# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 1 Introduction
DoF is the amount of signaling dimensions, respective dimension corresponding to an interference-free additive white Gaussian noise (AWGN) channel with signal-to-noise ratio (SNR) that increases proportionally with the overall transmit power [18]. The study of DoF initiated in ref. [19] found surprisingly high DoF, as SNR approached infinity. The results of ref. [19] in which users are able to transmit at a data rate equal to one-half of their capacity in an ideal interference-free channel motivated the work of refs. [17; 20], which presented the IA scheme in its linear form for the two user X-channel as a general principle. It was particularly interesting to see that the potential DoF that could be created largely depended on the alignment techniques involved. This implies that the signal space across the entire network nodes could potentially have numerous spatial dimensions as the overall number of transmit and receive antennas. However, achieving ideal signal alignment is a very complex task [19] of which techniques such as message sharing in the manner of CR, beamforming, zero forcing and successive decoding may be combined in many different ways across users, data streams and antennas to establish inner bounds on the DoF [19]. This overview will focus on the technique of message sharing. The earliest work to explore the increase in DoF with message sharing in the manner of CR was done in refs. [20; 21] for both the multiple-input multiple-output (MIMO) interference and X-channels. This is because the CR network can be seen as an interference channel when the SUs coexist with the PUs and the SU transmission is subjected to the PU receiver threshold as well as the cross interference between the SUs themselves. Thus the IA strategy tends to as expected fit in with CR systems mechanisms of managing interference between the PU and SU [10]. This work explored the impact of distributing a user's information with other the user's transmitter or receiver in that manner of singularity. In terms of performance, the DoF for the MIMO interference channel (IC) remained the same as without any form of cognition at either transmitters or receivers. Indeed, even this was a good enough result for further research bearing in mind that with all nodes having equal number of antennas, any increment on the number of antennas would yield higher data rates. However, the IC was shown to achieve higher DoF if both users have some form of cognition at the same time i.e., they either both make use of cognitive receivers, or they both make use cognitive transmitters or one has a cognitive transmitter although the other has a cognitive receiver. A number of other practical IA algorithms have been developed in the manner of message sharing such as refs. [22; 23], but these have primarily been developed for the single-tier K-user IC where each transmitter has an intended receiver, and the remaining transmitters are considered as interferers for that receiver. Despite these studies focusing on single-tier systems, they have provided a significant research platform that has been translated into mainstream two-tier CR networks. From all the work done to further exploit this research subject, it has emerged that broadly speaking there are two main system models or paradigms in the design and implementation of IA in two-tier CR networks [24]. The first paradigm considers a CR network having a number of SU pairs and a single PU-Tx and PU-Rx pair, where the PU-Tx is assumed far from its Rx and the SU-Rx's are considered not to be influenced by the interference from the PU-Tx (which is somewhat similar to the direct spectrum sensing scenario [7; 8]). The main goal of this IA approach is to choose appropriate transmit precoding matrices and receiver interference suppression subspaces for the SUs to ensure that individual SU-Rx can decode their own signals while maintaining an allowable interference level to the PU within the specified threshold by minimizing the interference leaked into the received signal subspace.