# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 4 Interference Alignment in Cognitive Radio: Second Paradigm
### Other Endeavours  
As mentioned earlier, there are quite a number of other equally significant algorithms to implement IA in CR that do not fall under the scope of both paradigms that have been discussed. The work done in ref. [130] using vandermonde-subspace frequency division multiplexing (VFDM) is quite similar to the second paradigm. Rather than using unused eigenmodes left by the PU, this work exploits the extra dimensions of the cyclic-prefix (CP) of orthogonal frequency-division multiplexing (OFDM), so that the SU's transmission is projected onto the null space generated by the CP. This enables the SUs to transmit without causing any interference to the PUs. It then goes on to minimize inter-cell interference by developing a chordal-distance scheme called exhaustive search algorithm, in order to maximize the transmission rates of the SUs. The intra-cell interference is also minimized by using a heuristic algorithm. Compared to the traditional time-division multiple-access (TDMA) scheme, the proposed scheme can support more interference-free symbols to be transmitted by SUs simultaneously. Since IA has been established as an effective approach to eliminate the interference of SUs in CR networks, the work in ref. [12] proposes a time resource auction scheme based on game theory to exploit IA for an overlay CR network. This work uses the given related equilibrium functions to balance the benefits of using IA as an effective approach of eliminating the interference of SUs on the PU. Simulation results are presented to show the effectiveness of the proposed scheme.  
Furthermore, the work in ref. [131] breaks the restriction that SUs can only transmit on the idle sub-channels of the PU system by introducing IA based spectrum sharing into general CR networks and more specifically for distributed multi-user multi-antenna CR networks. Rayleigh quotients of channel matrices are utilized to predict the maximum interference from each SU and based on these predictions, the SUs with less interference to PUs are permitted access. As a result, the number of accessing SUs, the transmit power of each active SU-Tx as well as the sum rate of SUs are all increased. Given the nature of the time-variant channel condition between SUs and PUs, an adjustable transmit power baseline is selected to achieve a better trade-off between power gain and spatial DoF. This helps to solve the problem of low interference constraints that hinders SUs from being able to access spectrum holes.  
The work in ref. [59] does not only focus on effectively eliminating the interference among users in CR networks, it also proposes to increases the transmission rate of the PU that guarantees its priority over the SUs. This is achieved by proposing an optimal transceiver design (OTD) strategy, in which two partial-IA based techniques are suggested to implement the precoding matrices of SUs, in which the interference is aligned at the PU-Rx with a reduced overhead and complexity. Then the PUs precoding matrix is implemented to increase its throughput consequently. Additionally, their decoding matrices are re-designed to increase the performance of SUs. Simulation outcomes showed the effectiveness of the proposed scheme. The work in ref. [132] proposed that the PUs trade spectrum for secrecy to enable SUs access the licensed spectrum as long as they help to secure the PUs transmission in the presence of an eavesdropper. Both PUs and SUs are allowed to cooperate with each other by exchanging CSI (but not information data). Achievable DoF of both PU and SU pairs are characterized in the presence of an eavesdropper that intends to intercept the PUs data.