impinges on a rough surface, the reflectedenergy is spread out (diffused) in all directions due to scattering;
Doppler effect: When radio wave travels between two objects, the wavelengthchanges if one or both of them are moving. The Doppler effect is observedwhenever the source of waves is moving with respect to an observer.
The free space propagation model is usually used to predictreceived signal strength, when the transmitter and receiver havea clear, unobstructed line-of-sight (LoS) path between them.
In free-space propagation environments the received signalpower decays with the square of the propagation path length,and the received signal power can be expressed as
Pr(d) = 10 log10
[
PtGT GR
(
λ
4πd
)2]
dBm (dBW) (1)
where Pt, Pr(d): transmitted and received power, GT , GR:antenna gains, d: distance between the transmitter and receiver,and λ: wavelength of the radio signal.
Shadowing slow fading is mainly caused by terrain andtopographical features in the vicinity of the mobile receiver, suchas small hills and tall buildings;
In slow-fading analysis, the effects of both fast-fading andpath-loss must be removed;
Local-mean: The fast fading is removed by deriving the so-calledlocal-mean, which is obtained by averaging the signal level overa distance of typically some 20 wavelengths.
Fast fading is also referred to as small-scale fading, which accountsfor the rapid variation of signal levels, when the user terminal moveswithin a small or local area. There are many physical factors in theradio propagation channel, which result in fast fading, whichtypically include
Multipath propagation;
Doppler effect;
Carrier-frequency, bandwidth and symbol rate of the transmittedsignal, etc.
Figure 3: Illustration of multipath propagation of radio signals, where the receivedsignal at the MS consists of N multipath signals generated by the reflecting objectsaround the mobile terminal.
Narrowband - Fast Fading Consider the transmission of a narrowband signal, which is
expressed as
s(t) = <s(t) exp (j2πfct) (3)
where <x denotes the real part of x, s(t) is the complexbaseband signal depending on the specific baseband modu-lation scheme employed, fc represents the carrier-frequency.
Due to multipath propagations and Doppler frequency shifts,the received signal can be expressed as
Figure 5: Envelope distributions of a Rayleigh fading channel, when assumingthat the normalized Doppler frequency shift is fDT = 0.1, where T represents thesampling spacing.
Rayleigh fading channels belong to a class of channels,where the received envelopes of faded signals obey Rayleighdistribution;
Rayleigh distribution is commonly employed for describingthe statistical time varying nature of the received envelope inisotropic scattering environments, where exists no LoS prop-agation path between the transmitter and the receiver;
Fast Fading - Rician Fading Rician distribution is commonly used for describing the statistical time
varying nature of the received envelope, when a signal is transmitted overan environment, where, in addition to many reflecting objects around thereceiver, exists a LoS propagation route between the transmitter and thereceiver;
It can also be used for describing the envelope distribution of the receivedsignal, when it contains a dominant non-faded component, although thisdominant component is not the LoS one;
The Rician PDF is given by
pα(t)(y) =2(K + 1)y
Ωexp
[
−K − (K + 1)y2
Ω
]
I0
(
2y
√
K(K + 1)
Ω
)
(11)
where K represents the ratio of the power in the specular component andthat in the scattering components of the received signal.
Nakagami-m distribution is a generalized distribution, whichoften gives the best fit to land-mobile and indoor-mobile mul-tipath propagation environments;
A good fit to these widely varying propagation scenarios isachieved by varying single parameter of m in the Nakagami-m distribution;
Nakagami-m distribution offers features of analytical conve-nience, which makes it possible to evaluate wireless sys-tem’s performance by using both analytical and numerical ap-proaches.
For narrowband signal, the signal bandwidth, say Ws, is sufficiently smallin comparison with the coherence bandwidth (∆f)c = 1/Tm of the corre-sponding wireless channel, i.e., Ws/(∆f)c = WsTm << 1;
Narrowband channel belongs to flat fading channels, where all the fre-quency components of the transmitted signal behave similarly;
For wideband signal, the signal bandwidth, Ws, may be significantly higherthan the coherence bandwidth (∆f)c = 1/Tm of the corresponding wire-less channel, i.e., Ws/(∆f)c = WsTm >> 1;
Consequently, two frequency components separated by a frequency ofthe coherence bandwidth or beyond may behave significantly differently;
Hence, wideband channels are typically frequency-selective fading chan-nels.
Envelope Correlation as A Function ofFrequency Separation
Assume Nakagami fading channels. Then, when the excessdelay-spread obeys the exponential distribution, it can be shownthat the correlation coefficient as a function of the frequency sep-aration ∆f = fv − fu, for the envelopes at fu and fv, can beexpressed as
ρE(∆f) ≈ Γ2(
m + 12
)
4m[
mΓ2(m) − Γ2(
m + 12
)]
1
1 + σ2τ (2π∆f)2
(13)
where στ represents the mean value of the excess delay spread.
Figure 11: Illustration of the envelope correlation coefficient of (13), when theexcess delay-spread of the channel obeys the exponential distribution.
Let the transmitted signal be a narrowband signal with thesymbol duration Ts, and the coherence time of the channel be(∆t)c;
When (∆t)c > Ts resulting in 2fDTs < 1, the fading amplitudewithin one symbol duration is highly correlated or simply thesame. This type of fading process is referred to as time non-selective fading or slow fading;
When (∆t)c < Ts resulting in 2fDTs > 1, the front and rearparts of a given symbol may experience independent fading.Correspondingly, a fading process having this characteristicsis referred to as time-selective fading or fast fading.
In practice, a wireless channel may simultaneously satisfy thefrequency-selective fading condition of WsTm > 1 and thetime-selective fading condition of 2fDTs > 1;
In this case, a signal transmitted over this type of wirelesschannels experiences both frequency-selective fading andtime-selective fading;
This type of channels is classified as time-frequency-selectivefading channels.
Figure 15: Illustration of the time-frequency selectivity of a 10-path wireless chan-nel associated with the normalized Doppler frequency spread of fDT = 0.02.
Envelope Correlation as A Function ofTime-Frequency Separations
Assuming Nakagami fading channels and that the excessdelay-spread obey the exponential distribution with the pa-rameter of στ , then, the envelope correlation coefficient as afunction of ∆f and ∆t can be expressed as
Ultrawide Bandwidth (UWB) Systems -Characteristics
UWB characterizes transmission systems with instantaneous spectral oc-cupancy in excess of 500 MHz, or a fractional bandwidth of more than20%;
Currently, UWB is mainly recommended for short-range (such as in-door and sensor networks), high-speed (which may be upto hundreds ofMbits/s) multiple-access communications;
High processing gain and low power spectral density;
Fine delay resolution probably resulting in a huge number of multipathcomponents;
Accurate position location and ranging;
Property of material penetration due to low frequency components.
The measurements in UWB channels show that the envelopeamplitudes do not follow a Rayleigh distribution. Either log-normal or Nakagami distribution can equally be used for fittingthe measurement data;
Multipath components arrive at the receiver in group (clus-ters). Cluster arrival time obeys Poisson distribution;
The arrival time of the multipath components within a clusteralso obeys Poisson distribution;