AFP Appendices

3.11.1 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

Neighbourhood cause Importance Function Resulting IF using the default values from the table above

Coverage

Min(O)+Delta(O){Max(Di)(Di)+(100%-Max(Di))(O)}+Min(Di)+Delta(Di)(Di) 10%+20%{10%(Di)+90%(O)}+1%+9%(Di)

Adjacent layer (Min(A)+Max(A))/2 45%

Adjacent transmitters Min(A)+Delta(A){Max(Di)(Di)+Max(O)(O)+

(100%-Max(Di)-Max(O))(A)}+Min(Di)+Delta(Di)(Di)

30%+30%{10%(Di)+30%(O) +60%(A)}+1%+9%(Di) Co-site transmitters Min(C)+Delta(C){Max(Di)(Di)+Max(O)(O)+

(100%-Max(Di)-Max(O))(A)}+Min(Di)+Delta(Di)(Di)

60%+40%{10%(Di)+30%(O) +60%(A)}+1%+9%(Di)

• Set Min(Di) and Max(Di) to 0% if you do not want to take into account the distance factor in the importance calculation.

• If the Min and Max value ranges of the importance function factors do not overlap, the neighbours will be ranked by neighbour cause. With the default values for minimum and maximum importance fields, neighbours will be ranked in this order:

co-site neighbours, adjacent neighbours, and neighbours allocated based on coverage overlapping.

• If the Min and Max value ranges of the importance function factors overlap, the neighbours may be ranked differently. There can be a mix of the neighbourhood causes.

• The default value of Min(O) = 1% ensures that neighbours selected for symmetry will have an importance greater than 0%. With a value of Min(O) = 0%, neighbours selected for symmetry will have an importance field greater than 0% only if there is some coverage overlapping.

Figure 3.15: Inter-Transmitter Distance Computation D

d

d = D1+xcos–xcos

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 TRG_i in the assignment A

For example:

• When i is NH,  g is a single member group containing one of the frequencies assigned at TRG_i. 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 TRG_i.

= Number of TRXs in TRG_i  g is the set of frequencies assigned to TRXs of TRG_i. (|g| = number of TRXs in TRG_i).

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 TRG_i.  g is the set of frequencies assigned to n TRXs of TRG_i.

We assume all the groups assigned to TRG_i to have the same length.

• TS_i: Number of timeslots available for each TRX in TRG_i

• TL_i: Traffic load of TRG_i (calculated or user-defined) of a single TRX in TRG_i divided by TS_i

• TSU_i: Downlink timeslot use ratio (due to DTX) at TRG_i

• CF_i: Cost factor of TRG_i (AFP Weight)

• QMIN_i: Minimum required quality (in C/I) at TRG_i

• PMAX_i: Percentage permitted to have quality lower than QMIN_i at TRG_i

• REQ_i: Required number of TRXs at TRG_i

A communication uses the group g in TRG_i 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.

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.

3.11.1.1 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 .

= + + + +

,

represents the missing TRX cost component represents the separation component

represents the additional cost component (interference, cost of changing a TRX) 2^ARFCN

x x

A_{i g} g2^ARFCN

A_{i g} = 1

A_{i g} = 0 A_{i g}

A_{i g}

A_{i g} A_{i g} = n

TL_i = #Erlangs

P_{i i' g }  A P_{i i' g }  A

P_{i i' g }  A

ATOM i  ATOM k  

 _mis _sep _comp

_corr _dom

 _mis _sep _comp _corr _dom

_mis

_sep

_comp

Atoll 3.3.2 Technical Reference Guide for Radio Networks

• 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 box.

• 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 box.

• 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 box.

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 box 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 box is selected, the algorithm compares with the quality target specified for i, :

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.

3.11.1.2 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 box of the Atoll AFP module.

3.11.1.2.1 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 TRG_i and TRG_k. 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 TRG_i assigned the group g, caused by the th TRX of TRG_k 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 box.

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