# Handover-Driven Interference Management for Co-Channel Deployment of Femto- and Macro-Cells
## 5 Control Algorithm
It is expected in general that the path loss of a user to a femtocell is smaller than that to a macrocell, so there may exist femtocell \(n\) enabling user \(j\) to have lower \(P_{j}^{(n)}\) and \(Q_{j}^{(n)}\) than those with the macrocell, thus leading to reduced interference. This is one reason why the handover approach achieves enhanced performance. After this handover, for downlink (uplink), the macrocell (other macrocell users) becomes a new interference source while femtocell \(n\) (its users) no longer causes interference due to the orthogonal RB allocation within the cell. Let the expected DL interference from the source cell (macrocell \(m\)) after the handover be denoted by \(\Delta I_{DL,src}^{(m)}\) and that from the target femtocell \(n\) before the handover be denoted by \(\Delta I_{DL,trgt}^{(n)}\). That is, by the handover, the new interference term \(\Delta I_{DL,src}^{(m)}\) is added to and the existing term \(\Delta I_{DL,trgt}^{(n)}\) is removed from the total DL interference experienced by user \(j\), which can be interpreted as load adjustment (load-balancing) between the cells. If femtocell \(n\) is selected such that \(\Delta I_{DL,src}^{(m)}<\Delta I_{DL,trgt}^{(n)}\), i.e., appropriate load-balancing is applied, the resulting DL interference experienced by user \(j\) is reduced, which is another reason why the handover approach obtains performance gain. Assume that the long-term probabilities for a user to be allocated each RB are evenly distributed. Then, \(I_{DL}^{(n)}(\mathbf{p})\) is rewritten as  
\[ \begin{array}{rl}I_{DL}^{(n)}(\mathbf{p})&=\;I_{DL}^{(m)}(\mathbf{p})+\Delta I _{DL,src}^{(m)}-\Delta I_{DL,trgt}^{(n)}\\ &=\;I_{DL}^{(m)}(\mathbf{p})+h_{m,j}E[p_{j}]^{\prime}\in\mathcal{U}_{m}-\{j\} ]-h_{n,j}E[p_{j}]^{\prime}\in\mathcal{U}_{n}]\end{array}  \tag{5}\]  
where \(m\) indicates the source macrocell. If cell \(n\) broadcasts \(E[p_{j}]^{\prime}\in\mathcal{U}_{n}]\) (the average per-RB DL transmit power) in SI, the macrocell can obtain the information by commanding users to report it. Similarly, it is also assumed that \(I_{UL}^{(n)}(\mathbf{p})\) is broadcast by cell \(n\) and reported by users to the macrocell. Thus, the macrocell has all the information required to calculate \(P_{j}^{(n)}\) and \(Q_{j}^{(n)}\). Using this calculation result, the transmit-power vectors are defined as \(\mathbf{P}^{(n)}(\mathbf{p})\triangleq[p_{1},\ldots,P_{j}^{(n)}(\mathbf{p}), \ldots,p_{N}]\) and \(\mathbf{Q}^{(n_{j})}(\mathbf{q})\triangleq[q_{1},\ldots,Q_{j}^{(n_{j})}( \mathbf{q}),\ldots,q_{N}]\). Next, the macrocell determines the target femtocell of user \(j\) such that a maximum decrease of its cell load is obtained at this iteration. This is expressed as  
\[n_{j}^{*}=\arg\max_{n_{j}}\{\Delta_{m,DL}^{(n_{j})}(\mathbf{p})+\Delta_{m,UL} ^{(n_{j})}(\mathbf{q})\} \tag{6}\]  
where  
\[ \begin{array}{l}\Delta_{m,DL}^{(n_{j})}(\mathbf{p})\triangleq\rho_{m}( \mathbf{p})-\rho_{m}(\mathbf{P}^{(n_{j})}(\mathbf{p})),\\ \Delta_{m,UL}^{(n_{j})}(\mathbf{q})\triangleq\rho_{m}(\mathbf{q})-\rho_{m}( \mathbf{Q}^{(n_{j})}(\mathbf{q})).\end{array} \]  
The above problem should be solved for each user. Thus, the search space size of the per-user handover control problem is \(M\times F\). Finally, the serving cells and transmit powers at \(t+1\) are determined as  
\[\begin{array}{l}\mathbf{n}(t+1)=\mathbf{n}^{*}\triangleq[n_{1}^{*},\ldots,n _{M}^{*},n_{M+1},\ldots,n_{N}]\\ \mathbf{p}(t+1)=\mathbf{P}^{(\mathbf{n}^{*})}(\mathbf{p})\triangleq[P_{1}^{(n _{1})}(\mathbf{p}),\ldots,P_{M}^{(n_{M})}(\mathbf{p}),\\ \quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad \  
users stay within their serving femtocells while their power allocations are updated. When outbound (from femtocell to macro- or other femtocell) handovers are allowed as well, femtocells make handover decisions on their users in the same way as the macrocell does. It is now shown that the above algorithm converges to an optimum.