# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 4 Interference Alignment in Cognitive Radio: Second Paradigm
### Leakage Interference  
Despite the condition that a zero interference constraint to the PU Rx has to be satisfied by the SU, the performance of IA in realistic propagation environments still causes LIF [122; 123] i.e., the interference power that remains in the received signal after applying receiver interference suppression matrices. With this in mind, the work in ref. [122] proposes the subsequent two categories of OIA: Singular value decomposition (SVD)-based OIA and antenna selection-based OIA. The suggested OIA works with merely local CSI at the transmitter, without iterative processing, dimension extension, and inter-node or inter-cell synchronisation. For the proposed schemes for the SVD-based OIA, individually SU designs the weight vector that minimizes the LIF making use SVD-based beamforming. For the antenna selection-based OIA, the best transmit antenna is selected at each SU, which shows results in sum-rate gain as the number of antennas at each user grows. However, the user-node scaling state in relation to SNR does not necessarily change when the number of antennas remains constant. An improved version of minimizing LIF is the work done in ref. [123], which considers a number of MIMO SU links in the presence of MIMO PUs as well. This work proposes an iterative algorithm to find the precoders and reception filters for both the PU and SU networks unlike the work in ref. [122], after which the transmission of the PUs is maximized by SWF. The cognitive IA problem is then formulated by defining the required iterative conditions for this paradigm to mitigate the harmful effects of the SUs transmission on the PU. The rates of the SU links are then maximized by employing water-filling algorithm similar to the PUs. It is observed that the proposed iterative algorithm converges faster than earlier schemes, while its complexity is not much more than ref. [79].  
Interference Cancellation  
The IC technique was initially used in refs. [124; 125] that zero forces the intra-cell interference in the primary cell with the aid of the cognitive base station. The interference caused by the primary base station on the SUs are also cancelled using dirty paper coding (DPC), which provides outer bounds on the achievable DoF as well as showing that the achieved sum DoF is strictly larger than the case when cognitive message sharing is unavailable.  
A similar strategy was then used in ref. [125] for the case of downlink of cellular networks to achieve outer bounds on the DoF through IA. IA helps the PUs and SUs using SWF to enable efficient utilisation of the available DoF, by cancelling intra-cell interference within the PU link with pre-coding matrices and zero-forcing the intra-cell interference within the SUs. The achievable sum rates within the PUs and the SUs were then maximized by applying SWF to calculate the optimal transmit power matrices \(Q^{p}\) and the source covariance matrix \(Q^{g}\) for the PU and SU respectively.  
This concept is made that much clearer by the work done in ref. [126], which adopts a SIC technique similar to ref. [68], but also allows the SUs to not only make use of the unused eigenmodes left by the PU, but to also make use of the non-free eigenmodes. The SUs do so by using SIC to remove the effect of the PU signal in order to decode the transmitted SU signal. Although this work consists of multiple SUs, unlike the work in ref. [68], each PU channel is shared by only one SU to avoid co-interference between the SUs. Thus, after maximizing the PUs transmission in order to release some eigenmodes, a space alignment algorithm is used to study the effect of multiple SUs on the cognitive MIMO-MAC sum rates. After applying perfect or imperfect SIC, this scheme selects the best SUs based on their channels and their corresponding closed-form sub-optimal power solutions to transmit on the used eigenmodes of the PU, thus achieving higher sum-rates. The numerical results for Rayleigh fading channel indicated that the low-complexity selection structure performs similarly to the previous optimal solutions.