# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 3 Interference Alignment in Cognitive Radio: First Paradigm
### Techniques For IA in CR Networks
#### 3.2.2 Leakage of Interference Signals/Distributed Algorithm IA
The distance between the subspace of the received signal from each SU-Tx at the PUs and the set of interference subspaces at the PU is minimized. However, this particular solution consists of multiple PUs and presents an argument for when individual SUs attempt accessing the spectrum one after the other. Assuming local CSI is present at the PUs and global CSI is available at the SU, an optimization problem was defined so as to cause non or minimal interference to the PUs. The IA schemes discussed so far all assume perfect local CSI. In practice however, it is inevitable that the CSI is corrupted by estimation errors, which will likely lead to diminished the system performance [13; 81]. Equally potentially impeding to practical implementation of IA is finite SNR [81], because while the performance of IA at high SNR is adequate, it is far from optimal at moderate to low SNR [82]. It is based on these two drawbacks that the work in ref. [82] described a technique to counter CSI errors as well as providing the motivation for the work in ref. [83], where a more vigorous IA strategy for CR network comprising of CSI ambiguity is presented. It also proposes adopting a weighted optimization method related with the leakage interference to increase the system performance at low and moderate SNR [84]. Recalling the condition of distributed IA algorithms, ref. [83] proposes a robust joint signal IA design that transforms the transmit optimization and receive subspace selection limitation into a limited number of linear matrix disparities that are both optimal and solvable by interior point methods [85]. The proposed design of ref. [83] decreases the leakage of interference signals from the SU-Tx while preserving interference to the PU-Rx below a satisfactory level. The drawback of this solution however, lies in its intricacy making it impossible to prove that the iterations diverge to the universal ideal [23]. Solutions discussed so far have made several assumptions on network resources. This makes it necessary to consider allocation, utilization and performance of these resources in such a way that they do not negate ultimate goal of improving network performance. The work in ref. [86] presents distributed resource allocation algorithms to maximize the sum-rate of any-to-any links under per-node transmit-power and CR interference constraints. The first algorithm is developed when the CR interference constraints are absent. The issue thus amounts to weighed sum-rate maximization for MIMO ad hoc networks with per-node power constraints when other user interferences are treated as noise. The CR interference constraints are then added for the second algorithm, which incorporates a decomposition technique that ensures the constraints are enforced even during the iterative procedure. Thirdly, an alternate centralized algorithm was then developed based on network duality so that existing network duality results were extended to the ad hoc network configuration under the CR interference constraints. Therefore, by viewing this optimization as a multi-beam beamforming problem without loss of optimality, these novel algorithms iteratively updates receive beamformers, transmit-powers and transmit-beamformers in cycle to attain an optimal solution. Similarly, the work in ref. [87] presented a performance analysis of MIMO IA with user selection, where a transmitter sends the data stream of the selected user providing the maximum effective SNR, in order to derive the effective SNR of combining IA with minimizing LIF. By deriving exact closed-form expressions of the bit error rate (BER) and outage probability of the small-cell system, this resource optimization procedure work shows a marked gain in performance compared with conventional iterative solutions [79; 88].