Appendix b Clear-air enhancements and fading b.1 Introduction

This Appendix gives the calculation method for clear-air enhancements and fading. Section B.2 calculates the climate-related, path-dependent, quantity Q_0ca which is required by the function Q_caf(A) defined in § B.4. Q_caf(A) may be called many time for the same path. Q_caf(A) gives the percentage of the non-rain time for which a fade level of A exceeds the median signal level during non-rain conditions. Q_caf(A) is used for surface paths. Section B.5 defines the function Q_caftropo(A) that is used for troposcatter paths.

B.2 Characterize multi-path activity

The first part of the multi-path fading calculation characterizes the level of multi-path activity for a given path. It is a preliminary calculation which needs to be completed once for a given path and frequency.

A factor representing the statistics of radio-refractivity lapse rate:

(B.2.1)

The parameter N_d65m1 is a parameter characterizing the level of multipath activity for the mid-point of the path. It appears in Table 3.1 and is obtained as described in § 3.4.2.

The notional zero-fade worst-month percentage time characteristic of the deep-fade part of the distribution is calculated as follows. The method depends on whether the path is LoS or NLoS for median time, as determined in § 3.7.

For LoS path:

Calculate the notional zero-fade annual percentage time, Q_0ca, using the procedure given in § B.3 with the following inputs:

                km (B.2.2a)

                mrad (B.2.2b)

                m (B.2.2c)

where d, _p and h_lo appear in Table 3.1 and are calculated in §§ 3.2 and 3.3.

For nLoS path:

In the NLoS case, the notional zero-fade time is evaluated from each antenna to its radio horizon, and the larger of the two results is selected, as follows.

Calculate the notional zero-fade annual percentage time at the transmitter end, Q_0cat, using the procedure given in § B.3 with the following inputs:

                km (B.2.3a)

                mrad (B.2.3b)

with    m (B.2.3c)

where d_lt, θ_t, h_ts and i_lt appear in Table 3.1.

Calculate the notional zero-fade annual percentage time at the receiver end, Q_0car, using the procedure given in § B.3 with the following inputs

                km (B.2.4a)

                mrad (B.2.4b)

with    m (B.2.4c)

where d_lr, θ_r, h_rs and i_lr appear in Table 3.1 and are calculated in §§ 3.3 and 3.7.

The notional zero-fade annual percentage time for the whole path is now given by the larger of the times associated with the transmitter and receiver:

                % (B.2.5)

B.3 Calculation of the notional zero-fade annual percentage time

This section calculates the notional zero-fade annual percentage time, Q_0ca. The calculation in § B.2 is needed either once or twice depending upon the path type. It requires three input values, d_ca, ε_ca and h_ca, which are specified each time this section is invoked.

Calculate the notional zero-fade worst-month percentage time:

                % (B.3.1)

where K is calculated in § B.2 and f appears in Table 3.1.

Calculate the logarithmic climatic conversion factor:

  |_mn| ≤ 45 (B.3.2a)

  otherwise (B.3.2b)

where _mn is the path mid-point latitude and appears in Table 3.1.

If C_g > 10.8, set C_g = 10.8.

Calculate the notional zero-fade annual percentage time:

               % (B.3.3)