microwave radio system performance calculation
TRANSCRIPT
= Confidential =
MICROWAVE RADIO SYSTEM
SYSTEM PERFORMANCE CALCULATION
PROCEDURE
(According to ITU-R P.530-8)
NEC Corporation
1. Quality of a Microwave Link
For a well-designed path which is not subject to diffraction fading or surface reflections, multipath propagation is the dominant factor in fading below 10 GHz. Above this frequency, the effects of precipitation tend increasingly to determine the permissible path length through the system availability objectives. In principle, the necessary reduction in path length with increase in frequency, reduces the severity of multipath fading. These two main causes of fading are normally mutually exclusive.
ITU defines both “error performance objective” and “availability” to represent the quality of a microwave link. Their related terms are defined in the recommendations ITU-T G.826, ITU-R F1491, and ITU-R F1493. Following is a brief description of them.
The error performance events defined are
ES (Errored second): a one second period during which one or more EB’s (errored block) occurs.
SES (Severely errored second): a one second period during which 30% or more of EBs occurs.
BBE (Background block error): an errored block not occurring as part of SES.
Error performance parameters defined are severely errored second ratio (SESR), background block errored ratio (BBER), and errored second ratio (ESR). It is generally agreed that SER and BBER will also be satisfied once SESR meets the objective. The error performance objective of SESR is used and is defined as follows.
Long haul
Rate(Mbps)
1.5 to 5 5 to 15 15 to 55 55 to 160 160 to 3500
Severely errored second ratio (SESR)
0.002 A 0.002 A 0.002 A 0.002 A 0.002 A
where A = (A1 + 0.01) Llink / 500 for 50 km ≦ Llink ≦ 500 km
A = A1 + 2 10-5 Llink for Llink > 500 km
A1 is provisionally been agreed to be in the range of 1% to 2%.
Short haul
Rate(Mbps)
1.5 to 5 5 to 15 15 to 55 55 to 160 160 to 3500
Severely errored second ratio (SESR)
0.002 B 0.002 B 0.002 B 0.002 B 0.002 B
Where B is provisionally been agreed to be in the range of 7.5% to 8.5%. B = 0.075 is used unless otherwise specified by the customer.
Access
Rate(Mbps)
1.5 to 5 5 to 15 15 to 55 55 to 160 160 to 3500
Severely errored second ratio (SESR)
0.002 C 0.002 C 0.002 C 0.002 C 0.002 C
Where C is provisionally been agreed to be in the range of 7.5% to 8.5%. C = 0.075 is used unless otherwise specified by the customer.
Note that A1% + B% + C% shall not exceed 17.5%, while B% + C% shall be in the range of 15.5% and 16.5%.
For example, error performance objective for SDH (155 Mbps, link: 50 km) = 0.02 (0.01 + 0.01) 50 / 500 60 60 24 30 = 10 sec/month.
A path fails to satisfy this Recommendation if any parameter exceeds the allocated objective in either direction at the end of the given evaluation period. The suggested evaluation period is 1 month.
On the other hand, “availability” is the ratio of the time that the link is available to the total time. This serves as a guideline to the service that can be expected on average over a period of one year. Table 2.1 shows how percentage availability relates to outage time per year.
Availability Outage Time Outage per year
99.9% 0.1% 9 hours
99.99% 0.01% 1 hour
99.999% 0.001% 5 minutes
99.9999% 0.0001% 30 seconds
Table 2.1 Link Availability and outage time
Availability is largely a function of fade margins and the amount of signal fading and is best determined by field measurement. The availability parameters defined are
UR (Unavailability Ratio): unavailability of a 3000S system may be due to propagation effects, equipment failures, human intervention and interference or other causes.
AR (Availability Ratio): AR = 1 – UR. If a period of SES occurs that is longer than 10 consecutive seconds, the system will change from an available state to an unavailable state. To change back to available, it requires a period of 10 consecutive seconds with non-SES.
The availability objective is defined as follows.
AR = 1- (Bj Llink / LR + Cj) where
j: section of national portion, j = {1 = access network, 2 = short haul, 3 = long haul}
LR: reference length = 2500 km.
The lower limit of Llink used to scale the objectives is Lmin = 50 km.
Access portion Short haul portion Long haul portion
B1 C1 B2 C2 B3 C3
0 5 10-4 0 4 10-4 3 10-3
for 250 km≦ Llink < 2500 km
1.9 10-3
for 50 ≦ Llink
< 250km
0for 250km ≦ Llink < 2500km
1. 10-4
for 50 ≦Llink < 250km
For example, availability objective for SDH (155 Mbps, link: 50 km) = 1 – (1.9 10-3 50 / 2500 + 1.1 10-4) = 0.999852. Therefore, unavailability = (1-0.999852) 60 + 24 365 = 77 min/year.
It is stated in ITU-R F1093 that, given the split between availability and error performance objectives, precipitation effects contributes mainly to unavailability and multipath propagation mainly to error performance.
For the purpose of designing a radio network, NEC has adopted the following approaches to measure its equipment against the criteria set forth above.
1. Total Outage Probability
The total outage probability that is specified in ITU-R P.530-8 is calculated against the error performance objectives.
If diversity techniques are not employed, the total outage probability is the sum of the probability of outage due to non-selective frequency fading, the
probability of outage due to selective frequency fading, and the probability of outage due to XPD (cross polar discrimination).
If diversity techniques are employed, the total outage probability is the sum of the probability of outage when frequency diversity is used, the probability of outage when space diversity is used, the probability of outage when both space and frequency diversity are used with 2 receivers, and the probability of outage when both space and frequency diversity are used with 4 receivers.
2. Rain attenuation
For the system at frequency above 10 GHz (above 6 GHz if rain intensity is higher than 100 mm/h), rain attenuation has to be considered. The outage probability due to rain attenuation that is specified in ITU-R P.530-8 is calculated against the availability objectives.
However, NEC and TEKOMSEL agreed that the outage probability due to rain attenuation is also calculated against the error performance objectives.
2. Link Budget Analysis
Fade Margin
A signal degrades as it moves through free space – in other words, the loss would occur in a region, which is free of all objects that might absorb or reflect radio energy. It is calculated for miles or kilometers using one of the following formulas.
Lfs = 96.6 + 20*log10 F + 20* log10 D where
Lfs = free space loss in dB
F = frequency in GHz
D = path length, in miles
or
Lfs = 32.4 + 20*log10 F + 20* log10 D where
Lfs = free space loss in dB
F = frequency (GHz)
D = path length, in kilometers
Free space loss can also cause data errors referred to as inter-symbol interference (ISI). It is essential to provide adequate link margin to overcome this loss. The amount of extra RF power radiated to overcome this phenomenon is referred to as fade margin. Fade margin is one of the more important factors in determining the availability of the microwave link. The higher the fade margin, the more reliable the link is. The two main events that cause the desired signal to fade are multipath clear air fading (flat fading) and rain fading. Rain fading will be discussed in section 1.6. Here,
Flat fade margin = Receive signal level – Receiver sensibility threshold
At first, a very important step in the link budget is to determine the minimum signal strength required at the receiver input to successfully receive a signal. It is referred to as receiver sensibility threshold (Prx) and is denoted in dBm. It is a function of modulation technique, which dictates the required system bandwidth, and thus contributes to the noise power, and the desired BER.
Receiver Signal Level (RSL) is the expected strength of a signal when it reaches the receiving radio. It can be calculated as follows.
Receiver Signal Level = Ptx – Ltx + Gtx – Lfs + Grx – Lrx
Ptx: transmitter output power
Lfs: free space path loss
Gtx: transmitter antenna gain
Grx: receiver antenna gain
Ltx: transmitter feeder loss
Lrx: receiver feeder loss
Note that RSL does not account for antenna alignment errors or path fading phenomena, such as multipath reflections, signal distortions, variable atmospheric conditions, and obstructions in the path.
In addition, system gain is obtained through the following formula:
System Gain = Ptx – Prx
Ptx: transmitter output power
Prx: receiver sensibility threshold
Propagation Loss
In the design of line-of-sight radio relay system, in addition to the free space loss mentioned above, the transmitted signal suffers other types of path loss as it propagates through the air. They are
Fading due to multipath arising from surface reflection; Attenuation due to atmospheric gases; Diffraction fading due to obstruction of the path by terrain obstacles; Attenuation due to precipitation;
Radio signals are reflected over smooth surfaces, such as a body of water, a flat stretch of earth, or a metal roof that they cancel out the direct signal and bring down the radio link. See figure below.
To avoid such failure, a path should be designed so that the reflected signal is dispersed by an uneven surface before it reaches the receiver and cancels out the direct wave. Reflection Point analysis will quickly determine, for example, whether there is a significant risk of signal destruction due to reflection off the terrain and where such areas are likely to be. Armed with such information, the System Designer can avoid site deployment in those areas, or in extreme cases, take special precautions to minimize the deleterious effects. Typically, this may take the form of adjusting the height or changing the position of one or both of the antennas to deliberately shift the reflection point from the area of risk to another, less problematic point along the link path.
Attenuation due to Atmospheric Gases
Combinations of irregularities and fluctuations in atmospheric temperature, humidity, and pressure cause more than one and often many propagation paths to exist between the transmitting antenna and the receiving antenna. As the atmospheric conditions vary, the routes and distances of paths also vary, causing signals of differing phases and amplitudes to arrive at the receiving antenna at the same instant.
The attenuation on a path of length d (km) is given by
Aa = a * d where
a = 0 + w
0: attenuation due to dry air absorption
w: attenuation due to water vapor; 0 and w values can be obtained in ITU-R P676. Note that for frequency below 10GHz, the 0 and w values are small enough that they can be disregarded. For frequency higher than 10GHz these values are significant and should be taken into account in the propagation loss calculation.
Diffraction Fading
Diffraction is a propagation phenomenon that allows radio waves to propagate beyond obstructions via secondary waves created by the obstruction. This type of fading is the factor that determines the antenna height. In other words, by allowing sufficient clearance from obstacles along the path, correct performance of the link can be assured. Clearance requirements are usually stated as a combination of a percentage of the first Fresnel zone radius and a K factor (the ratio of the effective Earth radius to the actual Earth radius). For example, a common requirement is that 100% of the first Fresnel zone radius should be clear of all obstructions at a K factor of 4/3.
Figure 2.1 Fresnel zone for a radio link
In Figure 2.1, what is called Fresnel zone is shown. It is the volume of space enclosed by an ellipsoid, which has the two antennas at the ends of a radio link at its foci. When the ellipsoid just touches the tip of the diffracting object as demonstrated at point C, such area is occupied by the strongest radio signal and is called the First Fresnel Zone.
The following formula is used to calculate the path clearance of the First Fresnel Zone.
h (in meter) = 17.3 (d1 * d2 / f * ( d1 + d2))1/2 where
f = frequency (GHz)
d1 = path length between A and C, in kilometers
d2 = path length between B and C, in kilometers
or
h (in feet) = 72.1 (d1 * d2 / f * ( d1 + d2))1/2 where
f = frequency (GHz)
d1 = path length between A and C, in miles
d2 = path length between B and C, in miles
A general rule of thumb is that the link is very close to the free space value if 60% of the First Fresnel Zone is clear of obstructions. However, different countries with the different climate may specify a more precise value. For example, Radio Agency in UK specifies 0.577F1 for minimum path clearance.
Example. We have a 10 km LOS path over which we wish to establish a link in the 13 GHz band. The path profile indicates that the highest point on the path is 3 km from one end, and the direct path clears it by about 5 meters (16.4ft) – do we have adequate Fresnel zone clearance?
From the equation above, with d1 = 3 km, d2 = 7 km, and f = 13 GHz, we have h = 6.95 m for first Fresnel Zone clearance. A clearance of 5 m is about 71% of this, so it is sufficient to allow negligible diffraction loss.
Note that for the zero clearance, which is at a position level with the top of the obstacle, the signal power density is down by some 6 dB. If
necessary, this could be overcome with, for example, an additional 3 dB of antenna gain at each end of the link.
Therefore, the effective value of K-factor, which is obtained in accordance with the path length, and the Fresnel zone clearance radii are the essential elements in determining the antenna height.
In addition, when planning for paths longer than seven miles, the curvature of the earth might become a factor in path planning and require antenna be located higher off the ground. The additional antenna height needed can be calculated using the following formula:
h = d2 / 8 where
h = height of earth bulge (in feet)
d = distance between antennas (in miles)
Therefore, the minimum antenna height at each end of the link for paths longer than seven miles (for smooth terrain without obstructions) needs to take into account path loss due to both diffraction fading and earth bulge.
Flat Fading
When multiple copies of the transmitted signal arrive at the receiver via different path, “multipath” effect occurs. Since each arriving wave can combine destructively or constructively depending on their phase, multipath propagation causes certain areas to have low signal power and vice versa. This is known as multipath fading, which can be categorized as either flat fading or frequency selective fading.
In the case of flat fading, the received signal spectrum remains a close replica of the transmitted signal spectrum except for a change in amplitude. It is also referred to as non-frequency selective fading. Flat fading occurs when the Root Mean Square delay spread of the channel is much smaller than the symbol period of the transmitted signal. According to ITU-R 530-8, the method for predicting the percentage of time (PW) that fade margin (A) corresponding to a specified bit error ratio (BER) is exceeded in the average worst month is as follows
PW (%) = K d3.6 f0.89 (1 + |p|)-1.4 10-A/10 where
d: path length in km
f: frequency in GHz
K, referred to as geoclimatic factor is derived as follows in the case of inland links. The definition of inland links and coastal links of various types are defined in pp. 130-131 of the ITU-R P.530-8 recommendation.
K = 5.0 * 10-7 * 10-0.1(C0 – CLat – CLon) * PL1.5 where
CoAltitude of lower antenna and type of link terrain Co (dB)
Low altitude antenna （0 – 400m）- Plains 0
Low altitude antenna （0 – 400m）- Hills 3.5
Medium altitude antenna （400 – 700m）- Plains 2.5
Medium altitude antenna （400 – 700m）- Hills 6
High altitude antenna （> 700m）- Plains 5.5
High altitude antenna （> 700m）- Hills 8
High altitude antenna （> 700m）- Mountains 10.5
Where the type of terrain is unknown, the following values are used.
Altitude of lower antenna (in the range above mean sea level) Co (dB)
Low altitude antenna （0 – 400m） 1.7
Medium altitude antenna （400 – 700m） 4.2
High altitude antenna （> 700m） 8
CLatlatitude CLat (dB)
Latitude ≤ 53°N or 53°S 0
53°N or 53°S < Latitude < 60°N or 60°S -53+ Latitude
Latitude ≥ 60°N or 60°S 7
CLonlongitude CLon (dB)
Europe and Africa 3
North and South America -3
All others 0
The value of the climatic variable PL is estimated by taking the highest value of the –100N units/km gradient exceedance from the maps for the four seasonally representative months of February, May, August and November in Figure 7 to 10 of recommendation ITU-R P.453. An exception to this is that only the maps for May and August should be used for latitude greater than 60°N or 60°S.
Path inclination p is calculated as
|p| (mrad) = |ht – hr| / d where
d: path length in km
ht, hr: antenna height in meters above sea level
Thereafter, the probability of outage Pns due to the non-selective component of the fading is Pns = PW / 100. Note that the outage probability is here defined as the probability that BER is larger than a given threshold.
Frequency Selective Fading
When the RMS delay spread of the channel is more than about 10% of the symbol period, the wireless channel alters the received signal spectrum. This is referred to as frequency selective fading. In frequency selective fading, the channel is dispersive and the received waveform has intersymbol interference (ISI). Note that unlike analogue systems, an increase in fade margin will not improve the performance of digital
system due to frequency selective fading. The outage probability is here defined as the probability that BER is larger than a given threshold. According to ITU-R 530-8, the method for predicting the selective outage probability is as follows.
Ps = 2.15η (WM 10-BM
/20 τm2 / |τr, M| + WNM 10-BNM / 20 τm
2 / | τr, M|)
: Multipath activity parameter = 1 - exp(-0.2 * Po0.75)
Po : Multipath occurrence factor = Pw (%) /100, A = 0
m: mean time delay = 0.7 * (d / 50)1.3 (ns)
d : Propagation Distance (km)
Wx: Signature width (GHz)
B M: Minimum signature (phase notch) depth (dB)
B NM: Non-minimum signature (phase notch) depth (dB)
r, x : Reference delay (ns) used to obtain the signature, with x denoting either minimum phase (M) or non-minimum phase (NM) fades.
Techniques for Alleviating Propagation Effects
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.
Techniques without Diversity
In order to reduce the effects of multipath fading without diversity there are several options that can be employed. The guidance is divided into three groups: reduction of the levels of ground reflection, increase of path inclination, and reduction of path clearance.
Link should be sited where possible to reduce the level of surface reflections thus reducing the occurrence of multipath fading and distortion. One of the techniques is to tilt the antenna slightly upwards. A trade-off must be made between resultant loss in antenna directivity and the improvement in multipath fading conditions.
Increase of path inclination is known to reduce the effects of beam spreading, surface multipath fading and atmosphere multipath fading. Therefore, 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 to improve multipath effect is less known. However, for the space diversity configuration one antenna might be positioned with low clearance.
Diversity Techniques
Diversity is a technique to reduce the effect of fading by selecting or combining the outputs of two or more receivers which has less correlation than each other in terms of the quality of received signals. Diversity techniques include space and frequency diversity. Frequency diversity should be avoided whenever possible simply because of limited availability of valuable radio frequency resources together with the increasing demand for transmission capacity in public networks.
Space Diversity
When two antennas are placed more than a wavelength or so apart, correlation factor between the two received signals can be reduced and the diversity can be increased. The only tradeoff is the physical placement of another antenna. The outage probability for a space diversity system is calculated as follows.
Step 1:
Calculate the square of non-selective correlation coefficient,
kns(s)2 = 1 – Ins * Pns /
Pns: Outage Probability due to flat fading
: Multipath activity parameter = 1 - exp(-0.2 * Po0.75)
Ins(s): Vertical space diversity improvement factor
Ins(s) = {1 – exp (-3.34 * 10-4 S 0.87 f –0.12 d 0.48 Po -1.04)} * 10 (A – V) / 10
A: Fading margin
Po: Pw * 10A/10 / 100 fading occurrence factor
Pw: percentage of time fade depth A is exceeded in the
average worst month
S: Vertical separation (Centre to Centre) of receiving antennas
f: Frequency (GHz)
d: Path length (km)
V : |G1 – G2|
G1, G2: gains of two antennas (dBi)
Step 2:
Calculate the square of selective correlation coefficient, ks(s)2
0.8238 for rw ≦ 0.5
ks(s)2 = 1 – 0.195 (1 – rw) 0.109 – 0.13 log (1-rw) for 0.5 < rw ≦ 0.5
1- 0.3957 (1 – rw) 0.5136 for rw > 0.9628
where the correlation coefficient of the relative amplitudes is
rw = 1 – 0.9746 (1 – kns(s)2) 2.170 for kns(s)
2 ≦ 0.26
= 1 – 0.6921 (1 – kns(s)2) 1.034 for kns(s)
2 > 0.26
Step 3:
Calculate non-selective outage probability for space diversity
Pdns = Pns / Ins(s)
Step 4:
Calculate selective outage probability for space diversity
Pds = Ps2 / { (1 – ks(s)2)}
Ps: outage probability due to dispersive fading
: Multipath activity parameter = 1 - exp(-0.2 * Po0.75)
Step 5:
Total outage probability due to space diversity is
Pd(s) = (Pds 0.75 + Pdns 0.75) 1.33
This equation is good for both 1+0 with SD and hot standby with SD systems.
Frequency Diversity
To increase the frequency diversity one could send half of the symbol energy in one frequency band and the other half in another band. By doing this the probability that both frequency bands are heavily faded is less than if there is only one frequency, therefore the probability of guessing a correct symbol at the receiver can increase. The drawback of frequency diversity is that more bandwidth is needed to transmit the same amount of information.
The outage probability for a frequency diversity system Pd(f) is calculated using the same procedure as for space diversity except that in Step 1 I ns(f) is calculated differently.
Ins(f) = 80 / f * d (Δf / f) * 10 F/10
Δf: Frequency Separation (GHz) If Δf > 0.5 GHz, use Δf = 0.5
f: carrier frequency (GHz)
d: path length (km)
F: Flat fade margin
This equation is good for 1+1, Twin-path, N+0 and N+1 systems.
Space and Frequency Diversity with 2 receivers (Pd(s,f))
Step 1:
The non-selective correlation coefficient is found from
kns =kns(s) * kns(f) where kns(s) and kns(f) are the non-selective correlation coefficients computed for space diversity and frequency diversity respectively.
The next steps are the same as those for space diversity.
Space and Frequency Diversity with 4 receivers
Step 1:
Calculate the diversity parameter mns
mns =3 * (1 - kns(s)2 ) * (1 – kns(f)
2)
Step 2:
Calculate the non-selective outage probability employing SD and FD
Pdns = Pns4 / mns
Pns: outage probability due to flat fading
Step 3:
Calculate the square of the equivalent non-selective correlation coefficient kns
2
kns2 = 1 – 0.5 * (1 - kns(s)
2 ) * (1 – kns(f) 2)
Step 4:
Calculate the square of selective correlation coefficient, Ks2 using the same procedure as for space diversity in Step 2.
Step 5:
Selective outage probability with SD + FD is calculated as follows.
Pds = { Ps2 / (1 – ks
2)} 2
Ps: Outage Probability due to dispersive fading
: Multipath activity parameter = 1 - exp(-0.2 * Po0.75)
Step 6:
Total outage probability (Pd4(s,f)) is calculated using the same procedure as for space diversity Step 5.
Total outage probability using diversity techniques
Pd = Pd(s) + Pd(f) + Pd(s,f) + P4d(s,f)
XPD Deterioration
Electromagnetic waves are vector quantities, i.e. they are polarized. The preferred (desired) polarization radiated by an antenna is termed co-polarization; the orthogonal polarization is termed cross-polarization. If
polarization can be made pure enough, orthogonally polarized waves can travel together without interference and be separated by properly designed receiving antennas. The ability of antennas to discriminate in this manner is measured by the cross-pol ratio, or polarization isolation and, is called Cross Polarization Discrimination (XPD). For example, transmitting two OC3 signals on the same frequency pair by using opposite polarity can increase XPD, and thus double system capacity.
However, due to the combined effect of multipath and cross-polarization patterns, the XPD can also deteriorate sufficiently to cause co-channel interference and, to a lesser extent, adjacent channel interface for small percentage of time. The reduction in XPD can occur during both clear-air and precipitation conditions and should be dealt with separately. The prediction of outage due to precipitation will be discussed in section 3.12. The calculation of outage due to clear-air effect is as follows.
Step 1:
XPDg + 5 for XPDg ≦ 35
XPD0 =
40 for XPDg > 35
where XPDg is the NEC’s guaranteed minimum XPD at bore sight for both the transmitting and receiving antennas.
Step 2:
Next evaluate the multipath activity parameter. Refer to section 3.6.4.
Step 3:
Determine the parameter Q
Q = -10 * log ( kxp x η / Po)
where
0.7 for one transmit antenna
kxp =
1 – 0.3 * exp { -4 * 10-6 * (st / λ)2} for two transmit antenna
Po : Multipath occurrence factor = Pw (%) /100, A = 0
In the case where two orthogonally polarized transmissions are from different antennas, the vertical separation is st (m) and carrier wavelength is λ (m).
Step 4:
Derive the parameter C from
C = XPDo + Q
Step 5:
The probability of outage Pxp due to clear-air cross polarization can be calculated from
Pxp = P0 * 10 – M XPD / 10
Po : Multipath occurrence factor = Pw (%) /100, A = 0
C - Co / I without XPIC
XPD margin M XPD =
C - Co / I + XPIF with XPIC
Co / I : carrier to interference ratio for a reference BER
XPIF : laboratory-measured cross-polarization improvement factor
(XPIF for PASOLINK series 64QAM is 18 dB, 128QAM is 20dB).
Rain Attenuation
The attenuation becomes significant as the size of the raindrops becomes comparable to the wavelength of the signal. Rain attenuation increases as raindrops become larger, more frequent, and the frequency of the link becomes higher (the wavelength becomes smaller). Typically, rain outages are only a concern in frequency bands above 10 GHz.
Step 1:
Obtain the rain rate R0.01 exceeded for 0.01% of the time. If not available, an estimate can be obtained from the information given in ITU-R P.837.
Step 2:
Compute the specific attenuation γR (dB/km)
γR = kRα (dB/km) where
R= R0.01 (mm/h)
k = [kH + kV + (kH – kV)cos2 cos2] / 2
= [kH H + kVV + (kH H – kVV) cos2cos2] / 2k
is the path elevation angle ( = 0 in most severe case)
is the polarization tilt angle relative to the horizontal.
( = 0 for horizontal polarization and = 90 for vertical polarization)
kH, kV, H, and V is listed in Table 1 of ITU-T P.838-1.
Step 3:
Compute the distance factor
r = 1 / (1 + d / do)
d : effective path length
do = 35 exp (-0.015 * R0.01) for R0.01 ≦ 100 mm/h
do = 35 exp (-1.5) for R0.01 > 100 mm/h
Step 4:
An estimate of the path attenuation exceeded for 0.01% of the time is given by:
A0.01 =γR * deff =γR * d * r (dB) where
γR : kRα (dB/km)
d : effective path length
γ: 1 / (1 + d / do)
Step 5:
For the links located in the latitudes equal to or greater than 30˚, the attenuation exceeded for other percentage of time in the range of 0.001% and 1% may be deducted from the following.
Ap / A0.01 = 0.12 * p - (0.546 + 0.043 log10
p) where
p = { -0.546 + {(0.298116 – 0.172 * log {Ap / (0.12 * A0.01)} 0.5 ) / 0.086 (%)
This formula has been determined to give factors of 0.12, 0.39, 1 and 2.14 for 1%, 0.1%, 0.01% and 0.001% respectively.
Step 6:
For the links located in the latitudes below 30˚, the attenuation exceeded for other percentage of time in the range of 0.001% and 1% may be deducted from the following.
Ap / A0.01 = 0.07 * p - (0.855 + 0.139 log10
p) where
p = { -0.855 + {(0.731025 – 0.556 * log {Ap / (0.07 * A0.01)} 0.5 ) / 0.278 (%)
This formula has been determined to give factors of 0.07, 0.36, 1 and 1.14 for 1%, 0.1%, 0.01% and 0.001% respectively.
Step 7:
If worst-month statistics are desired, calculate the annual time percentages p corresponding to the worst-month time percentages pw
using climate information specified in ITU-R P.841.
pw = (p / 0.3) 1/ 1.15 (%)
Prain is the percentage of time that rain attenuation exceeds flat fade margin for the specified BER in the average year.
prain = (p / 100)
The reduction of XPD during precipitation affects the total availability of the system and should be taken into account in outage calculation.
Step 1:
Determine the path attenuation, A0.01 exceeded for 0.01% of the time from equation (41).
Step 2:
Determine the equivalent path attenuation, Ap
Ap ＝ 10 ((U – Co / I + XPIF) / V) (dB)
U ＝ Uo + 30 x log f (dB)
ｆ = Carrier Frequency （GHz）
Uo＝15 dB
Co / I : carrier to interference ratio at reference BER
XPIF: laboratory-measured cross-polarization improvement factor （8dB if 64QAM is used; 20dB if 128QAM is used.）
If XPIC is not used, XPIF = 0
V(f) = 12.8 x f 0.19 for 8 ≦ f ≦ 20GHz
V(f) = 22.6 for 20 < f ≦ 35GHz
Step 3:
Determine the following parameters m and n:
23.6 x log ( Ap / 0.12 x A0.01 ) if m ≦ 40
m =
40 Otherwise
n ＝ ( -12.7 + (161.23 – 4 x m )0.5 ) / 2 - 3 ≦ n ≦ 0
Step 4:
PXPR = 10 (n – 2)
Total Outage Probability
The total outage probability due to clear-air effects is calculated from
Pns + Ps + PXP
P t =
Pd + PXP if diversity is used
The total outage probability due to rain is calculated from taking the larger of Prain (outage probability due to precipitation) and PXPR (outage probability due to precipitation in the case of XPD).
The outage prediction methods given for digital radio systems have been developed by ITU from a definition of outage as BER above a given threshold. The outage due to clear-air effects is apportioned mostly to performance and the outage due to precipitation, predominantly to availability.
Interference Assessment
Longer multipath delay spreads have another consequence: overlap of received data symbols with adjacent symbols, known as intersymbol interference (ISI).
The most usual types of interference for microwave systems are co-channel interference and adjacent channel interference. The cause of it can be either external, or within the system.
Co-channel Interference
Co-channel interference is caused by other signal residing at the same frequency as the desired signal.
Digital modulations such as 64 QAM, 16 QAM, and QPSK require significantly different specifications with respect to signal to noise and co channel interference. For example, in the modulation characteristics of 64QAM, it requires a co-channel interference rejection of at least 32.6dB. This means that to prevent receive sites from having interference generated within the system at the point of transmission, the antennas must have more than 32.6dB of transmit power. On the other hand, the same station operating at QPSK would only require an antenna with 19.6dB of rejection in the opposite station.
It is imperative to co-ordinate with all other neighboring links to allow minimal physical separation from each other to avoid co-channel interference from nearby RF equipment that operates at the same frequency. In this case, interference to and from the proposed link is assessed taking into account the path profile between the two stations.
Use is made of antenna radiation patterns to obtain the gain of antennas in the direction of unwanted signals.
Adjacent Channel Interference
Adjacent channel interference is caused by RF leakage on the operational channel from a neighboring RF equipment using an adjacent frequency. This can occur when an adjacent channel user is operating in close proximity to the user’s receiver, or when the user's signal is much weaker than that of the adjacent channel user.
Imperfect receiver filters which allow nearby frequencies to leak into the passband. A near-far effect could happen if near-by transmitter captures receiver in wrong band. To cure this problem, better filtering, sufficient guard band, clever channel assignment and maximize frequency separation between channels are the few techniques used today.
Interference Limits
The interference limits are derived as follows.
Interference limit = Reference sensibility for BER (=10-6) – D/U ratio.
The maximum co-channel and adjacent channel interference limits, at the receiver input, from a single unwanted source should be available at the local RF authority.
EIRP
What makes RF equipment work is to deliver RF signal over the air to the opposite station, which can recover and restore the signal back to its original form. That means at the receiver, a certain level of input signal strength has to be maintained while the signal traveled through the air.
Effective (Equivalent) Isotropically Radiated Power (EIRP) is the measured power of a radio signal radiating from a transmitter antenna 'as if it were radiating from a point-source uniformly in all directions' (isotropic). EIRP calculation is important as it is related to possible undue interference to the adjacent channel, which is used by other operators. Determining the amount of power the radio uses to transmit and receive signals also relates to operating costs. It represents the combined result of the transmitter's RF power plus any antenna gain (any focusing of the power), as compared to a radiating antenna (with no reflector) in space. It is calculated as follows.
EIRP = RSL + Lrx– Grx + Lp
RSL: Receiver signal level
Lrx = Receiver feeder loss
Grx = Receiver antenna gain
Lp = Path loss
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