CH 2. The Mobile Radio Environments and Diversity Techniques. Contents. Link Analysis Path Loss Models Fading in Mobile Cellular Environments Long-term Fading Short-term Fading Fading Signal Generation: Jakes’ Model Time Dispersion of Signal due to Fading
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ERP: effective radiated power at antenna, Pt: power at the output of the transmit power amplifier, Lc: cable loss, Gt: transmit antenna gain Gr: receive antenna gain, Lp: propagation loss, N: noise power at receiver
Pr(d): receive power, d: distance, Pt: transmit power, Gt: transmit antenna gain Gr: receive antenna gain, l: wavelength, path loss exponent = 2
d:distance(km), f:carrier frequency (MHz)
d: distance (km) between the base station and the mobile station hb: height (m) of the base station antenna, path loss exponent = 3.84
path loss slope = - 38.4dB/decade
f: carrier frequency (MHz), hb: antenna height of the base station (m) hm: mobile antenna height (m), d: distance (km)
Fig. 2.1 Comparison of path losses for urban scenarios
(hb=30m, fc=881.5MHz, hm=1.5m).
d: distance (km), f: carrier frequency (MHz), hb: BS antenna height (m) hm: MS antenna height (m), : the same as the Hata model
Fig. 2.2 An example of mobile cellular environments.
Fig. 2.3 Radio signal strength in fading environments.
rL,dB=10log10rL, s: standard deviation of rL,dB, m: mean of rL,dB
An, fc: amplitude and carrier frequency, fD,n: Doppler shift of n-th path signal given by
with v and qn denoting the mobile speed and angle between mobile and signal.
Fig. 2.4 An example to illustrate the fading rate at the mobile station.
Fig. 2.5 Rayleigh fading signal at mobile for v = 100km/h and f =1960MHz.
Fig. 2.6 Doppler spectrum for a mobile in Rayleigh fading environments.
The wavelengths are
The time for a mobile to travel from one fade to the next fade is
s2: power of a direct component, s2: variance of the in-phase or quadrature phase component, Io: modified 0th-order Bessel function, total power of indirect components: 2s2
M: number of oscillators, N: number of multi-paths, M=(N/2-1)/2
v: mobile speed, l: signal wavelength.
Pk: power of kth path, trms: time delay of kth signal, trms: rms delay C: constant
Fig. 2.7 Time dispersion of signal.
Fig. 2.8 Multipath delay profile.
Fig. 2.9 Multipath delay profile.
Since the bit duration is significantly larger than the rms delay spread, a serious ISI may not occur.
Since in this case the delay spread is so much more than the bit duration, a serious ISI would normally occur if the system is a TDMA system.
Table 2.1 Typical measured values of rmsdelay spread.
Fig. 2.10 Two multi-path signals separated by time t.
Fig. 2.11 The channel response as a function of frequency.
==> There is no serious inter-symbol interference (ISI).
==> There is a serious ISI in TDMA systems.
Fig. 2.12. Selection diversity receiver model.
ai, ji: fading envelope and phase of the i-th path signal, s(t) : transmit signal ni(t): complex noise process, M: number of branches