CH%202.%20The%20Mobile%20Radio%20Environments%20and%20Diversity%20Techniques

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• CH 2. The Mobile Radio Environments and Diversity
  Techniques

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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
• Frequency Domain Effect of Time Dispersion
• Diversity Techniques

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Link Analysis 1

• Link analysis or Link budget analysis?
• The carrier-to-noise ratio (CNR) is the parameter
  of most interest in the link analysis of
  communication systems, along with signal-to-noise
  ratio (SNR).
• Link budget Detailed description on gain or loss
  of the CNR (or SNR) at each part of the
  communication link
• Link equation
• 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
• Instead of the CNR or SNR, the bit-energy-to-noise
  spectral density ratio, Eb/No, is also used in
  the link analysis of digital communication
  systems.

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Path Loss Models Free-Space Model 1,2

• Friss Equation the relationship between the
  transmit and receive powers in free space
• Pr(d) receive power, d distance, Pt
  transmit power, Gt transmit antenna gain Gr
  receive antenna gain, l wavelength, path loss
  exponent 2
• The free-space propagation loss in linear scale
  is
• Using fl c, where c is the speed of light, the
  free-space loss in log-scale is
• 
  
• d distance (km), f carrier
  frequency (MHz)
• The free space model is mostly used in satellite
  or deep-space communications.

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Path Loss Models Lee Model 1,2

• The propagation loss in cellular environments is
  much higher than the free-space loss due to the
  obstacles between the base station and the mobile
  station.
• The simplified formula developed by W. C. Y. Lee
  in cellular environments is
• d distance (km) between the base station
  and the mobile station hb height
  (m) of the base station antenna, path loss
  exponent 3.84
• In log-scale, we have
• path loss slope - 38.4dB/decade
• The generalized form of the Lee model is much
  more complicated and is quite useful in the link
  analysis for terrestrial environments.

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Path Loss Models Hata Model 1,2

• The Hata model is based on extensive field
  measurements in urban environments and is valid
  for 150MHz1500MHz.
• f carrier frequency (MHz), hb antenna
  height of the base station (m) hm mobile
  antenna height (m), d distance (km)
• The parameters a(hm) and Ko are used to account
  for mobile environments.
• There are certain ranges in which the model is
  valid, that is,
• Note that the path loss slope is

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Path Loss Models Observations 1
Fig. 2.1 Comparison of path losses for urban
scenarios (hb30m, fc 881.5MHz,
hm1.5m).
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Path Loss Models COST231- Hata Model 1,2

• The COST231-Hata model is an extension of the
  Hata model for 1500 2000 MHz range where most
  PCS systems may operate.
• The path loss in the COST231-Hata model is
• d distance (km), f carrier frequency
  (MHz), hb BS antenna height (m) hm MS
  antenna height (m), the same as the
  Hata model
• The COST231-Hata model can also be used only in
  case where

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Fading in Mobile Cellular Environments 1-3

• The phenomenon of a signal strength fluctuation
  due to the obstacles between the transmitter and
  receiver is called fading.

Fig. 2.2 An example of mobile cellular
environments.
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Fading in Mobile Cellular Environments (cont.)

• The fading is classified into long-term fading
  and short-term fading, and the signal strength
  r(t) can be expressed as the product of long-term
  fading and short-term fading components

Fig. 2.3 Radio signal strength in fading
environments.
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Long-term Fading Shadowing Effect

• The local mean of the signal strength, rL(t), is
  a random process caused by shadowing effect due
  to large obstacles such as buildings and hills,
  etc.
• The slow and large fluctuation of the local mean
  is called the long-term fading.
• Empirical studies have shown that the local mean
  has the log-normal distribution such that
• rL,dB 10log10 rL, s standard deviation
  of rL,dB, m mean of rL,dB
• The standard deviation s of the local mean in a
  cellular environment is typically around 8dB.

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Short-term Fading Rayleigh Fading

• The signal fluctuation due to the multi-path
  signals reflected from the obstacles around the
  receiver is called short-term fading or
  multi-path fading.
• Two representative short-term fadings Rayleigh
  fading and Rician fading
• When there is no direct path, received signals
  are made up of a group of reflections from
  obstacles and none of the reflected paths is
  dominant.
• The reflected signals arrive at slightly
  different times, with different amplitudes, and
  with different phases.
• In this case, the envelope of a received signal
  is Rayleigh distributed.
• Assuming the number of mutipaths is N, the
  composite signal at the receiver is
• 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.

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Short-term Fading Rayleigh Fading (cont.)

• The in-phase and quadrature phase representation
  of the received signal is
• where
• The terms in the summations of the above
  equations can be assumed independent random
  processes. If N is large, both rI(t) and rQ(t)
  become independent zero-mean Gaussian random
  processes by the central limit theorem.
• Therefore, the signal envelope has a Rayleigh
  distribution with the pdf of
• where

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Short-term Fading Rayleigh Fading (cont.)

• In case where there are many scattered waves
  coming from all directions, the signal
  fluctuation repeats every half wavelength of the
  carrier, that is, the fading rate corresponds to
  half wavelengths.

Fig. 2.4 An example to illustrate the fading rate
at the mobile station.
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Short-term Fading Rayleigh Fading (cont.)
Fig. 2.5 Rayleigh fading signal at mobile for v
100km/h and f 1960MHz.
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Short-term Fading Rayleigh Fading (cont.)

• In mobile communication environments, the Doppler
  spectrum of the carrier signal follows the
  Clarkes model, as shown in Fig. 2.6.

Sc(f)
Fig. 2.6 Doppler spectrum for a mobile in
Rayleigh fading environments.
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Short-term Fading Rayleigh Fading (cont.)

• Example
• Assume that we use a carrier frequency of 900 MHz
  for cellular and 1.9 GHz for PCS, and that the
  vehicle speed is 25 m/sec.
• Compare the fading rate at mobile between
  cellular and PCS signals, and find the maximum
  Doppler frequencies.
• The wavelengths are
• The time for a mobile to travel from one
  fade to the next fade is

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Short-term Fading Rayleigh Fading (cont.)

• Therefore, the fading rates are 150 Hz for
  cellular and 317 Hz for PCS, respectively.
• The maximum Doppler frequencies are

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Short-term Fading Rician Fading 2,4

• For a multi-path fading channel containing direct
  components, rI(t) and rQ(t) have non-zero mean,
  and the signal envelope has a Rician
  distribution, i.e., 4
• 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
• Ks2/(2s2) is the Rice factor or the Rician
  K-factor. When K0, the channel exhibits Rayleigh
  fading, while when K approaches to infinity,
  there becomes no fading.
• The Rician fading is often observed in
  micro-cell, indoor environments, or satellite
  communications.

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Fading Signal Generation Jakes Model 4

• Jakes model is a very effective channel
  simulator that generates Rayleigh or Rician
  fading signals by using a number of virtual
  oscillators.
• Assuming an isotropic scattering channel with N
  multi-path signals of equal strength, the complex
  fading signal r(t) can be expressed as 4
• where
• M number of oscillators, N number of
  multi-paths, M (N/2-1)/2
• v mobile speed, l signal wavelength.

• Rician fading signals can be generated easily by
  adding direct components to Rayleigh fading
  signals.
  

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Fading Signal Generation Jakes Model (cont.)

• Jakes model can be extended to provide up to M
  independent fading signals by simply giving the
  additional phase shift to each
  oscillator, that is,
• where

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Time Dispersion of Signal due to Fading 2

• In cellular environments, multi-paths arrive at
  different times, which results in the time
  dispersion of a received signal.
• In usual, the signal strength of a received
  signal is modeled to decay exponentially as a
  function of the time delay
• Pk power of kth path, trms time delay of
  kth signal, trms rms delay C
  constant

Fig. 2.8 Multipath delay profile.
Fig. 2.7 Time dispersion of signal.
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Time Dispersion of Signal due to Fading (cont.)
2

• There are several parameters to characterize the
  time dispersive properties of fading channels
  that is, mean excess delay, rms delay spread (or
  delay spread), etc.
• The mean excess delay is the first moment of the
  power delay profile and is defined as
• The rms delay spread (or delay spread) is the
  square root of the second central moment of the
  power delay profile and is defined as

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Time Dispersion of Signal due to Fading (cont.)

• Example
• Compute the mean excess delay and rms delay
  spread for the multipath delay profile given in
  the figure below.
• Determine if the delay profile will cause ISI
  (inter-symbol interference) to a mobile
  communication system using 50 Kbps as its data
  rate.

Fig. 2.9 Multipath delay profile.
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Time Dispersion of Signal due to Fading (cont.)

• Since the bit duration is significantly
  larger than the rms delay spread, a serious ISI
  may not occur.

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Time Dispersion of Signal due to Fading (cont.)

• Example
• Determine if the delay profile shown in Fig. 2.9
  will cause ISI to a mobile communication system
  using 1.2288 Mbps as its data rate.
• 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.
• However, if the system is a CDMA system such as
  the IS-95 or WCDMA, there is no significant ISI
  since the CDMA system uses a special form of
  diversity called path diversity to recover the
  signal using a rake receiver.

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Time Dispersion of Signal due to Fading (cont.)
2
Table 2.1 Typical measured values of rms delay
spread 2.
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Frequency Domain Effect of Time Dispersion 1

• We now examine the effect of time dispersion in
  the frequency domain.
• To this end, we assume that there are two
  multi-paths as shown in Fig. 2.10.

Fig. 2.10 Two multi-path signals separated by
time t.
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Frequency Domain Effect of Time Dispersion (cont.)

• The received signal is
• By taking a Fourier transform, we can obtain
• where
• and
• The channel response is illustrated in Fig. 2.11.

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Frequency Domain Effect of Time Dispersion (cont.)
Narrowband signal Frequency-Nonselective
Wideband signal Frequency-Selective
Fig. 2.11 The channel response as a function of
frequency.
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Frequency Domain Effect of Time Dispersion (cont.)

• In case where the signal bandwidth is
  significantly smaller than the inverse of delay
  spread, the signal is said to suffer from
  frequency-nonselective fading or flat fading.
• gt There is no serious inter-symbol
  interference (ISI).
• On the contrary, if the signal bandwidth is
  greater than the inverse of delay spread, the
  signal is said to suffer from frequency-selective
  fading.
• gt There is a serious ISI in TDMA systems.
• The BER performance of a TDMA system in
  frequency-selective fading environments is
  significantly worse than that in
  frequency-nonselective fading environments due to
  inter-symbol interference.
• In CDMA systems, however, the BER performance in
  frequency-selective fading environments can be
  better than that in frequency-nonselective fading
  environments due to path diversity.

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Diversity Techniques 2,5

• In mobile communication environments, a received
  signal sometimes suffers from severe impairments
  due to fading.
• Diversity technique (or diversity combining
  schemes) is a popular approach to reduce the
  effects of fading and to improve the reliability
  of communications using the diversity of
  communication channel.
• There are several types of diversity that can be
  used for mobile communication systems
• Time diversity repetition / interleaving /
  combining
• Frequency diversity wideband signal gt path
  diversity multi-path signals
• Space diversity multiple antennas at base
  station (antenna diversity), handoff
• Polarization diversity polarized antennas, etc.
• There are three diversity combining schemes
  selection diversity, maximal-ratio combining, and
  equal-gain combining schemes.

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Diversity Techniques Selection Diversity 5
Fig. 2.12. Selection diversity receiver model.
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Diversity Techniques Maximal-Ratio Combining 5

• Assume that all branch signals are combined such
  that
• 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
• It can be proven that the maximum SNR at the
  combiner output is obtained at
• That is, in a maximal-ratio combiner, each branch
  signal is weighted proportional to the magnitude
  of each branch signal together with phase
  compensation.
• The SNR at the combiner output equals the sum of
  the SNR of all branches.

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Diversity Techniques Equal-Gain Combining 5

• In equal-gain combiner, the magnitudes of branch
  weights are all the same.
• The output signal is simply given by
• where
• The performance of the three combining schemes is
  the better in the order of the maximal-ratio
  combining, equal-gain combining, and selection
  diversity.

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References

1. Samuel C. Yang, CDMA RF System Engineering,
   Artech House, 1998.
2. Theodore S. Rappaport, Wireless Communications,
   2nd Ed., Prentice Hall, 2002.
3. Gordon L. Stuber, Principle of Mobile
   Communication, 2nd Ed., Kluwer Academic
   Publishers, 2001.
4. John G. Proakis, Digital Communications, 4th Ed.,
   McGraw Hill, 2001.
5. V. K. Garg, IS-95 CDMA and cdma2000, Prentice
   Hall, 2001.