RCM -2- 1

1
Un-Fadded, Or Best Case Signal
2
Calculation of link loss budget

• There are now several components that we need to
  calculate to obtain a link design. These fall
  into two main categories.
• The strength of the signal received.
• We have looked at path loss due to the
  propagation of the signal in detail in terms of
  mechanisms, we will now consider several methods
  to calculate the statistical behaviour of this
  process.
• We have a component based model from which we can
  calculate the power delivered to the receiver,
  compeered to the power delivered by the
  transmitter.
• The noise level
• Thermal Noise
• Atmospheric Noise
• Man made Noise
• Cosmic Noise

3
Un-faded Signal At The Receiver

• We are now going to ignore all the fast and
  variable fade processes we have discussed, so
  that we can obtain a value of delivered power at
  the receiver in ideal conditions.
• First thing we need to do is calculate the signal
  power at the point where the receiving terminal
  is positioned.
• We do this by first considering the Equivalent
  Isotropic Radiation Power of the transmitter.
• To find the power at the receiver we consider
  only Free Space Loss, FSL, and atmospheric
  absorption, Al. This is power delivered at the
  receiver and we call it the Isotropic Receiver
  Power (IRP).
• This gives us the maximum power that can be
  delivered to the receiver, from this we need to
  understand how much of the power at any time is
• Delivered to the receiver.
• Usable by the receiver to extract information
  from.

4
Effects of Noise and C/N
5
The Useful Received Signal

• From the point of view of knowing how much energy
  is delivered to the receiver we must consider how
  it is effected by noise.
• The receiving system is itself generating a noise
  signal, to this the environment may be adding
  noise from other sources. The noise will simple
  add to the received signal, so it is now a matter
  of ensuring the delivered power of the wanted
  signal is large enough so that it we can
  distinguish it from the noise.
• Hence we are interested in the ratio of the
  signal strengths, or simply the signal to noise
  ratio, C/N.
• We know the power at the receiver, so we can
  define the C/N as
• Where PN is simply the total noise power

6
Thermal Noise (I)

• Thermal noise is caused by the thermal motion of
  particles, hence it emanates from all materials.
• Thermal noise is modelled as a white Gaussian
  stochastic process with power spectral density N0
  
• Where k is Baltzmanns constant (k 1.38x1023).
• T is the absolute temperature in Kelvins.
• For a bandwidth Limited signal of bandwidth B,
  then the noise power is.
• In dBs and at room temperature (T290k) this
  becomes, in Watts
• In milliwatts

7
Thermal Noise (II)

• The thermal noise level is frequently referred to
  as the thermal threshold. For a receiver
  operating at room temperature it is a function of
  the bandwidth of the receiver (in practical terms
  this is the IF bandwidth (BIF) measured in Hz and
  the noise figure in dBs of the receiver.
• Thus the thermal noise threshold Pt of the
  receiver can be calculated as follows

8
Noise Figure

• Consider an amplifier with a Gain Gp and a
  bandwidth B.
• At the amplifier input we have the signal plus
  the signal noise.
• At the output we have
• Where Te is the noise temperature of the
  amplifier referred to its inputs
• The noise figure for the amplifier is
• The portion of the noise figure arising from the
  internally generated noise is

9
Example Link Budget Calculation

• A receiver for a LOS link operating at 2 GHz and
  a bandwidth of 1MHz consists of an Antenna
  preamplifier with a noise temperature of 127K and
  a gain of 20 dB. This is followed by an amplifier
  with a noise figure of 12dB and a gain of 80dB.
• Compute the overall noise figure and equivalent
  noise temperature of the receiver!
• The receiving antenna gain is 40dB and the
  antenna noise temperature is 59K. If the
  transmitter antenna gain is 6dB and the expected
  path losses are 190dB, what is the minimum
  required satellite transmitter power to achieve a
  14 dB SNR at the output of the receiver?

10
CALCULATING FM MODULATION BANDWIDTH

• Frequency Modulation creates modulation sidebands
  that theoretically extend to infinite bandwidth.
  These sidebands consist of Bessel Functions of
  any order. From a practical standpoint the band
  occupancy of an FM modulated carrier only needs
  to count the Bessel Function sidebands of
  significant amplitude. The formula that
  calculates this bandwidth is called CARSON'S
  RULE.
• This rule requires knowing the modulating
  frequency Fm and the maximum frequency deviation
  ?Fp of the transmitted carrier.
• Example, a monaural RF band modulator will have a
  peak deviation of 75KHz and the highest audio
  frequency is 15KHz. To calculate the CARSON'S
  RULE bandwidth occupancy of this signal, add the
  highest audio frequency to the peak deviation
  (15KHz 75KHz 90KHz), then multiply by two to
  include both the upper and lower sideband (90KHz
  X 2 180KHz). Since there are many Bessel
  Function sidebands beyond 180KHz, FM channels
  must be spaced considerably farther apart than
  180KHz. The FCC has determined that a spacing of
  400KHz provides sufficient "Guard Band" to
  effectively prevent inter-channel cross-talk, but
  that 180KHz is sufficient bandwidth to receive
  the original modulation with less than 1
  distortion. The distortion is due to a failure to
  receive all of the modulation energy.
• Amplitude Modulation bandwidth can be considered
  exactly two times the highest frequency of
  modulation, while Frequency Modulation bandwidth
  is described by Bessel Functions that extend much
  higher than those of Amplitude Modulation. In
  fact the "FM Advantage" in signal-to-noise ratio
  stems exactly from spreading the modulation over
  a greater bandwidth than Amplitude Modulation.

11
Antenna Gain Calculation
12
Antennas

• Types parabolic reflectors, Cassegrain antenna,
  horns, passive reflective reflectors and antenna
  arrays.
• Parameters to analyse
• gain a function of the geometric surface and
  frequency.
• Beam Width
• Precision in the orientation is required.
• Radiation Diagrams

13
Antenna Gain (I)

• We are going to concentrate on Parabolic
  reflectors.
• These systems have side lobes that means signals
  can couple into the antenna in directions other
  than the line of sight. This will have
  significance when we are considering frequency
  planning.
• The gain of the antennas is one of the most
  flexible parameters we have in modifying the link
  budget, so we need a mechanism to calculate it.

14
Antenna Gain (II)

• The antenna Gain is given by
• Where ? is the antenna efficiency and Da is the
  antenna diameter.
• Should have a size much greater than Da and
  surface roughness much less than Da.
• If we measure Da in meters and move into dBs, we
  get
• The efficiency for such antennas is in range,
  55-65, we assume 55.

15
Passive Repeaters

• They are used to change the direction of the
  radio path.
• They can be either parabolic or flat reflectors.
• Examples
• Reflectors in far field
• Passive repeater with two parabolic antennas.
• Passive repeated with reflecting plane (The angle
  must not be too obtuse).
• Passive repeater with two reflecting planes in
  one point or two.
• Reflectors in near field. Places the antenna at a
  specified height.
• Calculation of attenuation in a path with passive
  reflectors
• Parabolic reflector (1)
• Flat reflector (2)
• The width of the beam decreases as the surface
  increases and it must not be lower than 1º.
• Periscope configuration (5.16)

16
Fade Margin Calculation
17
Other Random Processes

• In addition to the noise in the system that is
  seen as a random process, many other aspects of
  the system are subject to random processes.
• Many things are effecting the signals as they
  propagate.
• We cannot possibly know all the details of the
  environment through which the signal propagates,
  hence we have to model it by some degree of
  uncertainty.
• This randomness will have to be accounted for in
  both time and space.

18
Calculating Fade Margins

• As stated, so far we have calculated only
  Free-space and atmospheric attenuation losses,
  but we have examined in detail the mechanisms
  that would lead to Fading.
• We have until now only spoken superficially about
  the effects of the fading in real terms, but have
  made it clear the amount of fade is a dynamic
  process.
• This means that the changes in environment of
  weather conditions will cause changes in the fade
  level through time.
• We have a calculated value for the signal
  strength presented to the receiver, RSL, but this
  is in fact a maximum value.

The RSL value for a path subject to Freespace
and atmospheric attenuation only.
The real RSL value which varies in time due to
fading processes.
RSL
t
19
Statistical Nature Of Field Strength

• The complexity of the fading process and the
  number of parameters involved mean that we need
  to take a statistical view of the behaviour of
  the received field strength.
• The nature of the statistics is controlled by
  many factors. As stated before the terrain,
  climate and path length play a very significant
  role.
• Path lengths below 5 Kilometres can generally be
  regarded as fade free.
• We know that we have to obtained a specific level
  of C/N to actually receive the signal. This means
  in summary that to ensure the signal is received
  we need it to exceed a specific value which
  overcomes the thermal noise threshold.
• If the signal falls below this point the link can
  be considered to be non functioning.
• As the signal strength varies with time we can
  only ensure that the threshold is exceeded a
  certain percentage of the time.

20
Outage Time

• We have calculated the RSL and the noise
  threshold, so over time we can see when the link
  is functioning and when it is not,
• The parts in red are when the field strength
  falls below an acceptable value.
• This gives us an amount of time during which the
  link fails, the outage time.

RSL
Free-space and atmospheric losses
Fade Margin
Noise power threshold
t
21
Improving Outage Time

• We can design a particular RSLFS by increasing
  the transmission power, and/or the antenna gain
  etc.. Hence we can change the outage time by
  changing the RSL.
• In this case we have a much lower outage time,
  hence better performance.
• Of the many methods to support design, they are
  all effectively estimating the probable outage
  time for a limited set of input parameters.

Free-space and atmospheric losses.
RSL
Fade Margin
Noise power threshold
t
22
Using the Rayleigh Fading Assumptions

• Once you know what to calculate the trick is then
  to come up with a systematic method to do so.
• There are many models that are available and many
  organisations have come up with their own
  methodologies.
• The methods are based on finding the probability
  a field of a given strength will fall below a
  certain value for a known duration of time.
• If we assume that the fading is due entirely to
  multi-path conditions we can use the Rayleigh
  Distribution to calculate the worst fade
  conditions.
• The Rayleigh distribution in a microwave link is
  really a worst-case upper-bound value. Empirical
  measurements are also shown which indicate that
  other distributions are more appropriate,
  particularly over the shorter paths over land.
• As stated previously a complementary function can
  be defined that calculates the probability of
  exceeding a given value.

23
Rayleigh Fade Margin (I)

• The graph shows the depth of fade in decibels
  versus the fractional time the fade is in excess
  of the abscissa.
• In summary this means if you take a point along
  the abscissa, say 25dB, then the graph tells you
  that the link would be down 0.003 fractional part
  of the time
• Additionally the graph shows three separate
  curves a) The Rayleigh curve b) the Durkee
  curve and c) the curve used by the French P.T.T.
  
• This data is usually appropriate for a given type
  of terrain and climate and must be substituted
  when the conditions change.

24
Rayleigh Fade Margin (II)

• For quick calculations the following table can be
  used to calculate the fade margins required to
  support a link availability of a particular
  value.
• Any level of availability can be calculated by
  extrapolation. For example a link requiring
  99.95 time availability would require a 33dB
  Fade Margin.
• For example if the minimum un-faded C/N for the
  above link was 20dB, the link would require 20
  33 53 dB power level to meet the 99.95
  objective.

Time Availability () Fade Margin (dB)
90.0 99.0 99.9 99.99 99.999 8 18 28 38 48
25
Path Classification Method (I)

• This method is based on CCIR recommendations and
  empirical results supplied by Siemens.
• Siemens has classified into three categories
  depending upon characteristics of the path.
• The method only applies to overland links that
  have unobstructed LOS conditions.

26
Path Classification Method (II)

• Type A These paths have favourable fading
  characteristics, troposphereic effects are rare.
  They are over hilly country, but not over wide
  river valleys and inland water and in high
  mountainous country with paths hig above the
  valleys. They can also be characterised as being
  between a plain or a valley and mountains, where
  the angle of elevation exceeds 0.5o.
• Type B These are paths with average fading
  characteristics and are typically over flat, or
  undulating country where troposphereic effects
  may occur. They are also over hilly country, but
  not over river valleys or open water. They are
  also characterised as being over coastal regions
  in moderate climates, but not over over the sea.
• Type C These paths have adverse fading
  conditions. They are characterised as being over
  humid areas with ground fog being common. Paths
  that are low over flat country, such as wide
  river valleys and moors. They are typical of
  costal links in hot climates and paths in
  tropically regions with no angle of elevation.

27
Path Classification Method (III)

• They can be estimated with the following
  formulas.
• Where PW is the probability that the fade depth A
  is exceeded in one year.
• F radio carrier frequency in gigahertz.
• d path length in kilometres.
• A fading depth in decibels.

28
ITU-R 530 Method

• This is a more sophisticated method and takes
  into account the type of terrain over which the
  link must travel.
• It introduces the concept of a geoclimatic factor
  K. Of which there are 4
• Two types of K are used for over land links.
• Two types of K are used for over water links.

29
Fading On Multi-Hop Paths

• Experimental evidence indicates that, in
  clear-air conditions, fading events exceeding 20
  dB on adjacent hops in a multi-hop link are
  almost completely uncorrelated. This suggests
  that, for analogue systems with large fade
  margins, the outage time for a series of hops in
  tandem is approximately given by the sum of the
  outage times for the individual hops.
• For fade depths not exceeding 10 dB, the
  probability of simultaneously exceeding a given
  fade depth on two adjacent hops can be estimated
  from
• where P1 and P2 are the probabilities of
  exceeding this fade depth on each individual hop
  (see Note).
• The correlation between fading on adjacent hops
  decreases with increasing fade depth between
  10 and 20 dB, so that the probability of
  simultaneously exceeding a fade depth greater
  than 20 dB can be approximately expressed by
• NOTE  The correlation between fading on adjacent
  hops is expected to be dependent on path length.
  The first Equation is an average based on the
  results of measurements on 47 pairs of adjacent
  line-of-sight hops operating in the 5 GHz band,
  with path lengths in the range of 11 to 97 km,
  and an average path length of approximately 45
  km.

30
Attenuation Due To Hydrometeors

• Attenuation can also occur as a result of
  absorption and scattering by such hydrometeors as
  rain, snow, hail and fog. Although rain
  attenuation can be ignored at frequencies below
  about 5 GHz, it must be included in design
  calculations at higher frequencies, where its
  importance increases rapidly. On paths at high
  latitudes or high altitude paths at lower
  latitudes, wet snow can cause significant
  attenuation over an even larger range of
  frequencies. More detailed information on
  attenuation due to hydrometeors other than rain
  is given in Recommendation ITU-R P.840.
• At frequencies where both rain attenuation and
  multipath fading must be taken into account, the
  exceedance percentages for a given fade depth
  corresponding to each of these mechanisms can be
  added.

31
Techniques For Alleviating The Effects Of
Multipath Propagation (I)

• The effects of slow relatively non-frequency
  selective fading (i.e. flat fading) due to beam
  spreading, and faster frequency-selective fading
  due to multipath propagation can be reduced by
  both non-diversity and diversity techniques.

32
Techniques For Alleviating The Effects Of
Multipath Propagation (II)

• Techniques without diversity The guidance is
  divided into three groups reduction of the
  levels of ground reflection, increase of path
  inclination, and reduction of path clearance.
• Reduction of ground reflection levels Links
  should be sited where possible to reduce the
  level of surface reflections. Techniques include
  the siting of overwater links to place surface
  reflections on land rather than water and the
  siting of overland and overwater links to
  similarly avoid large flat highly reflecting
  surfaces on land. Another technique known to
  reduce the level of surface reflections is to
  tilt the antennas slightly upwards. Detailed
  information on appropriate tilt angles is not yet
  available. A trade-off must be made between the
  resultant loss in antenna directivity in normal
  refractive conditions that this technique
  entails, and the improvement in multipath fading
  conditions.
• Increase of path inclination Links should be
  sited to take advantage of terrain in ways that
  will increase the path inclination, since
  increasing path inclination is known to reduce
  the effects of beam spreading, surface multipath
  fading, and atmospheric multipath fading. The
  positions of the antennas on the radio link
  towers should be chosen to give the largest
  possible inclinations, particular for the longest
  links.
• Reduction of path clearance Another technique
  that is less well understood involves the
  reduction of path clearance. A trade-off must be
  made between the reduction of the effects of
  multipath fading and distortion and the increased
  fading due to sub-refraction. However, for the
  space diversity configuration one antenna might
  be positioned with low clearance.

33
Space Diversity
34
Frequency Diversity
35
Techniques For Alleviating The Effects Of
Multipath Propagation (III)

• Diversity techniques Diversity techniques include
  space, angle and frequency diversity. Frequency
  diversity should be avoided whenever possible so
  as to conserve spectrum. Whenever space diversity
  is used, angle diversity should also be employed
  by tilting the antennas at different upward
  angles. Angle diversity can be used in situations
  in which adequate space diversity is not possible
  or to reduce tower heights.
• The degree of improvement afforded by all of
  these techniques depends on the extent to which
  the signals in the diversity branches of the
  system are uncorrelated. For narrow-band analogue
  systems, it is sufficient to determine the
  improvement in the statistics of fade depth at a
  single frequency. For wideband digital systems,
  the diversity improvement also depends on the
  statistics of in-band distortion.
• The diversity improvement factor, I, for fade
  depth, A, is defined by
• I p( A ) / pd ( A )
• where pd (A) is the percentage of time in the
  combined diversity signal branch with fade depth
  larger than A and p(A) is the percentage for the
  unprotected path. The diversity improvement
  factor for digital systems is defined by the
  ratio of the exceedance times for a given BER
  with and without diversity.