# An Improved Radio Resource Management with Carrier Aggregation in LTE Advanced
## 3 System Model
### Proposed Greedy-Based Model  
The purpose of the proposed method is to maximize the user throughput and maintain the fairness by considering the probability of packet loss and HOL delay while minimizing the computational complexity. The weighted transmission rate of all users is calculated first. Then all possible gain of user \(i\) for assigning CC \(j\) are measured. Here, gain is defined as the difference between the weighted transmission rate based on available resources and the transmission rate of a user currently being allocated. If the weighted transmission rate is more than the current rate, user can transmit more data and thus can achieve the gain. By considering the queue length, if the maximum gain is better than zero, CC \(j\) with MSC \(l\) is assigned to user \(i\). If the weighted transmission rate with the variable \(\alpha_{i}\) and delay for each RB is higher than that of currently assigned, RB \(k\) is assigned to user \(i\). The step-by-step procedure of this algorithm is given below.  
Step 1: Let \(\Omega\) (\(j\), \(k\)) be the current transmission rate of the user which is currently being allocated with CC \(j\) and RB \(k\). As it is assumed that RBs of all CCs are not allocated to any user initially, \(\Omega\) (\(j\), \(k\)) is set to zero at the beginning stage. The weighted transmission rate \(W_{ij,k,l}\) of user \(i\), CC \(j\), RB \(k\), and MSC \(l\) is calculated by the instantaneous transmission rate and previous average transmission rate.  
Step 2: Let \(g\) (\(i\), \(j\), \(l\)) be the gain of user \(i\) after assigning CC \(j\) with MSC \(l\). The gain is calculated by the following equation.  
\[g(i,j,k)=\sum_{k=1}^{S}max(0,W_{i,j,k,l}-\Omega(j,k)) \tag{13}\]  
The difference between the weighted and current transmission rate is considered as the gain in (13). If the current rate \(\Omega\) (\(j\), \(k\)) is higher than the weighted rate \(W_{ij,k,l}\), there will be no gain for that particular user. After calculating all possible gains and queue length \(\xi_{j}\) of CC \(j\), assignment (\(i^{\prime}\), \(j^{\prime}\), \(l^{\prime}\)) with the highest gain can be found by (14):\[(i^{\prime},j^{\prime},l^{\prime})=argmax_{i\in Q_{j}\in R,l\in T}g(i,j,l)/\xi_{j} \tag{14}\]  
If the \(g\)\((i^{\prime},j^{\prime},l^{\prime})\) is more than zero, CC \(j^{\prime}\) with MSC \(l^{\prime}\) will be assigned to user \(i^{\prime}\). Otherwise, it will enter into the next iteration.  
Step 3: Then, HOL delay \(D_{l^{\prime},j^{\prime}}\) for user \(i^{\prime}\) and CC \(j^{\prime}\) is calculated by waiting time in the queue. After that, the variable \(\alpha_{i^{\prime}}\) of user \(i^{\prime}\) is calculated by the above Equations (7)-(12). This variable considers several criteria, such as the probability of packet loss and delay threshold.  
Step 4: For each RB \(k\) of CC \(j^{\prime}\), weighted transmission rate \(\sigma\)\((i^{\prime},j^{\prime},k,l^{\prime})\) of user \(i^{\prime}\) with variable \(\alpha_{i^{\prime}}\) and delay \(D_{i^{\prime},j^{\prime}}\) is calculated. If the \(\sigma\)\((i^{\prime},j^{\prime},k,l^{\prime})\) is higher than the transmission rate with currently assigned RB \(\Omega\)\((j,k)\), then RB \(k\) of CC \(j^{\prime}\) is assigned to user \(i^{\prime}\) and \(\Omega\)\((j,k)\) is set to \(\sigma\)\((i^{\prime},j^{\prime},k,l^{\prime})\).  
Step 5: Assigned CC \(j^{\prime}\) is removed from the list of available CC for user \(i^{\prime}\) so that CC \(j^{\prime}\) cannot be assigned twice to the same user. Moreover, it ensures that user \(i^{\prime}\) can be assigned maximum \(m\) CC.  
Step 6: Repeat Step 2-5 until it reaches to the following conditions: (a) all users have been assigned with the required CCs; (b) no further gain is possible after assigning a new CC; and (c) reaches to any terminating condition. The proposed greedy-based method of downlink resource allocation is given in Table 4.