# Handover Decision-Making Algorithm for 5G Heterogeneous Networks
## 3 Methodology  
This paper proposes a handover scheme that combines the dwelling time prediction technique and TOPSIS. The proposed method is less complicated than the intelligent-based handover algorithm because it does not require data training and learning, such as in the case of [PERSON] et al. [7]. The pseudocode of the proposed handover decision-making algorithm is shown in Figure 3. The MT initiates the handover process if the RSS of the serving network falls below the threshold value where it does not meet the user's service requirements. Figure 2: Prediction method to estimate travelling distance (\(l\)). The proposed algorithm will trigger the dwelling time prediction algorithm if any small cell network such as 5G or WLAN is detected [18]. The dwell time, \(t\), within the small cell network can be computed using the method presented in [18] by dividing the estimated travelling distance, \(l\), in the small cell network with MT speed, \(v\), in m/s, as expressed by Equation (3). The MT speed, \(v\), can be obtained through the vehicle speedometer. The dwelling time prediction algorithm only allows the small cell networks with an estimated connection time greater than two seconds to undergo network quality evaluation using the TOPSIS method. The TOPSIS method was selected because it can handle multi-criteria parameters and complex information in the handover process [11]. The network candidate with the highest score was to be selected as the targeted network. The handover parameters used by the proposed algorithm for handover decision making include RSS, throughput, cost, delay, bit error rate, and signal-to-noise plus interference ratio (SNIR). Each parameter was assumed to take monotonically increasing values and the positive ideal solution would consist of the best values of all parameters attained by all the alternatives. Meanwhile, if each parameter took monotonically decreasing values, the negative ideal solution would comprise the worst parameter values attainable from all alternatives. The TOPSIS network quality evaluation process is expressed as follows [19]:  
1. Decision matrix construction, \(a\) \[a= \begin{bmatrix}P_{1}&\dots&P_{j}&\dots&P_{n}\\ a_{11}&\dots&a_{1j}&\dots&a_{1n}\\ \vdots&&\vdots&&\vdots\\ a_{i1}&\dots&a_{ij}&\dots&a_{in}\\ \vdots&&\vdots&&\vdots\\ a_{m1}&\dots&a_{mj}&\dots&a_{mn}\\ \end{bmatrix} \quad \begin{array}{c}N_{1}\\ \vdots\\ N_{i}\\ \vdots\\ N_{m}\\ \end{array} \] (5) where \(N_{i}\) is the \(i\)th network candidate, \(P_{j}\) is the \(j\)th of type of handover parameter, \(a_{ij}\) represents the value of network parameter \(i\) with respect to \(j\), \(m\) is the maximum of row in the matrix, and lastly, \(n\) is maximum of column in the matrix. 2. Normalize the decision matrix using the normalization method expressed in Equation (6) and form the normalized decision matrix \(A\) as Equation (7). Figure 3: Pseudocode of the proposed handover algorithm. \[A_{ij}=\frac{a_{ij}}{\sqrt{\sum_{j=1}^{n}a^{2}{}_{ij}}}\quad\text{ for }\text{benefit }\text{attribute},\text{ }i=1,\text{ }2,\text{ }\ldots m,\quad j=1,\text{ }2,\text{ }\ldots n \tag{6}\]  
\[A= \begin{bmatrix}A_{11}&\ldots&A_{1j}&\ldots&A_{1n}\\ \vdots&&\vdots&&\vdots\\ A_{i1}&\ldots&A_{ij}&\ldots&A_{in}\\ \vdots&&\vdots&&\vdots\\ A_{m1}&\ldots&A_{mj}&\ldots&A_{mm}\end{bmatrix}  \tag{7}\]  
where the \(A_{ij}\) is the value of normalization from \(a_{ij}\). 3. The weighted normalized decision matrix, \(X\), is given as  
\[X=A*W= \begin{bmatrix}w_{1}A_{11}&\cdots&w_{j}A_{1j}&\cdots&w_{n}A_{1n}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ w_{1}A_{i1}&\cdots&w_{j}A_{ij}&\cdots&w_{n}A_{in}\\ \vdots&\vdots&\vdots&\vdots\\ w_{1}A_{m1}&\cdots&w_{j}A_{mj}&\cdots&w_{n}A_{mm}\end{bmatrix} = \begin{bmatrix} X_{11}&\cdots&X_{1j}&\cdots&X_{1n}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ X_{l1}&\cdots&X_{ij}&\cdots&X_{in}\\ \vdots&\vdots&\vdots&\vdots&\vdots\\ X_{m1}&\cdots&X_{mj}&\cdots&X_{mn}\end{bmatrix}  \tag{8}\]  
where \(W\) is the handover parameter weightage allocation matrix as expressed in Equation (9). \[W=