# Handover-Driven Interference Management for Co-Channel Deployment of Femto- and Macro-Cells
## 5 Control Algorithm  
A handover control algorithm to solve \(P1\) and \(P2\) is now presented. The proposed algorithm operates in a greedy manner, i.e., it makes a decision at each iteration without considering achievable gains at subsequent iterations. This greedy strategy enables the design of a simple algorithm and the analysis of its convergence behavior. The pseudo code of the algorithm is given in Algorithm 1. ```
1:\(t\) : Slot index
2:\(T_{H\O}\) : Interval of handover-controller activation (in terms of slots)
3:\(\mathcal{U}_{H\O}\) : User set to be handed over in the current iteration
4:\(N_{H\O}\) : Maximum allowed number of handovers per iteration
5:for slot \(t\)do
6: Update radio resource allocation for all user \(j\in\mathcal{U}\)
7:if\(t\) mod \(T_{H\O}==0\)then
8:\(\mathcal{U}^{\prime}\leftarrow\mathcal{U}\)
9:\(\mathcal{U}_{H\O}\leftarrow\{\}\)
10:for\(|\mathcal{U}_{H\O}|<N_{H\O}\)do
11: Obtain \(j^{*}\in\mathcal{U}^{\prime}\) according to Equation (12)
12:if\(\Delta_{m,DL}^{(n_{j})}(\mathbf{p})+\Delta_{m,UL}^{(n_{j^{*}})}(\mathbf{q})>0\)then
13:\(\mathcal{U}_{H\O}\leftarrow\mathcal{U}_{H\O}+\{j^{*}\}\)
14:endif
15:\(\mathcal{U}^{\prime}\leftarrow\mathcal{U}^{\prime}-\{j^{*}\}\)
17:endfor
18: Perform handover for all user \(j\in\mathcal{U}_{H\O}\)
19:endif
20:\(t\gets t+1\)
21:endfor
```  
**Algorithm 1** Handover control algorithm. For a greedy algorithm to reduce the number of handovers, it is beneficial to trigger more gainful handovers at each iteration than those of other sequences as well as those at subsequent iterations. That is, it chooses \(\mathbf{x}\) such that: (1) \(\Delta_{m}^{(\mathbf{x})}(t)\geq\Delta_{m}^{(\mathbf{x}^{\prime})}(t)\) for any feasible sequence \(\mathbf{x}^{\prime}\); and (2) \(\Delta_{m}^{(\mathbf{x})}(t)\geq\Delta_{m}^{(\mathbf{x})}(t+1)\). The rationale behind this strategy is as follows: First, consider two sequences \(\mathbf{x}_{1}\) and \(\mathbf{x}_{2}\) such that \(\Delta_{m}^{(\mathbf{x}_{1})}(t)\geq\Delta_{m}^{(\mathbf{x}_{2})}(t)\). Then, it is probable that, for arbitrary \(\rho_{m}^{(-)}\), \(\mathbf{x}_{2}\) does not reach \(\rho_{m}^{(-)}\) at the \(t\)th iteration while \(\mathbf{x}_{1}\) does. Second, suppose that \(\Delta_{m}^{(\mathbf{x}_{1})}(t)\geq\Delta_{m}^{(\mathbf{x}_{1})}(t+1)\) and \(\Delta_{m}^{(\mathbf{x}_{2})}(t)=\Delta_{m}^{(\mathbf{x}_{1})}(t+1)\leq\Delta _{m}^{(\mathbf{x}_{2})}(t+1)=\Delta_{m}^{(\mathbf{x}_{1})}(t)\). Similarly, for arbitrary \(\rho_{m}^{(-)}\), \(\mathbf{x}_{1}\) is likely to reach \(\rho_{m}^{(-)}\) earlier than \(\mathbf{x}_{2}\). Note that these conditions are meaningful because a greedy algorithm is assumed (there could be a sequence requiring less handovers while not meeting these conditions). An algorithm called _per-user control_ is designed so as to meet the above conditions. The handover of multiple users or only one user may be allowed at each iteration. The former will speed up convergence at the expense of more handovers than the latter due to the coarser control granularity. It is shown that both converge to a unique optimal assignment \(\mathbf{n}^{*}\). At each iteration, a macrocell first calculates the expected transmit power of its users when each of them is handed over to a candidate target femtocell while keeping the others in the macrocell. When user \(j\in\mathcal{U}_{m}\) is handed over to femtocell \(n\in\mathcal{F}\), his minimum transmit power needed to meet the target SINR \(\gamma_{j}\) within cell \(n\), denoted by \(P_{j}^{(n)}\) and \(Q_{j}^{(n)}\) for DL and UL, respectively, is obtained as\[ \begin{array}{l}P_{j}^{(n)}(\mathbf{p})=\gamma_{j}(I_{DL}^{(n)}(\mathbf{p})+\eta) /h_{n,j},\\ Q_{j}^{(n)}(\mathbf{p})=\gamma_{j}(I_{UL}^{(n)}(\mathbf{q})+\eta)/h_{j,n}\end{array}  \tag{4}\]  
where \(I_{DL}^{(n)}(\mathbf{p})\) and \(I_{UL}^{(n)}(\mathbf{q})\) are the average levels of DL and UL interference experienced by user \(j\) at a RB after user \(j\) is handed over to cell \(n\).