5.5 Cell-Group Specific Optimization of Handover Thresholds
5.5.2 Configuration of Handover Thresholds
5.5.4.2 Advantages over Cell-Specific Optimization
In this section, the advantages of optimizing the target cell threshold in cell-group specific way over cell-specific is highlighted analytically. The target cell threshold m = 2 of (2.32) is optimized with respect to the sum Ψ(κ) of its corresponding correction directives in KPI collection period κ. Using (5.12) and (5.26), the sum Ψ(κ) is expressed in KPI collection period κ as
Ψ(κ) = Dc(+),2(κ) + Dc(−),2(κ) = J2 X j=1 D(+),2c,j (κ) + D(−),2c,j (κ) (5.27)
where J2is the total number of selected subsetsSc,j(2) for target cell threshold. Moreover, as the matrix G2of (5.9) and (5.23) used to derive the correction directives of the target cell threshold is common for both optimization approaches, the following equalities hold: D(+),2c (κ) = J2 X j=1 Dc,j(+),2(κ) and (5.28) D(−),2 c (κ) = J2 X j=1 Dc,j(−),2(κ). (5.29)
The aim is to analyze the impact on Ψ(κ) when the target cell threshold is updated in cell-specific or cell-group specific way. For this purpose, the value of Ψ(κ) in the next period κ + 1 is expressed in terms of the correction directives of the current and next collection periods for both optimization approaches. In the following, the expression of Ψ(κ) is derived first for the cell-specific optimization approach then for cell-group specific optimization.
The sum of D(+),2c,j (κ) and D(−),2c,j (κ) is upper bounded by the total number Hc,j(2)(κ) of missed (TLHs) and successful handovers from cell c with respect to neighboring cells of set Sc,j(2) , i.e.,
D(+),2c,j (κ) + D(−),2c,j (κ)≤ Hc,j(2)(κ)∀j. (5.30) Any successful handover is counted as a mobility failure event if the UE detects an RLF shortly after, i.e., TEH or HWC.
5.5 Cell-Group Specific Optimization of Handover Thresholds 89
The set J2 of indices for the subsets Sc,j(m) of neighboring cells is decomposed in three disjoint sets as follows
U(2) c = n j ∈ J2|D(+),2c,j (κ) >> D (−),2 c,j (κ) o , (5.31) Vc(2) = n j ∈ J2|D(+),2c,j (κ) << D (−),2 c,j (κ) o , and (5.32) O(2)c = n j ∈ J2|D(+),2c,j (κ)≈ D (−),2 c,j (κ) o . (5.33)
The sets Uc(2), Vc(2) and O(2)c contain the indices of the subsets Sc,j(2) of neighboring cells requiring an increase, decrease and no change, respectively, in Q(2)c,j. Using these sets, the sum Ψ(κ) in (5.27) can be rewritten as
Ψ(k) = X µ∈Uc(2) D(+),2c,µ (κ) + D(−),2c,µ (κ)+ X ν∈Vc(2) D(+),2c,ν (κ) + D(−),2c,ν (κ) + X o∈Oc(2) Dc,o(+),2(κ) + Dc,o(−),2(κ). (5.34)
In cell-specific optimization, the handover threshold is updated based on the differ- ence in the values of the correction directives Dc(+),2(κ) and D(−),2c (κ) as described in Section 5.4.2.1. Three cases are distinguished as follows.
1. Dc(+),2(κ) >> Dc(−),2(κ): In this case, Dc(+),2(κ) is dominant in the cell and the handover threshold Q(2)c,j is increased. This action on the handover threshold aims at reducing Dc(+),2(κ) in the cell which is the sum of D(+),2c,j (κ) over index j. Thus, Dc,j(+),2(κ + 1) can be expressed as
D(+),2c,j (κ + 1) = ∆(+),2c,j · Dc,j(+),2(κ) ∀j (5.35) where the factor ∆(+),2c,j ≥ 0. In the best case, all the mobility failure events of Dc,j(+),2(κ + 1) are resolved, i.e., ∆(+),2c,j = 0.
Reducing Dc(+),2(κ+1) might lead to an increase in Dc(−),2(κ+1) as both correction directives require contradicting threshold actions to be performed on the same handover threshold Q(2)c . The correction directive D(−),2c,j (κ + 1) can be expressed as a fraction of the residual number of missed and successful handovers as
D(−),2c,j (κ + 1) = λ(−),2c,j ·Hc,j(2)(κ + 1)− Dc,j(+),2(κ + 1)
= λ(−),2c,j · R(−),2c,j (κ + 1) ∀j (5.36)
where the factor 0 ≤ λ(−),2c,j ≤ 1. The factor λ (−),2
c,j is upper bounded by 1 since the sum of the correction directives cannot be higher than Hc,j(2)(κ + 1) of (5.30).
90 Chapter 5: Automatic Optimization of Handover Thresholds
Using (5.34), (5.35) and (5.36), the sum Ψ(κ + 1) in collection period κ + 1 can be expressed in this case as
Ψ(k + 1) = X µ∈Uc(2) ∆(+),2c,µ · D(+),2 c,µ (κ) + λ(−),2c,µ · R(−),2c,µ (κ + 1) + X ν∈Vc(2) ∆(+),2c,ν · D(+),2c,ν (κ) + λ(−),2c,ν · R(−),2c,ν (κ + 1) + X o∈Oc(2) ∆(+),2c,o · D(+),2
c,o (κ) + λ(−),2c,o · Rc,o(−),2(κ + 1)
. (5.37)
It is shown in (5.37) that increasing the target cell threshold cell-specifically is proper with respect to all the neighboring cells of subsets Sc,j(2)
j∈Uc(2)
. However, this handover threshold update is inappropriate with respect to neighboring cells of subsets Sc,j(2)
j∈Vc(2)
. This is because D(−),2c,j (κ) j∈Vc(2)
is dominant with respect to these neighboring cells, and consequently the target cell threshold should be decreased. Hence, increasing Q(2)c may even degrade the mobility conditions with respect to the neighboring cells of subsets Sc,j(2)
j∈Vc(2)
. In addition, the target cell threshold should not be modified with respect to the neighboring cells of subsets
Sc,j(2)
j∈Oc(2)
because none of their corresponding correction directives can be well reduced without a significant increase in one of them.
2. Dc(+),2(κ) << Dc(−),2(κ): In this case, Dc(−),2(κ) is dominant in the cell and the handover threshold Q(2)c,j is decreased. This action on the handover threshold aims at reducing Dc(−),2(κ) in the cell which is the sum of D(−),2c,j (κ) over index j. Thus, Dc,j(−),2(κ + 1) can be expressed as
D(−),2c,j (κ + 1) = ∆(−),2c,j · Dc,j(−),2(κ) ∀j (5.38) where the factor ∆(−),2c,j ≥ 0.
Similar to the previous case, reducing D(−),2c (κ + 1) might lead to an increase in Dc(+),2(κ + 1). The correction directive Dc,j(+),2(κ + 1) can be expressed as a fraction of the residual number of missed and successful handovers as
D(+),2c,j (κ + 1) = λ(+),2c,j ·Hc,j(2)(κ + 1)− Dc,j(−),2(κ + 1)
= λ(+),2c,j · R(+),2c,j (κ + 1) ∀j (5.39)
where the factor 0≤ λ(+),2c,j ≤ 1.
5.5 Cell-Group Specific Optimization of Handover Thresholds 91 in this case as Ψ(κ + 1) = X µ∈Uc(2) λ(+),2c,µ · R(+),2c,µ (κ + 1) + ∆(−),2c,µ · Dc,µ(−),2(κ) + X ν∈Vc(2) λ(+),2c,ν · R(+),2c,ν (κ + 1) + ∆(−),2c,ν · Dc,ν(−),2(κ) + X o∈O(2)c
λ(+),2c,o · R(+),2c,o (κ + 1) + ∆(−),2c,o · D(−),2c,o (κ)
. (5.40)
It is shown in (5.40) that decreasing the target cell threshold cell-specifically is proper with respect to all the neighboring cells of subsets Sc,j(2)
j∈Vc(2)
. However, this handover threshold update is inappropriate with respect to neighboring cells of subsets Sc,j(2) j∈Uc(2) . This is because Dc,j(+),2(κ) j∈Uc(2)
is dominant with respect to these neighboring cells, and consequently the target cell threshold should be increased. Hence, decreasing Q(2)c may even degrade the mobility conditions with respect to the neighboring cells of subsets Sc,j(2)
j∈Uc(2)
. In addition, the target cell threshold should not be modified with respect to the neighboring cells of subsets
Sc,j(2)
j∈Oc(2)
because none of their corresponding correction directives can be well reduced without a significant increase in one of them.
3. Dc(+),2(κ) ≈ D(−),2c (κ): In this case, the cell c does not modify the target cell threshold Q(2)c . In principle, Dc(+),2(κ+1) and Dc(−),2(κ+1) should be equal to the previous values of Dc(+),2(κ) and Dc(−),2(κ), respectively. However, they might be different if other neighboring cells have updated their handover thresholds leading to a shift in cell borders in the next period. Therefore, the sum of D(+),2c (κ + 1) and D(−),2c (κ + 1) can be expressed in general as a fraction of Hc,j(2)(κ) as follows
Dc,j(+),2(κ + 1) + Dc,j(−),2(κ + 1)= λ(2)c,j · Hc,j(2)(κ + 1) ∀j (5.41) where the factor 0 ≤ λ(2)c,j ≤ 1. Keeping the target cell threshold unchanged is a proper action with respect to neighboring cells of subsets Sc,j(2)
j∈Oc(2)
. How- ever, this action is inappropriate with respect to neighboring cells of subsets
Sc,j(2) j∈Uc(2) and Sc,j(2) j∈Vc(2)
where one of the correction directives is dominant, and consequently their corresponding target cell thresholds should be increased or decreased, respectively. This case D(+),2c (κ) ≈ Dc(−),2(κ) is the most critical in cell-specific optimization since the automatic algorithm cannot react to the mo- bility problems of neighboring cells of both subsets of Sc,j(2)
j∈Uc(2) and Sc,j(2) j∈Vc(2) . In contrast to cell-specific optimization, a dedicated handover threshold is configured with respect to each subset of neighboring cells in cell-group specific optimization. Con- sequently, the appropriate target cell threshold action can be performed with respect
92 Chapter 5: Automatic Optimization of Handover Thresholds
to neighboring cells of each subset: The target cell threshold is increased with respect to neighboring cells of subset Sc,j(2)
j∈Uc(2)
, decreased with respect to neighboring cells of Sc,j(2)
j∈Vc(2)
, not changed with respect to neighboring cells of Sc,j(2) j∈O(2)c
. In cell-group specific optimization, the sum Ψ(κ + 1) in collection period κ + 1 can be written as
Ψ(κ + 1) = X µ∈Uc(2) ∆(+),2c,µ · D(+),2 c,µ (κ) + λ(−),2c,µ · R(−),2c,µ (κ + 1) + X ν∈Vc(2) λ(+),2c,ν · R(+),2 c,ν (κ + 1) + ∆(−),2c,ν · Dc,ν(−),2(κ) + X o∈O(2)c λ(2)c,o · Hc,o(2)(κ + 1). (5.42)
Thus, as opposed to cell-specific optimization, the cell-group specific approach can tackle the mobility failure events with respect to neighboring cells of Sc,j(2)
j∈Uc(2) and Sc,j(2) j∈Vc(2) even when Dc(+),2(κ)≈ Dc(−),2(κ). 5.5.4.3 Optimization Limitations
A handover threshold Q(m)c,j that is configured cell-group specifically cannot be adjusted by the automatic optimization algorithm if its corresponding correction directives are similar to each other, i.e.,
Dc,j(+),m ≈ D(−),mc,j . (5.43)
In this case, the mobility failure events occurring with respect to the subset Sc,j(m) of neighboring cells require contradicting actions to be performed on the same handover threshold Q(m)c,j , and consequently none of the correction directives can be well reduced without a significant increase in one of them. As it is shown in Section 5.5.4.1 that only the configuration of the target cell threshold in cell-group specific way is beneficial, the optimization limitation in (5.43) holds only for the target cell threshold, i.e., m = 2. If the serving cell threshold m = 1 is configured in cell-specific way as it should be, the automatic algorithm cannot update the serving cell threshold when
Dc(+),1≈ D(−),1
c . (5.44)
In this case, the mobility failure events occurring with respect to all neighboring cells require contradicting actions to be performed on the same serving cell threshold Q(1)c .