Microwave System Equations

Q: How is microwave reliability and outage time computed?

Q: Several types of equations are used for microwave calculations. These are described below:

Free Space Loss

The free space loss is computed based on the path length and frequency using the equation:

(1) A = 96.6 + 20 LOG(F) + 20 LOG(D)

where:

Rain Attenuation

The rain attenuation due to rainfall can be entered directly or computed by several different methods (see Ryde & Ryde, Medhurst, and CCIR).

When you direct TAP to calculate rain attenuation, you will enter a rainfall rate (in either inches or millimeters per hour) and the portion of the path affected by rain attenuation entered in the current units (miles or kilometers), or as a percentage of the total path.

After entering all of the required values, the attenuation values computed for the three models are displayed. When you select the desired value and return to the microwave link budget program the selected attenuation is incorporated in the fade margin and reliability calculations performed in this program.

TAP keeps track of the source of the rain attenuation value. If you accept the Medhurst value as described above, the Loss Mode will be marked "MED" in the link budget program to remind you of the attenuation model used to generate attenuation. However, if you enter any value directly, the mode will be marked "SPEC" (for specified).

Atmospheric Absorption

The loss from atmospheric absorption can be entered directly or computed by pressing the "Calculate Loss" button for the Absorption Loss field.

Absorption loss is computed as a function of the frequency using the complete length of the path. The loss value is determined from curves based on van Vleck (1947), providing separate values for and water vapor losses. The absorption loss is the sum of these two losses.

Terrain/Humidity Factor

The terrain and humidity factor used in the reliability calculation can be entered directly, or the value can be computed from humidity and terrain roughness information.

Lenkurt (1970) suggests the following values:

The terrain and humidity factor can be computed using the formula (from Roelofs, 1986):

(2) a = K x (W/50)-1.3

where:

(3) W =

where:

TAP keeps track of the source of the terrain/humidity value. If you calculate the value as described above, the Loss Mode will be marked "CALC". However, if you enter any value directly, the mode will be marked "SPEC" (for specified).

Climate Factor

The climate factor used in the reliability calculation can be entered directly or computed from average annual temperature information.

Lenkurt suggests the following values:

The climate factor can be computed using the formula (from Roelofs):

(4) B = T/50 x 3/12

where:

If you calculate the value as described above, the value will be marked "CALC" on printed output, and the temperature will be included. However, if you enter any value directly, the value will be marked "SPEC" (for specified).

Composite Fade Margin

The TAP fixed facility data base includes fields for digital fade margin values. These values can be used in addition to the computed thermal fade margin to compute a composite fade margin value.

The additional fade margins included are:

Dispersive Fade Margin (DFM) is the "contribution to outage that accounts for in-band distortion that can at times cause a digital system to fail when the AGC or flat fade is less than that required to reach the thermal noise threshold." ("Digital Radio Path Fade Margin Calculations", p.32, MDR-2000 Series Product Description, Rockwell International)

Adjacent Channel Interference Fade Margin (AIFM) is the contribution to system outage resulting "from the broad transmit spectra of digital systems that have sufficient energy that spills over into adjacent channel digital receivers." ("Digital Radio Path Fade Margin Calculations", p.32, MDR-2000 Series Product Description, Rockwell International)

External Interference Fade Margin (EIFM) is the "contribution to system outage from intersystem (foreign route) cochannel interference. Such interference can come from transmitters on the desired route (overreach, for example) or from transmitters from other routes in the vicinity." ("Digital Radio Path Fade Margin Calculations", p.32, MDR-2000 Series Product Description, Rockwell International).

EIFM can also be computed by pressing the Calculate button next to the EIFM field. EIFM is computed using the following equation:

(5) EIFM = RSL - T +(T/I) - (C/I)

where:

The fade margin values are entered in the fixed facility lookup or fixed facility data base editor. If you want to exclude any of the fade margin values from the composite fade margin calculation, enter a value of zero (0) or 99.9 for that fade margin value.

The composite fade margin is computed using the equation:

(6) CFM =
-10 LOG (10-DFM/10 + 10-TFM/10 + 10-AIFM/10 + 10-EIFM/10)

Where:

Frequency Diversity

The TAP fixed facility data base includes a field for frequency diversity. If frequency diversity is not employed, set the "Diversity Frequency" field to zero (0). If frequency diversity is used, enter the second frequency in MHz.

The improvement factor for frequency diversity is computed from the following equations, depending on the frequency of the system:

(7) Ifd[ 2 GHz] = 1.0000 (df / f) 10F/10

(8) Ifd[ 4 GHz] = 0.5000 (df / f) 10F/10

(9) Ifd[ 6 GHz] = 0.2500 (df / f) 10F/10

(10) Ifd[ 7-8 GHz] = 0.1250 (df / f) 10F/10

(11) Ifd[11-12 GHz] = 0.0833 (df / f) 10F/10

where:

The constant coefficient of the equation is interpolated linearly for intermediate frequencies. Frequencies above or below the specified ranges use the coefficients for the highest or lowest range, respectively.

If both spatial and frequency diversity are employed, the combined improvement factor is the product of the two values.

Reliability

The reliability of a system based on the computed fade margin is calculated based on the following equation (from Lenkurt)

(12) Undp = a x b x 2.5 x 10-6 x f x D3 x 10-F/10

where:

The percent reliability is computed from the outage probability by:

(13) %R = 100 x (1 - Undp)

Space Diversity

The reliability of the system generally can be improved by the use of a second receiving antenna located at a different height ("space diversity"). Both antennas (primary and diversity) feed the receiver through appropriate switching devices.

The space diversity improvement factor for vertically separated receive antennas is computed as:

(14) I = (7 x 10-5 x f x s2 x 10F2/10 ) / D

where:

The overall reliability with space diversity is computed by dividing the non-diversity outage probability by the improvement factor:

(15) Udiv = Undb/I

References:

Engineering Considerations for Microwave Communications Systems, 1975, GTE Lenkurt Incorporated.

Bullington, Kenneth, "Radio Propagation for Vehicular Communications", IEEE Transactions on Vehicular Technology, November 1977.

Roelofs, Stan, "Fade Margin Requirements for Microwave Systems", Microwave Reference Guide, 1986, Motorola.

"Digital Radio Path Fade Margin Calculations", p.32, MDR-2000 Series Product Description, Rockwell International

 

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