# Interference Alignment in Multi-Hop Cognitive Radio Networks under Interference Leakage
## 1 Introduction  
As mobile devices become widespread, wireless data traffic has been increasing significantly in the recent years. In order to meet the ever-increasing demand for high quality wireless communication standards, the Third-Generation Partnership Project (3 GPP) and Long-Term Evolution (LTE) technologies have emerged [1; 2]. Regarding the deployment of the next-generation wireless communication systems, the corresponding growth in the demand for wireless radio spectrum resources will appear. With a rapid increase in the number of connected devices and mobile users, improving spectrum utilization has now become an important concern in designing next-generation wireless communication networks [3]. Unfortunately, this situation will cause a severe shortage of spectrum resources. Thus, the solution methods for spectrum utilization have been attracting attention in recent years [4]. One of the candidates for solving the problem of spectrum shortage is the cognitive radio (CR) technology. CR has attracted considerable interest, as it can cope with the spectrum under-utilization phenomenon, as the efficient usage of the limited spectrum is important for mobile applications. CR canremedy this problem by allowing secondary (unlicensed) users (SUs) to share the same spectrum band with the primary (licensed) users (PUs). Thus, CR is a promising solution for providing quality of service and overcoming the problem of spectrum limitation in wireless networks. At the moment, spectrum usage is assigned for specific services with limited bandwidth based on the regulatory policy. This means that the unlicensed users will not be able to use the licensed frequency bands. However, the inefficient use of the licensed spectrum has been reported. CR allows the unlicensed users to exploit the unused frequency bands dynamically without causing harmful interference to the licensed users. For this reason, it has been proposed to improve spectral utilization and efficiency [5; 6; 7; 8]. That is to say, CR is an inspiring approach for wireless communication systems that can alleviate the spectrum scarcity problem and utilize the existing spectrum resources efficiently. The CR network is composed of a primary network (PN) in which the licensed users of the spectrum are employed and a secondary network (SN), whose unlicensed users can access the spectrum opportunistically. SN users can access the licensed spectrum by three well-known techniques: underlay, overlay, and interweave [5; 6; 7]. In the underlay approach, the SU can simultaneously communicate with the PU using the PU's spectrum guaranteeing that the SU does not cause any harmful interference to the PU. In this scheme, the interference caused by the transmission of the SUs should not exceed an acceptable threshold. That means, the underlay method allows SU transmission as long as the interference remains under the predefined threshold value [9]. In the overlay approach, the SU has knowledge about the PU's transmitting information and how it is encoded. While the PU broadcasts its information periodically, the SU can obtain it by decoding the data sequence; thus, the interference can be partially or completely removed. The interweave paradigm is based on the concept of opportunistic communications. The idea was raised from the underutilized spectrum. Spectrum holes, which are not fully utilized most of the time, can be exploited by SUs to operate in the licensed bands. Thus, the spectrum utilization is enhanced by the opportunistic reuse of the spectrum holes. The interweave approach requires the detection of the PUs' activity in the licensed frequency band [10]. CR technology can be capable of utilizing the spectrum efficiently as long as the interference between PUs and SUs is perfectly aligned.