# Cognitive Interference Alignment Schemes for IoT Oriented Heterogeneous Two-Tier Networks
## 5 Numerical Simulation Results  
In this section, the numerical results are presented. To evaluate the effectiveness of the proposed schemes, we compared the achieved sum rate of the IN-CIA and P-CIA algorithms with that of several existing precoding methods, as well as with different data streams and antenna configurations. In the simulations, we assumed there are three IoT nodes in the femtocell coexisting with a single antenna MU and a dual antenna MBS of the macrocell, and that identical transmit power is allocated for each user, i.e., \(K=3\), \(N_{T,p}=1\), \(N_{R,p}=2\) and \(P_{k}=P\), for \(k=p,\ 1,\ 2,\ 3\). Each cognitive pair transmits \(d=1\) data stream with \(N_{T,k}=3\) transmitting antennas at the IoT node and \(N_{R,k}=4\) receiving antennas at the MBS. Figure 2 shows the sum rate comparison of the IoT oriented femtocell with several existing interference suppression precoding algorithms. When the feasibility condition is satisfied, both the cooperative IA and P-CIA outperform the IN-CIA, and the performance converges in the high SNR region. This is because the cooperative IA achieves a slightly higher channel gain with the cooperation from the macrocell to eliminate the cross-tier interference, and the P-CIA further enhances the sum rate by jointly considering the desired channel gain, interference, and noise. It is also observed that the IA algorithms generally provide remarkable benefits over the orthogonality based precoding methods, since IA can obtain half of the degrees of freedom per channel use. In Figure 3, we compare the sum rate of the macrocell with several precoding algorithms. As the proposed cognitive IA schemes fully eliminate the cognitive interference caused to the macrocell, the MUs can achieve an almost identical performance with that of the non-cognitive homogeneous network. We can also see that the cooperative IA compromises the primary users in the macrocell to ensure better performance of the IoT oriented cognitive femtocell, which turns out to be a major limitation. The conventional non-cognitive IA algorithm that neglects the cognitive interference also causes significant performance degradation to MUs. Next, we consider scenarios with different numbers of data streams and antenna configurations to evaluate the performance of the proposed scheme. It can be seen from Figure 4 that the proposed cognitive IA algorithm can achieve the desired sum rate when the number of antenna meets the feasibility condition. However, the network performance would be severely degraded without enough antennas equipped as the feasibility condition requires. In such a case, to make the IA schemes feasible, we can either add more antennas at each transmitter/receiver or reduce the required degrees of freedom by cutting down the number of data streams in the network. To provide measurement results from a practical perspective, we evaluated the percentage of interference leakage, which is defined as the fraction of the interference power in the dimensions reserved for the desired signal [17]. The interference leakage percentage at each user is given as:  
\[p_{k}=\frac{\sum_{i=1}^{d_{k}}\lambda_{\mathbf{O}_{k},i}}{\text{tr}\{\mathbf{O }_{k}\}}\text{ for }k=1,\ \cdots,\ K. \tag{44}\]  
Figure 3: Sum rate comparison of the macrocell with different precoding algorithms. Figure 2: Sum rate comparison of the Internet of Things (IoT) oriented femtocell with existing precoding algorithms. where \(\mathbf{O}_{k}\) denotes the interference covariance matrix in (20), and \(\lambda_{\mathbf{O}_{k},i}\) is the \(i\)-th eigenvalue of the matrix in ascending order. The numerator and the denominator of (44) are the interference and desired signal powers at the receiver, \(k\), respectively. As can be seen from Figure 5, in the simulation, the expected total degrees of freedom for the two curves are 5 and 7, respectively. When the antenna configuration just satisfies the feasibility condition, the IA based network utilizes all the degrees of freedom to transmit data streams.