Diversity as a Means to Mitigate Fading
2.7.4.1 General. The first and most economic step to achieve required fade margins is to overbuild the link by using larger aperture antennas, improved receiver noise performance (i.e., use of a LNA in front of the mixer), and/or a higher transmitter output power. Under certain circumstances, the link design engineer will find that it is uneconomic to overbuild the link further. The next step, then, is to examine diversity as another method to mitigate fading and, at the same time, add a ''diversity improve ment factor,'' which can be translated directly to some 3 dB or more of system gain.
Diversity is based on providing separate paths to transmit redundant information. These paths may be in the domain of space, frequency, or time. In essence, the idea is that a fade occurring at time Ta on one of the redundant paths does not occur on the other. The ability to mitigate fading effects by diversity reception is a function of the correlation coefficient of the signals on the redundant paths. The higher the decorrelation, the more effective the diversity. Generally, when the correlation coefficient is < 0.6, full diversity improvement can be entirely achieved (Ref. 16).
The most commonly used methods of diversity are frequency and space diversity to minimize the effects of multipath fading. (In Chapter 9 another form of "space" diversity is introduced called "spatial diversity'' or path diversity.) Troposcatter and diffraction links (Chapter 5) often use a combination of frequency and space diversity, achieving still greater protection against the effects of fading.
Frequency diversity uses two different frequencies to transmit the same information. With space diversity, the same frequency is used, but two receive antennas separated vertically on the same tower receive the information over two different physical paths separated in space. These two types of diversity are shown conceptually in Figure 2.22.
Compared to space diversity, frequency diversity is somewhat less expensive to implement and has some operational and maintenance advantages. Its principal drawback is regulatory. As an example, the U.S. Federal Communications Commission (FCC) (Ref. 17) rules prohibit frequency diversity for common carriers unless sufficient evidence can be shown that frequency diversity is the only way to obtain the required system reliability. This ruling was established to preserve centimetric frequencies for working radio channels owing to frequency congestion in the centimetric bands and the demand for working frequencies. Therefore, in the United States, the first alternative should be space diversity.
2.7.4.2 Frequency Diversity. Frequency diversity offers two advantages. Not only does it provide a full order of diversity and resulting diversity gain, but it also provides a fully redundant path, improving equipment reliability. (See Appendix 1.)
To achieve maximum fading decorrelation, the separation in frequency of the two transmit frequencies must be on the order of 3-5%. However, because of congestion and lack of frequency assignments in highly developed countries, separations of 2% are more common, and some systems operate satisfactorily with separations under 1%. Figure 2.23 shows approximate worst-case multipath fading (Rayleigh) and diversity improvement for frequency diversity systems with different frequency separations. The figure shows that a 14-19-dB improvement may be expected for a link with a time
- Figure 2.22. Simplified functional block diagrams distinguishing frequency and space diversity operation on LOS radiolink.
availability requirement of 99.99% over the same link with no diversity, assuming Rayleigh fading.
2.7.4.3 Space Diversity. Because of the difficulty of obtaining the second diversity frequency to transmit redundant information, vertical space diversity may be the easier of the two alternatives, and in some cases it may be the only diversity alternative open to the designer. In fact, experience is now showing that space diversity has considerably lower correlation coefficients, with consequently much larger diversity improvements than was earlier believed.
It should be noted that a space diversity arrangement can also provide full equipment redundancy when automatically switched hot standby transmitters are used (see Section 14.3.5). However, this arrangement does not provide a separate end-to-end operational path as does the frequency diversity arrangement.
Of principal concern in the design of space diversity on a particular path is the amount of vertical separation. Reference 5 suggests a rule-of-thumb separation distance of 200 wavelengths or more. One wavelength at 6 GHz is 5 cm. The required separation, then, would be 5 X 200 cm or 10 m (about 33 ft). Reference 13 suggests 60 ft at 2 GHz, 45 ft at 4 GHz, 30 ft at 6 GHz, and 15-20 ft at 12 GHz. It will be appreciated that both antennas must meet the path profile clearance criteria, and the result will be taller towers.
Reference 13 provides a formula (modified from Vigants) to calculate the space diversity improvement factor Isd:
where / = frequency in gigahertz s = vertical antenna spacing in feet between antenna centers D = path length in statute miles
F = fade margin in decibels associated with the second antenna. The barred F factor is introduced to cover the situation where the fade margins are different on the upper and lower paths of the vertically spaced antennas. In such a case F will be taken as the larger of the two fade margins and will be used to calculate the unavailability (Und) in the computation for the nondiversity path. F in equation (2.44) will be taken as the smaller fade margin of the two, if different.
Reference 13 recommends that one first calculates the nondiversity path unavailability Pm/ [from equation (2.31)] and then one calculates the space diversity improvement factor Isd. The diversity outage (unavailability) or fade probability (Udiv) is given by
Example 20. Consider a 30-mi (48.3-km) path with average terrain that includes some roughness and where the climate is inland temperate. The operating frequency of the radiolink is 6.7 GHz and the fade margin incorporated is 40 dB. Calculate the unavailability and path availability for the nondiversity case and for the space diversity case with 40-ft vertical spacing.
Calculate Pmf using equation (2.31):
Pmf (%) = 6.0 X 10-5(1)(1)(6.7)(48.3)3(10)-40/10 = 6.0 X 10-5 X 1.675 X 112678.6 X 10-4 = 0.0011% or 0.000011
This corresponds to a path availability of 1 - 0.00011 or 99.9989%. Calculate Isd from equation (2.44):
f 250
Substitute this value into equation (2.45):
Udiv = 0.000011/250 = 0.000000044
The path availability for space diversity is then 1 - 0.000000044 = 0.999999956 or 99.9999956%.
Figure 2.24 is a useful nomogram to determine the space diversity improvement factor denoted Isd. The nomogram is taken from ITU-R 376-3.
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