# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 4 Interference Alignment in Cognitive Radio: Second Paradigm
### Multi User MIMO SU Link  
A factor mutual with the above mentioned research is that their entire system models make use of a single-user MIMO SU link therefore disregarding the effect of multiple SUs on the performance of a CR network. Actually, a single SU is unlikely to reliably detect the presence of a PU due to factors such as multipath fading impairments, low SNRs and sensing time constraints [7]. The literature has thus introduced research on utilising and evaluating the IA technique in a CR network that contains multiple SUs (Figure 4). The research work done in ref. [116], called opportunistic spatial orthogonalisation (OSO) is one of the earlier endeavours consisting of multiple SUs that permits both PU and the SUs to communicate simultaneously at the same frequency band and time slot. This particular work differentiates itself in two aspects: Firstly, the SUs do not require knowledge of the PU channel matrices. This leads to the second differentiator, which achieves the goal of forcing the signals from the SUs towards only a certain direction by utilising the randomness of the channel matrices and relying on multi-user diversity. Originally developed for single-input multiple-output (SIMO) scenarios, the OSO scheme has led to the interesting concept of OIA for the MIMO case, where it is shown that the ill-conditioned MIMO channel significantly increases the total throughput without much sacrifice of the PUs performance. The general concept behind OSO can be applied to a broad class of multi-user systems other than CR, and for some of them, the throughput gain will even be more prominent. Some of the algorithms such as symbol extensions, feasibility conditions of IA, LIF and IC, which are used to enhance IA in CR, have found reasonable opportunities to further exploit this multi-user scenario. A space-alignment (SA) technique based on symbol extension with multiple PUs was proposed in ref. [92], which gives a much higher performance than the single PU scheme in refs. [20; 24; 117; 118]. After spatial water filling (SWF) has been applied at the PU-Tx leaving some TOs unused, which the SU-Tx can exploit, this work avoids interference to the other PU-Rx's by demanding that the input power allocation matrix at the SU-Tx meets both the SUs total power constraints and a set of interference-power limitations at the other PU-Rx's. This work also describes a power allocation matrix at the SU-Tx that jointly maximises the transmission rate of the SU as well as ensuring the zero interference constraint at the PUs. The result is a higher transmission rate in the low SNR regime than ref. [24]. The multi-user scenario is extended further in the work done in refs. [119; 120], which are both based on the feasibility conditions of IA. The schemes developed in ref. [119] extends the work done in ref. [24] by also designing the SUs precoding matrices in such a way that exploits the free spatial dimensions left by the PU. In other words, no interference is generated at the PU-Rx. For a multi-user MIMO SU network, this work first extends the results of ref. [24], which show that for the SU-Rx not to be affected by the PU-Tx, it would have to null the PUs transmission. This would be the same as removing a number of antennas from both the Tx and Rx of the SU. For multiple SUs, the IA problem is achieved by simply converting it into a single-tier cognitive IA problem. Secondly, an iterative algorithm that exploits channel reciprocity is derived, which only necessitates local CSI at each node. The process involves a closed-form solution for the precoding matrices at the Tx's with the same number of antennas at each node (to satisfy the feasibility condition) and constant channel coefficients. A regrouping of the cognitive IA conditions is done to facilitate its formulation into a mathematical intersection of subspaces. Similarly, the work in ref. [120] also explores the feasibility condition of IA. This work essentially challenges the low achievable transmission rates of the SU network, especially in the higher SNR regimes.