Microwave Path Design, Link Budget, and Reliability System Equations

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:

A is the attenuation in dB.

F is the frequency in GHz.

D is the distance in miles.

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:

4 for very smooth terrain, including over water.

1 for average terrain, with some roughness.

.25 for mountainous, very rough, or very dry areas.

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

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

where:

K is a constant based on local area humidity:

2 for coastal humid areas.

1 for average or temperate areas.

.5 for dry areas.

W is the roughness of the terrain. This is the standard deviation of the path elevations taken at one mile intervals, not including the end points.:

(3) W =

where:

A is the average of the terrain at one mile intervals (excluding the end points).

E is the elevation of each of the terrain points at one mile intervals (excluding the end points).

S (E - A)2 is the sum of the square of differences between each elevation point and the average elevation.

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:

.5 for gulf coast or similar hot, humid areas.

.25 for normal interior temperate or northern areas.

.125 for mountainous or very dry areas.

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

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

where:

T is the average annual temperature in degrees Fahrenheit.

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).

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.

· 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:

RSL is the unfaded received signal level in dBm. Since the RSL is not known until later in the program, the computed EIFM value will not be displayed on the Receive Site screen.

T is the receiver threshold for 10-6 BER in dBm.

(T/I) is the threshold to interference ratio in dB.

(C/I) is the carrier to interference ratio in dB.

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:

CFM is the Composite Fade Margin.

DFM is the Dispersive Fade Margin.

TFM is the computed Thermal Fade Margin.

EIFM is the External Interference Fade Margin.

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:

f is the frequency in GHz

df is the diversity spacing in GHz

F is the thermal or composite fade margin

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:

Undp is the non-diversity outage probability.

a is the terrain factor.

b is the climate factor.

f is the frequency in GHz.

D is the path length in miles.

F is the fade margin in dB. For systems which include a space antenna, a fade margin is computed for each receive antenna (primary and diversity). The values will be different if the two receive systems have different antenna gains, transmission line lengths, or other losses. The higher value fade margin ("best case") is used for this non- outage calculation. The other fade margin value is used to compute the diversity as described below.

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:

I is the space diversity improvement factor

f is the frequency in GHz.

s is the vertical antenna spacing in feet.

D is the path length in miles.

F2 is the lower fade margin in dB. (In space diversity systems, fade margins are computed for both antennas. The larger fade margin value is used to compute the non-diversity reliability, and the smaller fade margin value is used to compute the space diversity improvement.)

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