Rec. Itu-r bo. 1696




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2.3 Overall system availability


The overall system availability defines the ability of the system to maintain its overall aggregate C/(N + I) above a given threshold over time. Path propagation fading in the links determines this availability performance over time.

Given that the use of UPC and/or on-board AGC maintains constant the satellite e.i.r.p. independently of the feeder-link fading, the uplink and downlink C/(N + I) are thus decoupled. Defining:



such that

and given that feeder link and service link path fading can be assumed to be uncorrelated, the overall aggregate is a function of the sum of two independent random variables. Thus the probability density function (PDF) of the overall aggregate (and thus of C/(N + I)) is the convolution of the PDFs of the uplink and downlink

Approximations can be used to obtain an upper bound and an approximated lower bound on the overall system availability, thus avoiding the somewhat complex calculations required for the exact solution. These approaches are described in the following sections.

The annual availability probability obtained below can be converted to worst-month availability using the conversion method from Recommendation ITU R P.841, for mean annual global (for planning purpose) or other climates.

2.3.1 Exceedance percentage as a function of fade level


In carrying out the calculation in the following sections, one needs to derive the exceedance probability as a function of the fade level. Recommendation ITU R P.618 does not provide a direct methodology to do so. Two methodologies are presented below.

The exceedance percentage for a given fade level can be found directly from a plot of the attenuation curve for the BSS link under study. Taking as an example the BSS link defined in Table 3, the total downlink propagation loss Apd (pd) is shown in Fig. 1 as a function of annual exceedance probability pd, calculated in accordance with Recommendation ITU R P.618. This plot shows for example that a 3 dB total downlink propagation loss corresponds to about 0.025% exceedance, or 99.975% availability. In a computer code implementation, the data points describing the curve can be stored in a table and when the required propagation fade level falls between two data points, an interpolation technique can be used to estimate the associated exceedance probability.

An alternative methodology to using plotted/tabulated attenuation curves is to develop computer code that will:

– calculate the propagation fade level for a given exceedance percentage of time as described in Recommendation ITU R P.618; and

– iterate for different values of exceedance percentage of time until the desired value of fade is achieved. This latter method is used to generate the results for the example in § 3.

Note that once the relationship between the exceedance percentage of time and attenuation level is obtained, equations (1) to (4) can be used to derive a corresponding relationship between the C/(N + I)u or C/(N + I)d and the exceedance percentage of time.




TABLE 3

Example system

Downlink frequency (GHz)

12

Polarization

Circular

Elevation angle (degrees)

30

Terminal latitude ( N)

50

Terminal longitude ( W)

10

Height above mean sea level (km)

0 (Calculated, Recommendation ITU R P.1511)

Terminal antenna diameter (cm)

60

Terminal antenna efficiency (%)

70

Season

Global mean annual climate




2.3.2 Exact system availability


To precisely determine the overall system availability Ps, it is necessary to derive the PDFs for each of and and to convolve these two PDFs to generate the PDF of the overall aggregate Equations (1) to (4) are used to find the relationship between the exceedance percentage of time (or unavailability pu and pd) and the associated uplink or downlink These relationships are the cumulative distribution functions (CDF) of the uplink and downlink Taking the derivatives of these functions provides the required PDFs. After convolving the two PDFs, we obtain the overall PDF that, when integrated, results into the CDF of the overall aggregate which then can easily be converted to a system availability corresponding to a given C/(N + I) threshold.

Section 1 of Appendix 1 to this Annex provides an example of implementation in a computer code of these calculations. There are obviously numerous other approaches that can be designed to arrive at the same results.


2.3.3 Approximated system availability

2.3.3.1 Upper bound


An upper bound of the overall system availability Ps can be obtained by assuming that an outage will occur when either the uplink or downlink C/(N + I) will fall below their respective QEF thresholds, such thresholds being defined as the point where an outage will occur under the condition that the other link is not rain faded. In this case, the system availability (Ps  100 – ps) is derived from:

(5)

where:


ps : overall system unavailability (%)

 : uplink exceedance or unavailability: probability (%) that the uplink C/(N + I) is below the uplink QEF threshold

 : downlink exceedance or unavailability: probability (%) that the downlink C/(N + I) is below the downlink QEF threshold.

Determination of the system availability when only one of the links is rain faded is a complicated process due to the need to consider availability-dependent cloud and scintillation fading in the overall link. For the feeder link, it can be assumed that the uplink rain margin will mitigate the cloud and scintillation fading during non-rain periods of time. In addition, under uplink rain, cloud and scintillation fading will be small contributors to the total path propagation fading. Thus cloud and scintillation fading can be ignored in the feeder link. However BSS downlinks have less margin, such that cloud and scintillation fading should be considered. Accordingly, an iterative approach is required to determine the overall system availability, to address the dependence of certain parameters such as cloud and scintillation fading and receiver noise temperature increase on system availability. Appendices 1 and 2 to this Annex present such an approach.


2.3.3.2 Approximated lower bound


In conventional BSS systems, clear sky C/(N + I)u is normally designed to be much higher than that of downlink. Even when high propagation attenuation exists in the uplink path, it is possible to maintain the C/(N + I)u well above the QEF threshold by implementing uplink fade mitigation techniques such as UPC and/or site diversity. Therefore, by assuming a constant minimum C/(N + I)u well above the QEF threshold and, if the effect of can be neglected, the overall system unavailability ps is derived from the downlink exceedance or unavailability (ps   directly, taking into account the constant C/(N + I)u.
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