# Cognitive Interference Alignment Schemes for IoT Oriented Heterogeneous Two-Tier Networks
## 2 System Model  
In this section, we first set up the system model of the IoT oriented two-tier cognitive network. Then, we show that the cross-tier interference induced by cognitive spectrum sharing will invalidate the full-IA algorithm, which motivates us to design cognitive empowered IA schemes. As shown in Figure 1, in compliance with the Fourth-Generation (4G) standard, such as LTE-A [21], we consider the uplink of a cognitive co-existing macrocell and IoT femtocell network, and assume that the transmissions are operated in the time-division duplex (TDD) mode. In the macrocell (primary tier), there is an \(N_{R,p}\) antenna MBS (as primary receiver) serving several MUs through single-carrier frequency division multiple access (SC-FDMA) [22]. The femtocell (cognitive tier) is comprised of an FBS (as cognitive receiver) and several IoT nodes distributed over the coverage area. For matters of spectral efficiency, the FBS is equipped with multiple antennas and an IA is introduced to enable space division multiplexing. As in tiered cognitive radio networks, the primary tier (macrocell) is oblivious to the cognitive tier (femtocell), and does not change its optimal precoding design; the cognitive tier should adapt its transmission to protect the primary tier from any undesired performance degradation. Hence, these two tiers are completely independent without any cooperation being established, and no cross-tier interference management strategy needs to be implemented at the primary tier. Since the macrocell operates in SC-FDMA, when accessing a certain licensed band, the femtocell is supposed to consider just one macrocell user (MU) in this band. However, this assumption does not decrease the generality of the proposed schemes. An extension to the model with multi-MUs per channel could be obtained by means of multiuser scheduling techniques [23] once the solution for the single MU case has been identified. More specifically, a \(K\)-user cognitive femtocell shares the licensed band with an MU simultaneously. There are \(N_{T,k}\) and \(N_{R,k}\) antennas at the \(k\)-th transmitter and the receiver in the femtocell, respectively, and a single antenna is equipped at the MU. We first focus on the full-IA algorithm without considering the cross-tier interference. When the MU is absent, the signal of the \(k\)-th IoT node can be recovered by full-IA at the FBS as:  
Figure 1: The two-tier cognitive network with coexisting macrocell and femtocell. \[\mathbf{y}_{k}=\mathbf{U}_{k}^{H}\mathbf{H}_{k,k}\mathbf{V}_{k}\mathbf{x}_{k}+\sum_{i=1,i \
eq k}^{K}\mathbf{U}_{k}^{H}\mathbf{H}_{k,i}\mathbf{V}_{i}\mathbf{x}_{i}+\mathbf{U} _{k}^{H}\mathbf{n}_{k}. \tag{1}\]  
Here, \(\mathbf{x}_{k}\in\mathbb{C}^{d_{k}\times 1}\) is the data of the IoT node, \(k\), with the transmit power constraint, \(P_{k}\), i.e., \(\mathbb{E}\Big{[}\|\mathbf{x}_{k}\|^{2}\Big{]}=P_{k}\). \(\mathbf{V}_{k}\in\mathbb{C}^{N_{Tx}\times d_{k}}\) and \(\mathbf{U}_{k}\in\mathbb{C}^{N_{Rx}\times d_{k}}\) are the full-IA precoding and decoding matrices, respectively. \(d_{k}\) is the number of data streams, and \(\mathbf{n}_{k}\in\mathbb{C}^{N_{Rx}\times 1}\sim\mathcal{CN}\Big{(}0,\sigma_{n}^{2 }\mathbf{I}_{N_{Rx}}\Big{)}\) is the additive white Gaussian noise vectors with a variance, \(\sigma_{n}^{2}\). For the Rayleigh channel, let \(\mathbf{H}_{k,k}\in\mathbb{C}^{N_{Rx}\times N_{Tx}}\) denote the \(k\)-th transmission channel matrix, and \(\mathbf{H}_{k,i}\in\mathbb{C}^{N_{Rx}\times N_{Tx}}\) denote the interference channel matrix from the \(i\)-th transmitter to the \(k\)-th receiver. The entries of the Rayleigh channel matrix are standard independent identically distributed (i.i.d.) with zero-mean and unit-variance. According to the full-IA algorithm, the co-tier interference among IoT nodes can be eliminated perfectly.