GBPPR Microwave Radio Path Analysis v2.80
- path.main.cgi Perl source
- path.cgi Perl source
- splat.tgz I put together a large (30+ GB) single file which contains the converted SPLAT! SDF terrain data files (SRTMv3 3-arc second, worldwide), 2021 NLCD data, and the fixed ptelev program. Download splat.tgz and move it to /usr, then tar xvzf splat.tgz to create the new /usr/splat directory which will contain all the necessary data files.
- SPLAT! v2.0-alpha These CGIs require a slightly modified version of SPLAT! v2.0-alpha.
- GitHub Entry
(Adapted from StarLink 2 application notes by Harris-Farinon)
The basic calculations associated with a digital microwave radio path analysis are simply the addition and subtraction of relative gains, losses, and power levels in dB or dBm, to arrive at an expected (or desired) Composite Fade Margin (CFM).
The gathering of those numbers and some of the preliminary calculations associated with path length and azimuths is a bit more difficult, depending on access to the correct tables, uses of computer calculations, and the like. The conversion of the expected or desired Composite Fade Margin into predictable short-term (multipath fade) and long-term (rain fade) outage time, Severely-Errored Seconds Ratio (SESR), path reliability, and rain availability requires even more sophistication.
This tutorial is intended to provide you a limited overview of the basic calculations associated with digital microwave radio path analysis and how to compare those results with recognized performance objectives.
Short-term (multipath fade) probability of outage (SESR) and annual outage time computations are based upon Vigant's widely-used field-verified model as defined for North American links1 and ITU-R Rep. 5302 for international links.
The ITU-R Rec. P.530 multipath outage prediction method (with Hosoya's space diversity improvement model) could produce results widely divergent from Vigants' model, especially for flatland paths using space diversity in difficult geoclimatic regions. For this reason, ITU-R Rec. P.530 short-term outage models will not be used with this software modeling system.
The long-term fade margin (rain fade) outage time computations use the Crane rain model, and access to Crane's rain tables3 for North America radio-relay links which are derived from ITU-R but optimized for this region. This Crane model accesses ITU-R rain regions and rain rate tables4 for international microwave path rain outage calculations.
The newer ITU-R Rec. P.530 rain availability model will also not be used for rain outage calculations. Instead, we'll apply Crane rain models to all rain outage and link availability calculations worldwide.
Determining free-space path loss is the next calculation in preparation of the link analysis. Free-space loss is defined as the loss that exists between two isotropic antennas in a free space, where there are no ground or atmospheric influences or obstructions; in other words, where losses due to refraction, reflection, and diffraction fade activity and atmospheric absorption do not exist.
Radio energy is lost with distance because of the triangular spreading of wavefront energy as it travels through space. In accordance with the inverse-square law, wavefront area quadruples for each doubling of distance, for a 10 * log10(1/4) = 6 dB increase in path loss.
Free-Space Loss
The free-space path loss calculation assumes the use of theoretical point-source or isotropic antenna at each end of the path. Radio frequency energy is radiated uniformly in all directions at the transmitting end while the receiving antenna provides no directivity.
The basic transmission loss in free-space is:
FS = 96.6 + (20 * log10(F)) + (20 * log10(D))
Where: FS = Free-space attenuation between antennas, dB
F = Frequency, GHz
D = Path length, miles
or
FS = 92.4 + (20 * log10(F)) + (20 * log10(D))
Where: D = Path length, kilometers
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The free-space path loss equation yields a relationship which is useful in dealing with link budget issues. Each 6 dB increase in transmit power equates to a doubling of range. Conversely, a 6 dB reduction in system losses (either by way of transmission line loss, either on receive or transmitter end) translates into a doubling of range.
Received Signal Level
The unfaded Receive Signal Level (RSL) is computed by introducing the Net Path Loss (NPL) between the radio transmitter output and the following radio receiver's input.
The microwave radio transmit power is reduced by the NPL as determined by free-space and atmospheric absorption losses, antenna gains, and all the feeder and network losses at both ends of the radio path, link, or hop, as it is variously called.
Note that it is possible to have too high of a received power level. This can overload (saturate) the front-end electronics of the the receiver saturation causing distortion or non-linear mixing of the received signal.
RSL = Pt - NPL
RSL = (Pt - Lf) + Gt - (Lfs + Labs) + Gr - (Lf + Lnet)
Where: RSL = Received power level, dBm
Pt = Transmit power, dBm
Gt = Transmit antenna gain, dB
Lfs = Free-space loss, dB
Labs = Absorption loss, dB
Gr = Receive antenna gain, dB
Lf = Coax or waveguide feeder loss, dB
Lnet = Additional network and other losses, dB
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Thermal Fade Margin
The Thermal (or Thermal Noise) Fade Margin (TFM) is the difference between the unfaded received signal level and the receiver's static or dynamic threshold, as measured with back-to-back digital radios, at a given Bit Error Rate (BER). A typical TFM on a microwave data link is 30 to 40 dB. Analog (audio/video) links can be 20 dB or lower.
There is usually a choice between selecting either the 10-3 BER dynamic (or "outage") threshold for outage computations or the 10-6 BER static threshold for other performance and availability computations.
This selection adjusts the receiver's threshold to correspond with the selected BER. The proper threshold RSL values to use should be provided by your radio's manufacture.
It is important to note that an internationally defined outage in a PDH (asynchronous) digital radio link corresponds to a 10-3 BER Severely-Errored Second (SES) event at the receiver's dynamic threshold. This threshold is very near the initiation of a T1 or E1 AIS alarm (loss of frame synchronization) condition in the connected PABX, channel bank, trans-multiplexer, etc. trunk point.
he digital radio's 10-6 BER static threshold or operating point is used for in-service radio and interference measurements (with attenuators) and as a measurement of circuit quality, not outage, although it is sometimes assigned as an "outage" threshold by some users.
The outage threshold of a SONET or SDH (synchronous) digital link is defined at its SONET/SDH multiplexer's Loss-of-Pointer (LOP) synchronization point coinciding with a 2 * 10-5 BER for STM-1 and STS-3 radios. However, only a very small difference, perhaps 0.5 dB, between this LOP and a 10-3 BER threshold point occurs.
If two signals reach the receiver in phase, then the signal is amplified. This is known as an "upfade." Upfades can also occur when the radio wave is trapped within an atmospheric duct. As can be seen from the following formula, higher upfades are possible for longer paths:
Upfademax = 10 * log10(D) - (0.03 * D)
Where: Upfademax = Maximum upfade, dB
D = Path distance, kilometers
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Dispersive Fade Margin
A few high-clearance digital microwave radio links with adverse path geometry are susceptible to dispersive (spectrum-distorting) fading, as well as interference and the flat fading mentioned earlier.
Dispersive fading may cause the loss of the digital radio receiver's quadrature lock (synchronization) due to amplitude or group delay slope and notch effects resulting in degraded error performance, including short- or long-term outage.
Powerful corrective measures combating dispersive fading include space diversity antennas, Forward Error Correction (FEC), Adaptive Time-Domain Equalization (ATDE), and Adaptive IF Slope Amplitude Equalization (ASAE). As the RF bandwidth or number of signaling states increases, the effect of dispersive fading increases, requiring more sophisticated countermeasures typical of today's digital microwave receivers.
Dispersive fading margin is a measure of robustness of a digital radio to spectrum distortions caused by the interaction of refractive or reflective multipath signals with the direct (desired) signal. This value is often found in the datasheets of more higher-end radios. The DFM for a digital radio is derived from its signature curve, which is derived by moving a high-level multipath notch through the receiver's IF passband at increasing depths to cause an outage. This "notch" results from the canceling null generated by the combining of the transmitter's direct signal with its (reflected) multipath signal delayed by 6.3 nanoseconds (6 feet or 2 meters).
For uniformity, the DFM for all digital microwave radios marketed in the U.S. are characterized using the Rummler model, a similar test where the multipath signal is delayed 6.3 nanoseconds compared to the direct signal.
As a general rule, a link DFM >50 dB will have no impact on path performance (outage or quality). However, if geometry calculations from the path profile reveal multipath (reflective) signals longer than about 10-20 nanoseconds, as between mountain top sites with excessive clearance, the DFM rapidly lowers with multipath delay This will degrade performance (increase RBER, ES, and outage SES) unless the amplitude of the multipath signal is lowered with adequate antenna discrimination. (Antenna discrimination is the ratio of any gain off-axis to the primary beam, essentially the ability of the antenna to not hear any signals off to the side.)
For example, if the multipath signal is delayed 30 nanoseconds, the radio DFM degrades to 33 dB and a total of about 20 dB (10 dB at each end) of antenna discrimination is required to optimize the path performance (Link DFM = Radio DFM + Antenna Discriminations). The multipath delay on most "flat land" microwave paths is <2 nanoseconds, equating to an inconsequential >60 dB DFM.
If the DFM is >50 dB, it is added to the Thermal Fade Margin (TFM) to derive the Composite Fade Margin (CFM) of the link in the absence of interference.
Good engineering practice aims to obtain the largest possible dispersive fade margin without countermeasures and to add them as required and as consistent with a favorable trade-off between transmission performance and cost-effectiveness.
Composite Fade Margin
The Composite Fade Margin (CFM) is derived by a "power addition" of the thermal fade margin and dispersive fade margin, which is then used for the final multipath outage calculations:
CFM = -10 * log10(10-DFM/10 + 10-TFM/10)
Where: CFM = Composite fade margin, dB
TFM = Thermal fade margin, dB
DFM = Dispersive fade margin, dB
Example: TFM = 40.0 dB # Thermal Fade Margin
DFM = 45.0 dB # Dispersive Fade Margin, 10 nanosecond echo)
CFM = 38.8 dB # Composite Fade Margin
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Unless there is a very high thermal fade margin (resulting from a short path or large antenna gain), the impact of a modern digital radio's dispersive fading margin upon the composite fade margin, and therefore upon the link design, should be negligible.
However, the radio's dispersive fading margin could be heavily degraded on some high-clearance paths with inadequate antenna discriminations to the resulting very long-delayed (>10 nanoseconds) multipath signal. The radio's dispersive fading margin could degrade from 50+ dB to 40 dB (or even much lower) with this long-delayed, high-amplitude multipath signal.
Is is essential that the antenna discriminations (antenna's frequency band, size, tilt, etc.) to the long-delayed specular reflection lower the echo's amplitude adequately to meet a minimum 50 dB link dispersive fading margin objective for no degradation in the link's error performance.
Intra-station and interlink interference from other microwave transmitters may also degrade the digital radio's threshold and, therefore, the link's fade margin. Although usually ignored in initial path design, interference is often limited to that level introducing <1 dB threshold (and fade margin) degradation into a link.
Once the composite fade margin has been determined, it is used to compute an expected Severely-Errored Second Ratio (SESR) and, in North America, the one-way path reliability based upon annual outage time.
Path reliability (from the annual short-term outage time computation) is influenced by the effects of:
- Multipath fading, defined by geographical propagation characteristics (climate and terrain) for given locales. Multipath fading tends to be a warm weather phenomenon.
- Average annual temperature defining the fade season for the same geographical region.
Composite fade margin is also an input for computing the expected two-way path availability in microwave links which accommodates all long-term (>10 CSES traffic disconnect) rain outage events. Path availability is computed from:
- Rain attenuation tables which assign coefficients based upon frequency and polarization.
- Rain rate tables based upon thunderstorm and similar high rain rate activity in all worldwide regions.
Of course, equipment antenna systems, infrastructure failures, and manual intervention (switching, etc.) and also cause long-term outage, but these are not included in this programs calculations. Rain outage is considered as a "self-healing" unavailability event, and unlike most other long-term outage events, is predictable.
The fade margin of a digital microwave radio path provides a "safety margin" to protect the microwave signal from the adverse effects (carrier-to-noise degradations) of multipath fading, interference, and rain attenuation.
Digital microwave link fade margins are usually much smaller than for analog radio, whose fade margins are often increased to provide baseband quieting (low thermal noise) even in short and non-fading links.
The provision of an adequate fade margin and path clearance to protect against composite fade margin degradations and outage due to surface ducting and terrain blockage, plus diversity on longer or otherwise vulnerable paths, make it possible to achieve per-hop propagation reliabilities with respect to Rayleigh-distributed multipath fading, exceeding 99.999%.
Path reliability, along with quality (RBER, Error Free Seconds, etc.), defines a digital radio link performance during traffic availability periods. Path availability relates to the time a given microwave link is operational for a specified period of time, typically a year.
With the exception of microwave links operating 10 GHz or higher in dense rain areas, the availability objective of most microwave links is 100%.
Predicted (measured) only during available (traffic connected) periods, path reliability is a measure of annual short-term (<10 CSES) one-way multipath fade outage occurring over a 2 to 4.5 month fade season:
Rain Availability, Multipath Reliability, and Outage Time
Outage Time* --------------------------------------------------------------
Path Reliability % Outage Time % 3-Month Fade Period Fade Period Month (Avg.) Fade Period Day (Avg.)
50.0 50.0 4380 hrs 360 hrs 12.0 hrs
80.0 20.0 1752 hrs 144 hrs 4.8 hrs
90.0 10.0 876 hrs 292 hrs 2.4 hrs
95.0 5.0 438 hrs 146 hrs 1.2 hrs
98.0 2.0 175 hrs 58 hrs 30.0 min
99.0 1.0 88 hrs 29 hrs 15.0 min
99.9 0.1 9 hrs 3 hr 1.4 min
99.99 0.01 52 min 18 min 8.6 sec
99.999 0.001 5 min 106 sec 1.0 sec
99.9999 0.0001 32 sec 11 sec 1.0 sec
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* Rain outage is distributed over an annual period, perhaps averaged over 10 or more years. Multipath outage is assumed to occur during a worst month (ITU) or over a fade season (3 months at 50°F for North American model calculations).
Outage Probability
In this section, the fractional probability of outage, U or Severely-Errored Second Ratio, is used rather than percentage probability. This is a probability of an outage occurrence, known internationally as the Severely-Errored Second Ratio or SESR.
The fractional "reliability" parameter, A is equal to:
A = 1 - SESR
Where: A = Reliability parameter
SESR = Severely-errored seconds ratio
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The percent reliability, as used in microwave radio, is equal to:
Aper = 100 * (1 - SESR)
Where: Aper = Reliability, in percent
SESR = Severely-errored seconds ratio
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Availability is sometimes incorrectly express as a percentage synonymous with path reliability.
A microwave link become "unavailable" (or "failed", disconnecting traffic) only after ten seconds of continuous outage (>10 CSES), such as with a typical rain outage event, whereas each second of multipath outage (up to 10 continuous SES) only degrades path reliability.
Message (voice or data) traffic is lost or disconnected only with long-term unavailability events, not short-term SES outage events.
North American Outage Calculations
In North America, the equation4 for the probability of short-term outage in a non-diversity path during the fade season is as follows:
Und = 0.4 * C * F * T * D3 * 10-CFM/10
or
Und = C * (F / 4) * 10-5 * D3 * 10-CFM/10
Where: Und = One-way probability of outage (SES/year) for a non-diversity path
F = Frequency, GHz
D = Path length, miles
CFM = Composite or thermal (flat) fade margin, dB
T = Average annual temperature, Fahrenheit
C = North American Climate/terrain factor:
6.00 : Influenced by surface ducting (flat, very humid)
4.00 : Average terrain, very humid climate
2.00 : Average terrain, humid climate
1.00 : Average terrain, average climate
0.50 : Dry desert climate
0.25 : Mountainous terrain and dry climate
or
C = X * (W / 50)-1.3
Where: X = North American Climate factor
2.0 : Very humid climate / Maritime temperate, coastal or high humidity/temperature
1.4 : Humid climate / Maritime sub-tropical
1.0 : Average climate / Continental temperate or mid-altitude inland
0.5 : Dry climate / high-dry mountainous
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Computation of the Vigants Terrain Roughness Factor
Terrain roughness is calculated from terrain heights from a reference level (sea level, for example) obtained from the path profile at one mile intervals, with the ends of the path excluded. The standard deviation of the resulting set of numbers is the terrain roughness, denoted by W.
Applicable values of W range from 20 feet (considered smooth) to 140 feet (rough). These values of 20 and 140 should be used when calculated values of W are below 20 and above 140. A value of 50 has been defined as normal.
For an example 19 mile path:
Point (mile) Ground Elevation (AMSL/ft) Ground Elevation2 1 600 360,000 2 625 390,625 3 515 265,225 4 440 193,600 5 480 230,400 6 450 202,500 7 400 160,000 8 420 176,400 9 460 211,600 10 420 176,400 11 450 202,500 12 480 230,400 13 450 202,500 14 420 175,400 15 390 152,100 16 480 230,400 17 520 270,400 18 550 302,500 --------------------------------------------------------------- Σ = 18 Σ = 8,550 Σ = 4,133,950 W = sqrt((4133950 / 18) - (8550 / 18)2) W = 63.5 feet |
For microwave systems needing the added protection of diversity (e.g. antenna space diversity) to meet outage objectives, the calculations for Und, the non-diversity outage probability, is identical to that above.
Diversity provides an improvement to the path reliability (reduces outage time). The probability of outage (SESR) or "unreliability" for a diversity system is calculated based on the following equation:
Ud = Und / Id Where: Id = Diversity improvement factor |
The diversity improvement factor differs for each type of diversity - space, frequency, hybrid, multiline, angle, etc.
Space Diversity Improvement Factor
The Vigants' space diversity improvement factor, Isd for space diversity, is shown below:
Isd = (7 * 10-5 * F * V2 * S2 * 10CFM/10) / D
Where: Isd = Space diversity improvement factor
V = Relative gain parameter. Gain of secondary antenna relative to the
primary antenna in dB is 20*log(V).
F = Frequency, GHz
S = Vertical antenna spacing, between centers, feet, S <= 50
D = Path length, miles
CFM = Composite Fade margin associated with the diversity antenna.
CFM is introduced when the fade margin differs between
the primary and diversity paths. CFM is then the lower
of the two fade margins.
Example:
V = 1, if both antennas have same gain
F = 6.7 GHz
S = 30 ft.
CFM = 34 dB
D = 25 miles
Isd = 42.41
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This formula is only accurate with the following parameters: Path Distances: 14-40 miles, Frequency: 2-11 GHz, Antenna Spacing: 10-50 feet, Relative Gain of Div. Antenna to Pri.: 0 to -6 dB, Fade Margin: 30-50 dB. Extrapolation from these values may lead to errors. In general, Separations for which the available improvement is less than 10 should not be used. If possible, separations of at least 30 feet should be used.
In general, more vertical spacing between antennas offers better path reliability. In a typical space diversity antenna setup, the "top" antenna is usually for the primary path and the "lower" antenna is for the diversity path. The rule of thumb for antenna spacing is as follows:
- 2 GHz = 60 to 80 feet
- 4 GHz = 45 to 50 feet
- 6 GHz = 30 to 40 feet
- 11 GHz = 25 to 30 feet
Angle Diversity
Angle diversity is a method of improving path reliability with a special antenna, but is now rarely used. Angle diversity has two feed vertically offset by about 1° (the smaller the better) in a single antenna. Angle diversity is occasionally suggested as a substitute for the venerable two-dish space diversity scheme where tower loading, aesthetics, antenna heights, and tower or building space is limited. Angle diversity is most effective when path outages are dominated by dispersive fade activity (dispersive fade outage greater than flat fade outage).
However, digital radios are now far more robust to dispersive fade activity, i.e. have DFMs some 20 dB higher, than the 1980s digital radios which inspired the wide use of angle diversity antennas. When used, an angle diversity improvement factor Iad may be assigned, but some extended period of exacting antenna alignment to the path's geoclimatic conditions may be required for optimum Iad.
Self-Healing Ring "Route Diversity" Improvement Factors
Ring (loop) systems will automatically route T1 and T1 trunks away from fading microwave paths, and therefor improve the performance (reduce outage) in these networks.
A improvement factor, Isr = 20 is typical for ring systems.
Frequency and Hybrid Diversity Improvement Factor
Frequency and hybrid diversity improvements can be computed for regions where regulatory rules so permit.
The hybrid diversity improvement factor, Ihd, is derived from the space diversity improvement, Isd shown above and the frequency diversity improvement factor Ifd described below:
Ihd = Isd * Ifd |
Above 3 GHz, Isd is always higher (better) than Ifd unless the diversity spacing, ΔF, exceeds about 5% (300 MHz in the 6 GHz band, for example).
Below 3 GHz, Ifd is usually larger than Isd and is therefore should be used for computations.
The higher T/R frequency must always be assigned to the upper antenna at the space diversity end of each hybrid diversity link for optimum performance.
The frequency diversity improvement factor, Ifd, is as follows:
Ifd = 50 * ΔF * ((10CFM/10) / (F2 * D))
Where: Ifd = Frequency diversity improvement factor
ΔF = Diversity spacing, GHz
CFM = Thermal or composite fade margin
D = Path length, miles
Example:
F = 6.7 GHz
ΔF = 0.16 GHz
CFM = 34 dB
D = 25 miles
Ifd = 18
So if 834 SES/year, the outage would be reduced to (834/18) or 47 SES/year
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Neither space diversity nor in-band frequency diversity provide improvement against rain attenuation, although out-of-band frequency diversity (such as 6 GHz/12 GHz) does.
For frequency diversity, the frequency separation should not be more than 5% of the central frequency and should be limited to 0.5 GHz maximum.
Outage Model Constraints
It is evident from the foregoing computations that:
- Any loss of fade margin (CFM) due to interference, power fading, antenna misalignment, etc. greatly increases outage time, from x10 (non-diversity) to at least x100 (space or freq. diversity) for a 10 dB loss in CFM.
- Doubling of path length increases multipath outage x8 (non-diversity) to x16 (space or freq. diversity).
- Frequency is irrelevant in space diversity links; outage time is proportional to frequency in non-diversity links.
- Outage time is proportional to the annual average temperature and to the climate-terrain characteristics.
- Outages dues to specific reflections from smooth terrain, exposed bodies of water, etc. are excluded from non-diversity computations and presume optimum dish spacings in space diversity computations.
Although is it not required in ITU calculations, the actual outage time over a one-month period can be computed by multiplying the probability of outage, SESR, times the number of seconds in a month (2,600,000). Annual outage in an ITU link or system may be computed from the following North America procedure.
In North American calculation procedures, the annual outage time due to multipath fade activity in a microwave link is computed over a one-year period. In this calculation, actual outage is defined as that occurring over a 2-4.5 month "fade season:"
Tyr = U * To * (T / 50)
Where: Tyr = Annual outage, SES/year
To = Fade season taken as 3 months (a combination of
two severe and two moderate fade months, or
2,680,000 to 8,040,000 seconds)
U = SESR = Non-diversity or diversity probability of outage
T = Average annual temperature, Fahrenheit
Extends the fade season in warmer areas and shortens it in
cooler climates (35 < T < 75)
Example:
U = 0.000318
To = 2680000 seconds
T = 45 °F
Ttr = 767.016 SES/year
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Objectives
The performance objectives are defined as the SESR objective for ITU-R links and systems.
No further calculation of actual outage time over a measurement period (e.g., month, year) in necessary.
As will be discussed later, the ITU any- or worse-month objective6 for a microwave system is:
The ITU-R probability of outage (SESR) objective6 for a high-grade reference 2500 km (1500 mile) system (E1 trunk) length is:
SESR_Obj = 0.0005 + (D / 2500) * 0.00004
Where: SESR_Obj = Performance objective
D = Path length, kilometers
U = 0.00054 * D / 2500
Where: U = Probability of outage
D = System (trunk) length, kilometers
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Although neither any-month nor annual outage seconds (SES/month or SES/year) are specified as an objective (only U), T may be computed from U:
Tmo = U * 2680000
Tyr = Tmo * 3 * (T / 50)
Where: Tmo = Outage objective, SES/month
Tyr = Outage objective, SES/year
T = Average annual temperature, Fahrenheit
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North American Multipath Outage (and Path Reliability) Objectives
The most common short-term one-way outage objective for a T1/E1 trunk, regardless of system length, is about 1,600 outage seconds per year (SES/yr), or 99.995% end-to-end propagation reliability.
This is as equally true of a 5-hop short-haul system as a 150-hop long-haul system, except that in a very long-haul (perhaps >50 hop) system, only half of the hops are considered as fading.
A 99.999% per-hop reliability (320 SES/yr outage) objective (floor) is often assigned to spur links and short systems of less than about 5 tandem hops.
Although computed over the fade season, this is considered an annual outage compared, perhaps, to Bell System short-haul (<250 mile), Bell System long-haul (4,000 mile), or other end-user objective.
Rain Outage and Availability Objectives
The long-term rain outage in a microwave radio link (<10 GHz) is often engineered to this same 99.995% objective - now an annual two-way rain availability, not one-way multipath reliability, objective.
This corresponds to an ITU-R per-hop availability objective since the 60-hop 2500 km ITU-R reference circuit end-to-end two-way availability objective7 of 99.7% scales to 99.995% availability objective for a typical 40 km link.
The 1,600 SES/year outage objective for a system (one-way T1 trunk) may be over links making up a part or whole of a long-haul system, a short-haul system, or other distance.
While the following computations are for link(s) making up a full short- or long-haul system, the 1,600 end-to-end SES/year outage allocation may be proportioned only to the actual number of tandem hops in an actual system.
For example, 1600/20 = 80 SES/year (99.99975% path reliability) per-hop objective for a 20-hop digital microwave system.
The Bell System short-haul one-way T1/E1 trunk outage objective (at its 10-3 BER SES outage point) is defined as:
TShortHaul = (1600 * D) / 250
Where: TShortHaul = Short-haul one-way outage objective, SES/year
D = Total path length, miles
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For long-haul radio the overall objective is 99.98%. However, long-haul transmission models assume that half of the hops never experience significant fading. In practice, long-haul paths should have at least one protection channel, which is required for equipment protection and maintenance and is used to provide frequency-diversity protection.
The Bell System long-haul one-way outage objective is defined as:
TLongHaul = (1600 * D) / 2000 (Original)
TLongHaul = (1600 * D) / 4000 (Updated)
Where: TLongHaul = Long-haul one-way outage objective, SES/year
D = Total path length, miles
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In considering how to establish realistic outage or reliability objectives, several things need to be kept in mind. A single overall design objective for not more than X hours, minutes, or seconds outage over some period such as a year is an over-simplification. The character of the particular kind of outage and its effect on the system should be taken into account, and perhaps there should even be different objectives for different types of outage.
For example, propagation outages due to multipath fading are usually short. An outage of an hour per year due to multipath might represent 1,000 or more individual outages, each averaging 1 second or less (1 SES) on a properly engineered path.
On the other hand, propagation outages totaling an hour per hop due to rain attenuation might consist of four or five individual outages averaging 10 to 15 minutes each.
The effects of long-term and short-term system outages on message trunks are very different. Short-term "unreliability" outage events do not disconnect circuits nor reduce (in most circuits) data throughout. Long-term "unavailability" events cause both traffic disconnect and loss of data throughput.
A distinction should be made between communication circuits for which an outage of a few seconds or a few minutes is just a nuisance or an inconvenience, and circuits for which such an outage might result in danger to life, great economic loss, or other catastrophic consequences. The suitability or unsuitability of a rain-affected band such as 18 or 38 GHz could differ widely for these two situations.
Even if the maximum possible reliability and availability objectives are established and a path or a system is engineered to the full limit of the state-of-the-art, the probability of outage can never be eliminated but only reduced to a very low value. Thus it is imperative to make any ultra-important services as fail-safe as possible against a loss of the communications channel. Therefore, regardless of the degree of reliability, a system should be engineered so that if an outage does occur, it can be tolerated or at least its effects at kept within acceptable bounds.
It seems that in some cases, perhaps many cases, a more relaxed attitude might be taken toward rain-induced outages than toward multipath outages, or even equipment outages. In several respects, rain outage is somewhat benign in nature. If the fade margins are kept high and the paths are not stretched too much, even in less advantageous areas the numbers of outages per year should not be very large and the length of individual rain outages on a hop should only rarely exceed 5 to perhaps 10 minutes.
Short (less than 2 second) microwave outages, common on a typical longer diversity or a shorter non-diversity digital microwave link with adequate fade margin, will not drop any telephone or data lines. Such outages quickly clear with all circuits remaining connected an little note taken of these transient events.
Critical real-time, non-repeatable control or data blocks are usually sent over data circuits that have X.25, X.35, etc. error detection which requests a resend of interrupted data from far-end buffers. Longer outages associated with low fade margins, rain, etc. disconnect all subscribers and may block access to the digital link for at least 10 seconds after each long-term outage event. Such traffic disconnects are unacceptable to most users. These more vulnerable links cleanly require diversity or ring protection.
For high reliability links (usually in long-haul systems with many hops in tandem), the per-hop objective may approach or exceed 99.9999%, allowing only 20-30 seconds per-hop outage per year.
Short-haul systems, up to about ten hops, often have a per-hop design objective of about 99.9995%, for 160 SES/year outage. Spur legs or short systems with 2-5 hops may be designed for something on the order of 99.999% per-hop path reliability, equating to 320 SES (5.3 minutes) outage per year. Objectives such as these are typical of those used in telephone, utility, and public safety networks. For other services, even dramatically lowered path reliabilities may be acceptable, even approaching 99.99% or about 1 hour outage per year.
It is important to note that the path reliability formulas and methods are for calculating short-term one-way outage. To calculate two-way outage, it is necessary to double the calculated multipath outage.
Unavailability outages due to rain fading do not have to be doubled since they occur simultaneously in both directions of transmission and are always two-way.
The principal gaseous absorption is by oxygen and water vapor. The attenuation due to oxygen is relatively constant in the 2 to 14 GHz frequency range.
Water vapor absorption, on the other hand hand, is highly dependent on the frequency, as well as the density of the water vapor (absolute humidity8, in grams per meter-cubed).
The following simplified formulas from ITU-R Report 719-1 have been developed for the purpose of calculating the attenuating effect of oxygen and water vapor within an accuracy of +/- 0.2 dB when compared to later ITU-R models.
Aoxy = [(6.6 / (F2 + 0.33)) + (9.0 / (F - 57)2) + 1.96] * F2 * 0.001
Where: Aoxy = Attenuation due to atmospheric oxygen, dB/kilometer
F = Frequency, GHz
Awv = 0.067 + (2.4 / ((F - 22.3)2 + 6.6)) * F2 * Vp * 0.0001
Where: Awv = Attenuation due to atmospheric water vapor, dB/kilometer
F = Frequency, GHz
Vp = Water vapor density, gram/m3
7.5 gram/m3 is the ITU-R value for ground-level water vapor density
corresponding to 50% humidity at 61F (16C) or 75% humidity at 50F (10C)
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Absorption coefficient of oxygen and water vapor for a water vapor density of 7.5 gram/m3 and a pressure of 1 atmosphere (Altschuler and Marr [1988]). The attenuation by water vapor may be estimated from Liebe (1985) tabulations or through the Ulaby et al. (1981) equation.
Rain Attenuation
Heavy rainfall, usually in cells accompanying thunderstorm activity, has a great impact on path availability above 10 GHz in some areas, and this long-term (5-15 min) outage time causes traffic disconnects. Such long-term outage is never added to short-term multipath outage previously discussed.
Rain outage increases dramatically with frequency, and then with path length. Increased outage at 23 GHz can require a 2-to-1 reduction in path length compared to 18 GHz for a given availability, for example. Extended 10 to 15 minute duration fades to over 50 dB have been recorded on a 3 mile (5 km) 18 GHz path in Houston, Texas, for example. The predicted annual outage may not occur for years, and ten accumulate over a single rainy season for a long-term average.
Early studies, both theoretical and experimental, resulted from the recognition of the importance of rain in designing microwave paths with availability objective in excess of 99.9%.
In recent years the emphasis has been on establishing predictive techniques for the statistical estimation of the attenuation probability distribution for a particular path.
Robert K. Crane3 has developed a model for determining the attenuation due to rain based on several factors, including path length, frequency, and point rain rates. These have been incorporated into this analysis, with Crane's formulas in Perl:
if ($frq_mhz >= 500 && $frq_mhz < 2000) { if ($polar eq "Vertical") { $Kv_y1 = 0.0000352; $Av_y1 = 0.880; $Kv_y2 = 0.0001380; $Av_y2 = 0.923; $A = $Av_y1 + (($frq_mhz - 1000) / (2000 - 1000)) * ($Av_y2 - $Av_y1); $K = 10 ** (log10($Kv_y1) + (($frq_mhz - 1000) / (2000 - 1000)) * (log10($Kv_y2) - log10($Kv_y1))); } elsif ($polar eq "Horizontal") { $Kh_y1 = 0.0000387; $Ah_y1 = 0.912; $Kh_y2 = 0.0001540; $Ah_y2 = 0.963; $A = $Ah_y1 + (($frq_mhz - 1000) / (2000 - 1000)) * ($Ah_y2 - $Ah_y1); $K = 10 ** (log10($Kh_y1) + (($frq_mhz - 1000) / (2000 - 1000)) * (log10($Kh_y2) - log10($Kh_y1))); } .... up to 100 GHz $Do = 3.8 - (0.6 * log($rate)); $B = 2.3 * ($rate ** -0.17); $c = 0.026 - (0.03 * log($rate)); $u = (log($B * exp($c * $Do))) / $Do; $VAR_A = ((exp($u * $A * $Do) - 1) / ($u * $A)); $VAR_B = ((($B ** $A) * exp($c * $A * $Do)) / ($c * $A)); $VAR_C = ((($B ** $A) * exp($c * $A * $dist_km)) / ($c * $A)); $Ar = ($K * ($rate ** $A)) * (($VAR_A - $VAR_B) + $VAR_C);
Where: $Ar = Attenuation, dB, which is usually only calculated over an effective
rain path, and not the total link distance.
$rate = Rain rate, mm/hr
$dist_km = Path distance, km
$frq_mhz = Frequency, MHz
$K, $A = Multiplier and exponent variables, which
are based on frequency and polarization (horz./vert.)
but can be calculated for any angle.
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Crane Regression Coefficients for Estimating Specific Attenuation
Frequency (GHz) Kh Kv Ah Av 1 0.0000387 0.0000352 0.912 0.880 2 0.000154 0.000138 0.963 0.923 4 0.00065 0.000591 1.121 1.075 6 0.00175 0.00155 1.308 1.265 7 0.00301 0.00265 1.332 1.012 8 0.00454 0.00395 1.327 1.310 10 0.0101 0.00887 1.276 1.264 12 0.0188 0.0168 1.217 1.200 15 0.0367 0.0335 1.154 1.128 20 0.0751 0.0691 1.099 1.065 25 0.124 0.113 1.061 1.030 30 0.187 0.167 1.021 1.000 35 0.263 0.233 0.979 0.963 46 0.350 0.310 0.939 0.929 45 0.442 0.393 0.903 0.897 50 0.536 0.479 0.873 0.868 60 0.707 0.642 0.826 0.824 70 0.851 0.785 0.793 0.793 80 0.975 0.906 0.769 0.769 90 1.06 0.999 0.753 0.754 100 1.12 1.06 0.743 0.744 |
United States point rain rate distribution values (mm/hour) versus percent of year rain rate is exceeded. Information is from work done by Robert K. Crane:
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Rain Rate Notes
- Drizzle = 0.25 mm/hour
- Fog = 0.5 mm/hour
- Light rain = 1.0 mm/hour
- Moderate rain = 4.0 mm/hour
- Heavy rain = 16.0 mm/hour
- Thunderstorm = 35.0 mm/hour
- Intense thunderstorm = 100.0 mm/hour
A greatly simplified rain attenuation model has been provided in ITU-R Rep. 530. This highly simplified model lends itself to calculator methods of computation, and provides attenuation values comparable to most rain regions, but widely different in others.
Rain attenuation at the higher microwave frequencies (>10 GHz) has been under study for more than 50 years. Much is known about the qualitative aspects, but the problems faced by the microwave transmission engineer - who makes qualitative estimates of the probability distribution of the rainfall attenuation for a given frequency band, polarization, path length, and geographic (rain distribution rate) area - remains more difficult.
In order to estimate this probability distribution, instantaneous rainfall data is needed. Unfortunately, the available rainfall data is usually in the form of a statistical description of the amount of rain which falls at a given measurement point over various time periods - generally at least an hour in length.
The rain-induced attenuation along a given path at a given instant in time is a function of the integrated effect of the rainfall existing at all points along the path. Rain attenuation if affected not only by the total amount of water in the path at that instant, but also by its distribution along the path in volume and (rain) drop size. For heavy rain rates, the instantaneous distribution of volume and drop size along the path is highly variable and is difficult to predict with any sort of accuracy from the kind of rainfall data generally available.
One of the earliest and most comprehensive attempts at developing a workable prediction method was carried out by Bell Laboratories in the 1950s, and was described in a classic paper by Hathaway and Evans (1958). A method of predicting annual outages for microwave paths operating in the 11 GHz common carrier band as a function of path length, fade margin, and geographical area within North America was developed in this paper.
This study has proved to be a worthwhile prediction tool and, even considering its limitations, is still one of the best references available for microwave engineers working within the United States. Additional studies have been conducted in Europe and Asia. The combined information has been reviewed and published by Robert K. Crane for North America paths and internationally in the ITU-R Rec. P.837 recommendations.
Increasing the fade margins, shortening path lengths, and increasing antenna sizes are the most readily available tools for reducing the per-hop rain outage in a given area. Route diversity (ring protection) or a lower, less vulnerable frequency band is often considered.
The total annual rainfall in an area as little relation to the rain attenuation for the area. Within the U.S., for example, the northwestern states have the greatest annual rainfall (in excess of 100 inches/2500mm per year) produced, however, by long periods of steady rain of relatively low intensity at any given time.
Other areas of the country with lower annual rate experience thunderstorms and frontal squalls that produce short duration rain rates of extreme intensity. It is the incidence of rainstorms of this type that determines the rain rates for an area and thus the high frequency microwave link's long-term path outage ("unavailability") characteristics.
Even the rain statistics for a day or an hour have little relationship to rain attenuation. A day with only a fraction of an inch of total rainfall may have a path outage due to a short period of concentrated, extremely high intensity rain. Another path that has days with several inches of total rainfall may experience little or no path attenuation because the rain is spread over a long time period or area.
The most common reason a preference for lower frequencies is the susceptibility of bands above 10 GHz to rainfall attenuation. Although the effect is present to some degree at lower frequencies, it increases rapidly with frequency. For example, a raincell intensity causing only a few dB of attenuation at lower frequencies could be sufficient to cause a path outage at 18 GHz.
Although fades caused by raincells are occasionally observed at lower frequencies (10-20 dB fades at 6 GHz have been recorded even in North America), this type of fade generally causes outages only on paths above 10 GHz. The outages are usually caused by blockage of the path by the passage of raincells (thunderstorms, etc.), perhaps 2.5-5 miles (4-8 km) in diameter and 5-15 minutes in duration on the path. Such fading exhibits fairly slow, erratic level changes, with rapid path failure as the raincell intercepts the path. The fades are non-selective in that all primary and diversity paths in both directions are affected simultaneously.
Vertical polarization is far less susceptible to rainfall attenuation than horizontal-polarized frequencies.
Increased fade margins is of some help in rainfall attenuation fading; margins as high as 45 to 60 dB, some with Automatic Transmit Power Control (ATPC), have been used in some highly vulnerable links for increased availability. When permitted, seldom-used cross-band diversity is totally effective - the lower-frequency path is stable (affected only by multipath fading) during periods when the upper-frequency path is obstructed by raincells. Route diversity (ring-protected paths separated by more than 5 miles/8 km) is also used successfully.
In summary, things to bear in mind in connection to rain attenuation fades are:
- Multipath fading is at its minimum during periods of heavy rainfall (cooler weather) with well aligned dishes, so the entire path fade margin is available to combat the rain attenuation (wet radome loss effects are minimized with shrouded antennas).
- Neither space diversity nor in-band frequency diversity provides any improvement against rain attenuation.
- Vertically-polarized microwave link rain outage is 40-60% less than with horizontal polarization.
Here is an online rain attenuation calculator which gives results similar to the Crane rain model.
Polarization
Advantages of vertical polarization:
- Vertically polarized waves are less affected by aircraft flying over the transmission path than are horizontally polarized waves.
- Vertically polarized antennas are more efficient for transmission over sea water at frequencies lower than 100 MHz. Ordinary line-of-sight antennas, less than 45 to 50 feet (15 meters) high, work best when vertically polarized. At higher frequencies, there is little difference in performance.
- Over water paths at frequencies above 3 GHz, it is advantageous to choose vertical polarization.
Advantages of horizontal polarization:
- Horizontal antennas are less likely to pick up man-made electrical interference such as that which comes from power lines and transformers. Such interference is usually vertically polarized.
- In fairly dense forests, horizontally polarized waves suffer less loss than vertically polarized waves. Also, standing wave effects are not as pronounced with horizontal polarization. Standing wave effects can cause great variation in the field strength of vertically polarized waves when antennas are moved among trees or buildings.
- In very dense jungles, there is no advantage in either type of polarization. Performance is poor in this environment for all types of polarization.
Notes
The World Geodetic System 1984 (WGS84) and the North American Datum of 1983 (NAD83) are both spatial reference systems used in North America. They were originally identical, but have since diverged and are now about 1-2 meters apart:
Purpose: WGS84 tracks the center of mass of the Earth, while NAD83 tracks the movement of the North American tectonic plate.
Ellipsoid: WGS84 uses the WGS 84 ellipsoid, while NAD83 uses the Geodetic Reference System (GRS80) ellipsoid.
Ground-based network: NAD83 has a ground-based horizontal control network, while WGS84 does not.
GPS: WGS84 is the default system used by the Global Positioning System (GPS).
Use: NAD83 is the national reference system used by most federal and provincial/state agencies in Canada and the U.S.
GIS, mapping, and CAD software are generally capable of transforming between the two datums, but the default is to treat WGS84 equal to NAD83. This can lead to shifted data, so it's important to intentionally set up the software packages to handle the transformation.