## Multipath Fading Calculation Based on Tia Tsb 10F

On digital microwave radiolinks, the fade margin consists of four factors that are power added and constitute the composite fade margin (CFM). These four factors are defined below:

TFM. Thermal fade margin (dB) (sometimes called the flat fade margin) is the fade margin discussed in Chapter 2, Section 2.7.2. TFM is the algebraic difference between the nominal RSL and the 1 X 10 3 BER outage threshold for flat (i.e., nondispersive) fades. Since interference affects unfaded baseband noise, TFM is the only fade margin that needs to be considered on analog LOS links.

DFM. Dispersive fade margin (dB), also to the 1 X 10 3 BER, is defined by the radio equipment manufacturer. It is determined by the type of modulation, the effectiveness of equalization employed in the receive path, and the multipath signal's delay time. This is standardized on manufacturer's datasheets as 6.3 ns. DFM characterizes the digital radio's robustness to dispersive (spectrum-distorting) fades. One means to improve DFM on some paths is to increase the antenna discrimination to reduce the level of longer-delay multipath signals, which can where TIBPD = T=

1 SFF

»Section 3.8.3 was extracted from Section 4.2.3 of TIA TSB 10-F (Ref. 23).

unacceptably degrade a link's DFM. According to TIA (Ref. 23), a DFM greater than 50 dB is a good baseline criterion. (Note the difference between DFM defined here and in Section 3.8.2.)

EIFM. External interference fade margin (dB) is a receiver threshold degradation due to interference from a total of the three (MEA factor)* external systems (usually 1 dB, but depends on CFM objective). In the absence of adjacent channel interference (AIFM), EIFM is simply IFM.

AIFM. Adjacent-channel interference fade margin (dB). Receiver threshold degradation is due to interference from adjacent channel transmitters on the same path due to transmitters in one's own system. This is normally a negligible parameter except in cases of frequency diversity and multiline hot-standby systems.

CFM = 10log(10yTFM/10 + 10yDFM/10 + 10-eifm/io + 1Q-aifm/io )

The outage time due to multipath fading in a nondiversity link is calculated by

where T = outage time in seconds r = fade occurrence factor T0 = (t/50)(8 X 106) = length of fade season in seconds t = average annual temperature in degrees Fahrenheit CFM = composite fade margin

I0 = space diversity improvement factor: factor = 1 for nondiversity;

> 1 for space diversity

The fade occurrence factor, r, is calculated from the basic outage equation for atmospheric multipath fading:

*MEA = multiple exposure allowance (dB). See Chapter 13, Section 13.3 for more discussion of MEA.

where c = climate - terrain factor (see Figure 3.15) * = climate factor (see Figure 3.16)

w = terrain roughness: 6 F w F 42 m for average 15 m or 20 F w F 140 ft for average 50 ft f = frequency (GHz) D = path length (km or mi)

The space diversity improvement factor I0 may be calculated by:

I0 = 1.2 X 10"3521 — I X 10CFM /10, 5 F 15 m ( metric)

= 7 X 10—5s2(d) X 10CFM /10, s F 50 ft ( English) ( 3.17)

where fade margins on both antennas are about equal, and s is the vertical antenna separation in meters (feet), center to center.

The space diversity improvement factor (I0) may underestimate diversity improvements for small antenna spacings and overestimate diversity improvement for large antenna spacings on "flat land''microwave links.

For the purposes of this text, average climate (* = 1), temperature [10°C (50°F)], and terrain roughness [15 m (50 ft)] conditions may usually be

Figure 3.15. Values of climate-terrain factor, c.
Figure 3.16. Values of climate factor, x (also see table below).

Hawaii/Caribbean Alaska c = 4/x = 2 c = 0.25/x = 0.5: coastal and mountainous areas c = 1 /x = 1: flat permafrost tundra areas in west and north Alaska assumed. This simplifies the outage time equation to

20fD3 X 10"CFM /10

It is seen from the above equations that nondiversity multipath outage increases directly as a function of the path length cubed (D3). Therefore short digital paths can usually meet outage objectives with less composite fade margin (more interference) since the outage probability of fading is low.

Since the total number of seconds in one year equals 31.5 X 106, the annual path reliability is computed from

required for a given outage time:

FM or CFM (nondiversity) = —10 log I ——3 I (metric)

I T 20 fD3

where T = outage time objective (s/yr) f = frequency (GHz) D = path distance (km or mi)

Space diversity improvement plays such a significant role in increasing path reliability, that it often allows higher interference levels that degrade (reduce) the composite fade margin of many digital links. By combining the nondiversity outage equation and the space diversity improvement factor equations, we arrive at the following equation for the annual outage in a space diversity path:

Note that the frequency term has disappeared from the space diversity outage equation and the annual outage now varies as a function of D4. Rearranging this equation to solve for the required fade margin or composite fade margin for a given outage time with space diversity gives:

I 2.5 X 10—4Ts2\ FM or CFM (space diversity) = —5 log I--I (metric)

Calculation of the required fade margins for nondiversity or space diversity links with the above equations may provide improved spectrum utilization

(efficiency) by permitting higher interference levels without overly degrading the required reliability for many short and diversity links. For example, if the required fade margin (above) is 25 dB, and the path calculations with no interference show 33 dB, an interference level 7 dB above the value calculated on the basis of threshold degradation [by equation (13.7), for instance] would probably not cause the hop outage to exceed objectives.

Since analog radios are nonregenerative, the baseband noise is additive on N tandem hops (typically per-hop noise plus 13 log N). Fading on different hops is noncorrelated, so the outage time (probability of outage) of a digital or analog radio system is equivalent to the sum of the outage times (probabilities of outage) of the individual hops. While the above outage and fade margin calculations are applicable to both analog and digital radio hops, analog radio noise buildup poses a more complex problem. With analog systems, one must consider the overall system noise objectives in parallel with the system reliability (outage) objectives. Most analog systems require significant increases in RSL above FM improvement threshold just to achieve acceptable baseband S/N.

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### Responses

• tekle
How to calculate interference fade margin?
5 years ago
• ABRHA
How to calculate the dispersive fade margin?
5 years ago