Microwave System EquationsQ: 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. providing separate values for and water vapor losses. W is the roughness of the terrain.25 for mountainous.: . 1986): (2) a = K x (W/50)-1. with some roughness.3 where: K is a constant based on local area humidity: 2 for coastal humid areas. or very dry areas. The terrain and humidity factor can be computed using the formula (from Roelofs. The loss value is determined from curves based on van Vleck (1947).5 for dry areas. Terrain/Humidity Factor The terrain and humidity factor used in the reliability calculation can be entered directly. very rough. Lenkurt (1970) suggests the following values: 4 for very smooth terrain. including over water. Absorption loss is computed as a function of the frequency using the complete length of the path. 1 for average terrain. . The absorption loss is the sum of these two losses. not including the end points. . or the value can be computed from humidity and terrain roughness information. 1 for average or temperate areas. This is the standard deviation of the path elevations taken at one mile intervals. (3) W = where: A is the average of the terrain at one mile intervals (excluding the end points).25 for normal interior temperate or northern areas. TAP keeps track of the source of the terrain/humidity value. the value will be marked "SPEC" (for specified). If you calculate the value as described above. the mode will be marked "SPEC" (for specified). 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. E is the elevation of each of the terrain points at one mile intervals (excluding the end points).5 for gulf coast or similar hot. if you enter any value directly. . If you calculate the value as described above. the value will be marked "CALC" on printed output. However. Lenkurt suggests the following values: . the Loss Mode will be marked "CALC". However. humid areas. (E . Climate Factor The climate factor used in the reliability calculation can be entered directly or computed from average annual temperature information.A)2 is the sum of the square of differences between each elevation point and the average elevation. . and the temperature will be included. .125 for mountainous or very dry areas. if you enter any value directly. MDR-2000 Series Product Description. the computed EIFM value will not be displayed on the Receive Site screen. p.T +(T/I) .32. EIFM is computed using the following equation: (5) EIFM = RSL .Composite Fade Margin The TAP fixed facility data base includes fields for digital fade margin values.32." ("Digital Radio Path Fade Margin Calculations".32. Rockwell International). 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". 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. Since the RSL is not known until later in the program. MDR-2000 Series Product Description. (T/I) is the threshold to interference ratio in dB. .(C/I) where: RSL is the unfaded received signal level in dBm. p. for example) or from transmitters from other routes in the vicinity. p. EIFM can also be computed by pressing the Calculate button next to the EIFM field." ("Digital Radio Path Fade Margin Calculations". T is the receiver threshold for 10-6 BER in dBm. Such interference can come from transmitters on the desired route (overreach. Rockwell International) External Interference Fade Margin (EIFM) is the "contribution to system outage from intersystem (foreign route) cochannel interference. These values can be used in addition to the computed thermal fade margin to compute a composite fade margin value. MDR-2000 Series Product Description. enter the second frequency in MHz. EIFM is the External Interference Fade Margin. If you want to exclude any of the fade margin values from the composite fade margin calculation. The fade margin values are entered in the fixed facility lookup or fixed facility data base editor.0000 (df / f) 10F/10 (8) Ifd[ 4 GHz] = 0. Frequency Diversity The TAP fixed facility data base includes a field for frequency diversity. set the "Diversity Frequency" field to zero (0). DFM is the Dispersive Fade Margin. AIFM is the Adjacent Channel Interference Fade Margin.5000 (df / f) 10F/10 (9) Ifd[ 6 GHz] = 0. 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.2500 (df / f) 10F/10 (10) Ifd[ 7-8 GHz] = 0. TFM is the computed Thermal Fade Margin. The improvement factor for frequency diversity is computed from the following equations.9 for that fade margin value. enter a value of zero (0) or 99.0833 (df / f) 10F/10 where: .1250 (df / f) 10F/10 (11) Ifd[11-12 GHz] = 0. If frequency diversity is used. If frequency diversity is not employed.(C/I) is the carrier to interference ratio in dB. depending on the frequency of the system: (7) Ifd[ 2 GHz] = 1. 5 x 10-6 x f x D3 x 10-F/10 where: Undp is the non-diversity outage probability. D is the path length in miles. the combined improvement factor is the product of the two values. or other losses. respectively.outage calculation. The percent reliability is computed from the outage probability by: . If both spatial and frequency diversity are employed. The values will be different if the two receive systems have different antenna gains. a is the terrain factor. transmission line lengths. 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. The higher value fade margin ("best case") is used for this non. f is the frequency in GHz. For systems which include a space antenna. The other fade margin value is used to compute the diversity as described below. Frequencies above or below the specified ranges use the coefficients for the highest or lowest range. F is the fade margin in dB. a fade margin is computed for each receive antenna (primary and diversity). b is the climate factor.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. Bullington. . 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.) 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. GTE Lenkurt Incorporated. 1975.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"). (In space diversity systems. and the smaller fade margin value is used to compute the space diversity improvement.(13) %R = 100 x (1 . s is the vertical antenna spacing in feet. fade margins are computed for both antennas. D is the path length in miles. F2 is the lower fade margin in dB. The larger fade margin value is used to compute the nondiversity reliability. IEEE Transactions on Vehicular Technology. November 1977. Kenneth. "Radio Propagation for Vehicular Communications". Both antennas (primary and diversity) feed the receiver through appropriate switching devices. MDR-2000 Series Product Description. 1986. "Digital Radio Path Fade Margin Calculations". Microwave Reference Guide. Motorola. "Fade Margin Requirements for Microwave Systems".32. Stan. p. Rockwell International .Roelofs.