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Worst Case Approach

 
To allow the Radiocommunication Bureau to treat submissions under Article 4 of Appendices 30 and 30A of the Radio Regulations that have parameters different from those described in Annexes 5 and 3 of those Appendices, the “Worst Case Approach” has been developed. It is applied to interference calculations when one or both signals employ a “non-standard” frequency or bandwidth and the interfering signal uses analogue modulation. 
 
The “Worst Case Approach” has been approved by the Radio Regulations Board (RRB) and has provisional status until relevant ITU-R Recommendations are available.
 
A description of the “Worst Case Approach” is provided below. This methodology is integrated into MSPACEg software and has been applied by the Bureau in its technical analyses since 1998.
 
1.  The “Worst Case Approach”
 
The “Worst Case Approach” is applied for calculation of interference from assignments using analogue modulation involving “non-standard” wanted or interfering assignments.
 
It is based on the variation of the relative protection ratio in dB as a linear function of the overlapping bandwidth. This relative protection ratio is the difference between the co-channel protection ratio and a protection ratio at a given frequency offset. It has a purpose similar to the adjustment factor described in ITU-R Rec. BO.1293-2, but with the opposite sign.
 
The following existing technical characteristics/models have been used for the development of the “Worst Case Approach”:
    • Existing protection ratio values for different interfering categories;
    • Protection mask provided in Figure 1 of Annex 6 of Appendix 30;
    • Protection mask provided in Figure 6 of Annex 5 of Appendix 30;
    • Ratios between bandwidth, channel spacing and protection masks’ elements (plateau part [1] and other
    • parts of the masks);
    • Adjustment factor notion as described in ITU-R Recommendation BO.1293-2
 
2. The "Worst Case Approach" for the Regions 1 and 3 Plans/Lists
 
Definitions:
Assuming that:
  • Fi, and Fw are the centre frequency values in MHz of the interfering and wanted channels respectively;
  • Bi, and Bw are the frequency bandwidths in MHz of the interfering and wanted channels respectively;
  • Ov is the overlapping bandwidth in MHz between the wanted and interfering channels;
  • fo is the frequency offset/difference in MHz between the wanted and interfering channels;
  • RelPR is the relative protection ratio in dB used to protect the wanted channel against the interfering
  • channel.
 
2.1  For WRC-97 Regions 1 and 3 Plan assignments having status “P” and “A”[2] and modifications to WRC-97 Regions 1 and 3 Plans:
 
The overlapping bandwidth Ov (between wanted and interfering assignments) is defined by the formula:
  
Ov = (Bi + Bw) / 2 - | Fi - Fw |​
 
 
The frequency offset/difference limit fol1 corresponding to the limit of the flat part of the protection mask can be expressed as follows, in the case of the Regions 1 and 3 Plan:
 
fol1 = 7 * (Bi + Bw) / 27​
 
assuming that the flat part of the protection mask provided in Figure 1 of Annex 6 of Appendix 30 is based on two identical interfering and wanted analogue signals using 27 MHz and having a plateau part of 10 MHz in the case of the relative protection ratio of 0 dB and of about 14 MHz in the case of the relative protection ratio of -7 dB.
 
E.g. in the standard analogue case where Bi=Bw=27 MHz, fol1 = 14 MHz.
 
The overlapping bandwidth limit Ovl corresponding to this frequency offset limit fol1 can be expressed as follows:
 
Ovl = 13 * (Bi + Bw) / (2 * 27) in the case of a wanted analogue signal​
  
E.g. in the standard analogue case where Bi=Bw=27 MHz, Ovl = 13 MHz.
 
The above formula defines the width of the flat part of the protection mask and results in a wider plateau than that of the WARC-77 mask. This formula has been chosen because it is in accordance with the interference effect produced in this part of the mask by the increase of the peak-to-peak frequency deviation of both the wanted and interfering signals which is an implicit consequence of the adoption of reduced co-channel protection ratios by WRC-97 (i.e. 30/24 dB instead of 40/31 dB respectively for the feeder-link and downlink Regions 1 and 3 Plans).
 
However, although it might not be necessary to have such a wide plateau, for simplicity and to be consistent with the worst case approach, the width of the plateau was derived from the WARC-77 protection mask at the -7 dB relative protection ratio level.
 
The width of the plateau resulting from the above definition in the case of signals with different bandwidths, either wider or narrower, varies in the same direction as that indicated by the results of the available measurements: i.e. the plateau is wider in the case of wider bandwidth signals and narrower in the case of narrower bandwidth signals.
The linear variation of the relative protection ratio as a function of the overlapping bandwidth is defined considering that this function f(x) = a*x + b must pass through the following two points:
 
(Ovl MHz, 0 dB) and (7.82 MHz, -8 dB)
                                                             0 = a * Ovl + b, and
                                                            -8 = a * 7.82 + b​
 
The resulting relative protection ration RelPR can be expressed as a function of the overlapping bandwidth Ov as follows:
 
RelPR = 0                                                      (dB) for Ovl < Ov
                                           RelPR = - 8 * (Ov - Ovl) / (7.82 - Ovl)            (dB) for 0 < Ov <= Ovl​
 
The linear function described above can also be expressed as a linear function of the frequency offset fo as follows:
 
RelPR = - [8 * (14 * (Bi + Bw) / (2 * 27) - |fo|)] / (7.82 - Ovl)   (dB)​
  
The above formula defines the slope of a protection mask which has a less steep slope than that of the WARC-77 mask. It has been chosen because it is in accordance with the effect produced on this part of the mask by the increase of the peak-to-peak frequency deviation of both the wanted and interfering signals which is an implicit consequence of the adoption of a reduced co-channel protection ratio by WRC-97.
 
The “analogue” approach defined above in the case of the WRC-97 Regions 1 and 3 Plans is applied to deal with both analogue to analogue and analogue to digital interference situations.
 
2.2  For the notified Plan assignments, which are in conformity with Appendices 30 and 30A, brought into Use, and for which the date of bringing into use has been confirmed to the Bureau before 27 October 1997 (having status “PE” and “AE”[3]; so called “existing” systems):
 
The same definitions as described in Section 2 above are used.
 
The formula for the overlapping bandwidth described in Section 2.1 above is also employed.
 
The frequency offset/difference limit fol1 corresponding to the limit of the flat part of the protection masks can be expressed as follows, in the case existing systems in the Regions 1 and 3 feeder-link or downlink Plans:
 
fol1 = 5 * (Bi + Bw) / 27​
  
assuming that the flat part[4] of the protection mask provided in Figure 1 of Annex 6 of Appendix 30 is based on two identical interfering and wanted analogue signals using 27 MHz and having a plateau part2 of 10 MHz in the case of the relative protection ratio of 0 dB.
 
E.g. in the standard analogue case where Bi=Bw=27 MHz, fol1 = 10 MHz.
 
The overlapping bandwidth limit Ovl corresponding to this frequency offset limit fol1 can be expressed as follows:
 
Ovl = 17 * (Bi + Bw) / (2 * 27) in the case of a wanted analogue signal​
  
E.g. in the standard analogue case where Bi=Bw=27 MHz, Ovl = 17 MHz.
 
As with other non-standard cases, the width of the plateau resulting from the above definition in the case of signals with different bandwidths, either wider or narrower, varies in the same direction as that indicated by the results of the available measurements: i.e. the plateau is wider in the case of wider bandwidth signals and narrower in the case of narrower bandwidth signals.
 
The linear variation of the relative protection ratio as a function of the overlapping bandwidth is defined considering that this function f(x) = a*x + b must pass through the following two points:
 
(Ovl MHz, 0 dB) and (7.82 MHz, -19 dB), in the case of existing systems in the feeder-link Plan; and
(Ovl MHz, 0 dB) and (7.82 MHz, -16 dB), in the case of existing systems in the downlink Plan​
  
In the case of existing systems in the feeder-link Plan, the resulting function is thus defined as follows:
 
0 = a * Ovl + b, and
                                                                       -19 = a * 7.82 + b​
  
In the case of existing systems in the downlink Plan, the resulting function is thus defined as follows:
 
0 = a * Ovl + b, and
                                                                       -16 = a * 7.82 + b​
 
The resulting relative protection ration RelPR can be expressed as a function of the overlapping bandwidth Ov as follows:
 
1. In the case of existing systems in the feeder-link Plan:
 
  RelPR = 0                                                 (dB) for  Ovl < Ov
                                                   RelPR = - 19 * (Ov - Ovl) / (7.82 - Ovl)     (dB) for 0 < Ov <= Ovl​
 
The slope of the protection mask defined by the second formula above, is steeper than that of the WARC-77 mask. It has been chosen because it is in accordance with the decision taken at the WARC-ORB-88 Conference to have a higher difference between the co-channel and the first adjacent-channel protection ratios in the case of the feeder-link Plan (40-21 = 19 dB) than in the case of the downlink Plan (31-15 = 16dB).
 
The feeder-link co-channel protection ratio of 40 dB was justified by the limitation of the effect of the feeder-link path into the downlink path, which should produce a reduction of 0.5 dB into the downlink co-channel protection ratio of 31 dB, as mentioned in Section 3.2 of Annex 3 of Appendix 30A.
 
Nevertheless, the WARC-ORB-88 Conference decided not to apply the same reduction for the first adjacent channel, which means that a relaxed protection against interference from this first adjacent channel was assumed.
 
The linear function described above can also be expressed as a linear function of the frequency offset fo as follows:
 
RelPR = - [19 * (10 * (Bi + Bw) / (2 * 27) - |fo|)] / (7.82 - Ovl)  (dB)​
 
 
2. In the case of existing systems in the downlink Plan:

RelPR = 0                                                (dB) for Ovl < Ov
                                                   RelPR = - 16 * (Ov - Ovl) / (7.82 - Ovl)    (dB) for 0 < Ov <= Ovl
 
The linear function described above can also be expressed as a linear function of the frequency offset fo as follows:
 
RelPR = - [16 * (10 * (Bi + Bw) / (2 * 27) - |fo|)] / (7.82 - Ovl)  (dB)​
 
The “analogue” approach defined above in the case of existing systems in the Regions 1 and 3 feeder-link or downlink Plans is applied to deal with both analogue to analogue and analogue to digital interference situations.
 
3.  The "Worst Case Approach" for the Region 2 Plan
 
The same definitions as described in Section 2 above are used.
 
The formula for the overlapping bandwidth as described in Section 2.1 above is also employed.
 
The frequency offset/difference limit fol1 corresponding to the limit of the flat part of the protection mask can be expressed as follows, in the case of the Region 2 Plan:
 
fol1 = 8.36/2 * (Bi + Bw) / 24 = 4.18 * (Bi + Bw) / 24​
 
assuming that flat part[5] of the protection mask provided in Figure 6 of Annex 5 of Appendix 30 is based on two identical interfering and wanted analogue signals using 24 MHz and having a plateau part2 of 8.36 MHz in the case of the relative protection ratio of 0 dB.
 
E.g. in the standard analogue case where Bi=Bw=24 MHz, fol1 = 8.36 MHz.
 
The overlapping bandwidth limit Ovl1 corresponding to this frequency offset limit fol1 can be expressed as follows:
 
Ovl1 = (24-8.36) * (Bi + Bw) / (2 * 24) in the case of a wanted analogue signal​
  
 
E.g. in the standard analogue case where Bi=Bw=24MHz, Ovl = 15.64 MHz.
 
The width of the plateau resulting from the above definition in the case of signals with different bandwidths, either wider or narrower, varies in the same direction as that indicated by the results of the available measurements: i.e. the plateau is wider in the case of wider bandwidth signals and narrower in the case of narrower bandwidth signals.
The first linear variation of the relative protection ratio as a function of the overlapping bandwidth is defined considering that this first function f1(x) = a1*x + b1 must pass through the following two points from the formulae associated to Figure 6 of Annex 5 of Appendix 30:
 
           (Ovl1 MHz, 0 dB) and (Ovl2 MHz, -12.45694 dB),
            where:   Ovl2 = (24-12.87) * (Bi + Bw) / (2 * 24)
              0 = a1 * Ovl1 + b1 
             -12.45694 = a1 * Ovl2 + b1​
  
Similarly, the second linear function f2(x) = a2*x + b2 must pass through the following two points:
 
            (Ovl2’ MHz, -12.45198 dB) and (Ovl3 MHz, -22.1225 dB)
             where:   Ovl3 = (24-21.25) * (Bi + Bw) / (2 * 24)
             -12.45198 = a2 * Ovl2 + b2
             -22.1225 = a2 * Ovl3 + b2​
 
Similarly, the third linear function f3(x) = a3*x + b3 must pass through the following two points:
 
            (Ovl3’ MHz, -22.12 dB) and (Ovl4 MHz, -37.94 dB)
             where:   Ovl4 = (24-29.16) * (Bi + Bw) / (2 * 24)
             -22.12 = a3 * Ovl3 + b3
             -37.94 = a3 * Ovl4 + b3​
 
The resulting relative protection ration RelPR can be expressed as a function of the overlapping bandwidth Ov as follows:
 
           RelPR = 0  (dB)                                                                                               for Ovl1 < Ov
           RelPR = - 12.45694 * (Ov - Ovl1) / (Ovl2 - Ovl1)  (dB)                                    for Ovl2 < Ov <= Ovl1
           RelPR = - (22.1225-12.45198) * (Ov - Ovl2) / (Ovl3 - Ovl2)-12.45198  (dB)   for Ovl3 < Ov <= Ovl2
           RelPR = - (37.94-22.12) * (Ov - Ovl3) / (Ovl4 - Ovl3)-22.12  (dB)                   for  Ovl4 <= Ov <= Ovl3​
 
The slope of the mask resulting from the above definition in the case of signals with different bandwidths varies in the same direction as that indicated by available measurements: i.e. the slope is less steep for wider bandwidth signals and is more steep for narrower bandwidth signals.
 
The “analogue” approach defined above in the case of the Region 2 Plan will be applied to deal with both analogue to analogue and analogue to digital interference situations.
 
The relative protection ratio, described above, has to be associated with the Region 2 Protection Ratios defined in Section 3.4 of Annex 5 of Appendix 30 and derived from the template in Figure 6. However, in order to maintain the level of accuracy provided by the formula, which describes the template in Figure 6 of Annex 5 of Appendix 30, it is required to calculate the Region 2 Protection Ratio values with a higher precision. MSPACEg software (since version 1.90) applies the following protection ratio values, derived from this Figure:
 
           28 dB              for co-channel signals;
           13.57468 dB   for adjacent-channel signals;
           -9.94 dB          for second adjacent-channel signals.​
            
[1] Corresponds to the part of the signal where the spectral power density has an almost constant maximum value.
[2] See Articles 11 and 9A of Appendices 30 and 30A respectively.
[3] See Articles 11 and 9A of Appendices 30 and 30A respectively.
[4] Corresponds to the part of the signal where the spectral power density has an almost constant maximum value
[5] Corresponds to the part of the signal where the spectral power density has an almost constant maximum value.