(IF) function (IF) function with default Min and Max default values
5.9 AFP Appendices
5.9.1 The AFP Cost Function
The notations listed hereafter are used to describe the cost function:
• TRG: Group of TRXs
• TRGs: Set of all the TRGs
• : If and only if
• : Size of any group g
• ARFCN: Set of all the frequencies
• : Set of all the subsets of frequencies
• : The largest integer
• : Number of times a group is assigned to TRGi in the assignment A For example:
- When i is NH, g is a single member group containing one of the frequencies assigned at TRGi. If |g| is not 1 or if g does not contain a frequency assigned at i, then .
- When i is BBH, can be either 0 or equal to the number of TRXs in TRGi.
= Number of TRXs in TRGi g is the set of frequencies assigned to TRXs of TRGi. (|g| = number of TRXs in TRGi).
When we talk about "TRXs of i using g", and in the case of BBH, then there are |g| such virtual TRXs, each using the entire group g and having a virtual MAIO [0, |g| - 1].
- When i is SFH, must be less than or equal to the umber of TRXs in TRGi. g is the set of frequencies assigned to n TRXs of TRGi.
We assume all the groups assigned to TRGi to have the same length.
• TSi: Number of timeslots available for each TRX in TRGi
• TLi: Traffic load of TRGi (calculated or user-defined) of a single TRX in TRGi divided by TSi
• TSUi: Downlink timeslot use ratio (due to DTX) at TRGi
• CFi: Cost factor of TRGi (AFP Weight)
• QMINi: Minimum required quality (in C/I) at TRGi
• PMAXi: Percentage permitted to have quality lower than QMINi at TRGi
• REQi: Required number of TRXs at TRGi
A communication uses the group g in TRGi if its mobile allocation is g. The probability to be interfered is denoted by (i’ is the TRX index). Different TRX indexes may have different MAIOs. is a function of the whole frequency assignment. The precise definition of the term “to be interfered” is provided afterwards. The probability penalty due to violating a separation constraint is . It is a function of the whole frequency assignment as well.
The term “Atom” will be used in the following context:
For two TRGs, i and k,
i and k are synchronised, have the same HSN, the same MAL length and the same hopping mode.
• In the Results, Atoll displays only the transmitters for which it finds new neighbours.
Therefore, if a transmitter has already reached its maximum number of neighbours before starting the new allocation, it will not appear in the Results table.
g
2ARFCN
x x
Ai g g2ARFCN
Ai g = 1
Ai g = 0
Ai g Ai g
Ai g Ai g =n
TLi =#Erlangs
Pi i' g A Pi i' g A
Pi i' g A
ATOM i ATOM k
NH TRGs or BBH TRGs are always in separate atoms. If two TRGs interfere but are not in the same atom, these can be taken as unsynchronised. The quality of unsynchronised TRGs is a function of all possible frequency combinations. For synchronised TRGs, pairs of frequencies emitted at the same time are known.
5.9.1.1 Cost Function
The Atoll AFP cost function is a TRX based cost and not an interference matrix entry based cost. It counts the impaired traffic of the network TRXs in weighted Erlangs.
The cost function is reported to the user during the AFP progress with the help of its 5 components: , ,
, and .
= + + + +
where,
represents the missing TRX cost component represents the separation component
represents the additional cost component (interference, cost of changing a TRX) represents the corrupted TRX cost component
represents the out-of-domain frequency assignment cost component
In the above equations,
• i’ is the TRX index belonging to .
• is the number of missing TRXs for the subcell i.
• is the cost value for a missing TRX. This value can vary between 0 and 10. The default cost value is set to 1 and can be modified in the AFP module properties dialog.
• is the number of corrupted TRXs for the subcell i.
• is the cost value of a corrupted TRX. This value can vary between 0 and 10. The default cost value is set to 10 and can be modified in the AFP module properties dialog.
• is the number of TRXs, for the subcell i, having out-of-domain frequencies assigned.
• is the cost value of a TRX with out-of-domain frequencies assigned. This value can vary between 0 and 1. The default cost value is set to 0.5 and can be modified in the AFP module properties dialog.
And, as mentioned earlier, a virtual TRX is considered in case of BBH.
If i’ is valid, the algorithm evaluates the cost of a valid TRX. This cost has two components, and .
• is the separation violation probability penalty.
• is complementary probability penalty due to interference and the cost of modifying a TRX.
If the option “Take into account the cost of all the TRXs” available in the AFP module properties dialog is selected, then,
and
Or if the option “Do not include the cost of TRXs having reached their quality target” available in the AFP module properties dialog is selected, the algorithm compares with the quality target specified for i,
:
If ,
Then and .
Otherwise,
Both and will be equal 0.
is the same as (separation violation probability penalty) and the same as
(complementary probability penalty due to interference and the cost of modifying a TRX) in most cases. These are explained in detail in the next sections.
5.9.1.2 Cost Components
Separation violation and interference cost components are described hereafter. Parameters considered in the cost function components can be fully controlled by the user. Some of these parameters are part of the general data model (quality requirements, percentage of interference allowed per subcell), while others (such as separation costs and diversity gains) can be managed through the properties dialog of the Atoll AFP module.
5.9.1.2.1 Separation Violation Cost Component
The separation violation cost component is evaluated for each TRX. Estimation is based on costs specified for the required separations.
Let denote the required separation constraint between TRGi and TRGk. Let denote the user defined separation penalty for a required separation “s” and actual separation “z”. is used instead of
as abbreviation.
is considered to be the effect of a separation violation on the th TRX of TRGi assigned the group g, caused by the th TRX of TRGk assigned the group .
denotes the overall weight of the separation violation cost component. This value can be between 0 and 1, set to 1 by default. It can be modified in the AFP module properties dialog.
represents the weight of the specific separation constraint between i and k. This specific weight depends on the type of separation violation and follows the following priority rule:
1. Exceptional pairs 2. Co-transmitters 3. Co-site 4. Neighbours
For example, if a pair of subcells are co-site and neighbours at the same time, they will be considered as co-site because higher priority. Hence, of these subcells will be the weight of co-site relations. If only a neighbour relation exists between two subcells, then will be further weighted by the neighbour relation importance. The value of remains between 0 and 1. The default weights of each type of separation are available in the Separation cost tab.
If
• The AFP module properties dialog takes probability percentages as inputs while this document deals in probability values.
SEP_CONSTRi k Costs z
Then
In the above equations, is the number of frames in the MAL g. .
Let denote the instantaneous frame number from 0 to .
While modulo and is the frequency in g,
And modulo and is the frequency in g’.
In addition, frequencies belonging to a MAL with a low fractional load, and breaking a separation constraint, should not be weighted equally as in a non-hopping separation breaking case. Therefore, the cost is weighted by an interferer diversity gain.
The separation gain, denoted by is basically a function of the MAL length (and, of course, of the hopping mode). With frequency hopping, the effects of DTX and traffic load become more significant (due to the consideration of the average case instead of the worst case). For this reason, it is possible to consider these effects in through the relevant option available in the Advanced tab of the AFP module properties dialog.
Without this option, the is:
is the user defined interferer diversity gain (dB) for a given MAL length. It is used in definition as well.
On the other hand, if this option is selected, the becomes,
Where ,
And
More than one separation violations may exist for a TRX. Many “small” and have to be combined to form one cost element, the . This is done through iterating over all violating assignments and by summing up an equivalent to the probability of not being violated while considering each separation violation as an independent probability event. This sum is naturally limited to 100% of the TRX traffic, and is given by,
In the above formula, if , then , so that interference with itself is not taken into account.
5.9.1.2.2 Interference Cost Component
The interference cost component is evaluated for each TRX. Its estimation is based on interference histograms calculated for pairs of subcells. In addition, it takes into account frequency and interferer diversity gains and models frequency hopping and gain due to DTX.
When estimating , the following problems are encountered:
Note:
• Interference histograms are described in User Manual (GSM GPRS EGPRS project management, GSM GPRS EGPRS network optimisation, GSM GPRS EGPRS generic AFP management). Interference histograms can also be exported to files. For further description, refer to "Interferences" on page 190.
P''i i' g A
• The QMINi C/I quality indicator corresponds to the accumulated interference level of all interferers while the C/I interference histograms correspond to pair-wise interferences.
• Both QMINi and the histograms correspond to a single frequency. In case of a MAL containing more than one frequencies, interferences on several different frequencies of a MAL must be combined.
This estimation, presented below, is the simplest possible as it solves the first problem by linear summation and truncation at the value of 1 and it solves the second problem by averaging and adding the two diversity gains:
• , the frequency diversity gain, and
• , the interferer diversity gain.
Hereafter, denotes the global weight of interference cost component. This value can vary between 0 and 1 and is set to 0.35 by default, which can be modified in the AFP module properties dialog.
Let be the number of frames in the MAL g. . Let denote the instantaneous frame number from 0 to .
Let be the j’th MAIO of , where j is one of the TRXs.
The value of is one of
If TRGk is NH, then .
If TRGk is BBH, then .
As said earlier, in case of BBH, we consider virtual TRXs, the jth TRX has the MAIO j.
Let be the ith frequency in the group g.
Similar to the definition of , is defined as an interference event. is the effect interference on the th TRX of TRGi assigned the group g, caused by the th TRX of TRGk assigned the group .
Since , these are both represented by .
Where,
In the above formula, if , then , so that interference with itself is not taken into account.
The sum is limited to 100% of the TRX traffic. is quite similar to . The
only difference is the frequency diversity gain, , added to . F_DIV g
ii'kgg'k' 'ii'kgg'k' 'ii'kgg'k'
i' k' g'
5.9.1.2.3 I_DIV, F_DIV and Other Advanced Cost Parameters
When combining interference effects (or separation violation effects) on different frequencies belonging to a MAL, the following considerations should be taken into account:
1. Non-linearity of Frame Error Rate (FER) with respect to average C/I conditions and MAL length.
2. Interference Diversity Gain. This factor represents that the effect of average negative effects over user geographic location are directly proportional to the MAL length.
3. Frequency Diversity Gain. This factor models the gain due to diversity of multi-path effects and should be applied to the interference cost component only.
4. The fact that long MALs with synthesized hopping permit discarding the worst case estimation and include a gain due to DTX and low traffic load at the interferer end.
The Advanced properties tab shown in the figure below facilitates modelling these effects.
The Interference Diversity Gain table lists the values of I_DIV provided as a functions of MAL length. This gain is applied to the interference cost component and to the separation constraint violation cost component. Therefore, it provides a means to model the non-linear FER effects and interference diversity both. The default values in this table correspond to the curve . This equation generates values somewhat lower than empirical best-found values (this is because we prefer a slightly pessimistic cost function to be on the safe side).
The other table contains the F_DIV values, which are the same as the I_DIV values by default.