# Interference Alignment for Cognitive Radio Communications and Networks: A Survey
## 4 Interference Alignment in Cognitive Radio: Second Paradigm
### Water-Filling Techniques For IA in CR Networks
#### 4.2.1 Spatial Water Filling (SWF)
Another point of interest is the calculation of the input covariance matrix \(P_{CM}\) that will maximize the transmission rates for the opportunistic SUs transmission link. Once \(P_{CM}\) has been solved; the optimal power allocation can be defined as a function of the power constraint \(\overline{P}\) i.e., \(P_{PA}=diag(\overline{p_{1}},\,\overline{p_{2}},\ldots,\overline{p_{i}})\). The work in ref. [24] used \(P_{PA}\) to determine how the opportunistic SU spreads its total power among  
Figure 5: Single user multiple-input multiple-output (MIMO) link. the identified TOs, allowing the opportunistic SU to achieve higher transmission rates. Each transmit opportunity can also be seen as separate spatial signaling dimension such as those provided by time, frequency, antennas, etc. in order to achieve higher DoF on the MIMO Channel [93]. The work done in ref. [114] was an earlier attempt based on this model, where the PU leaves some of it eigenmodes unused to enable cognitive transmission. In this work, the unused eigenmodes are not only used for aligning the SU transmission to convey data as their transmission status is also used as a coding scheme to transmit cognitive codewords. Thus a jamming signal (non-information signal) that is known at the destination and can be easily removed is sent when the CR codeword indicates \"transmission\" for a spatial direction that is used for primary transmission. This ensures a minimum cognitive rate equal to the number of antennas and corresponds to a simple implementation. The outcome of the work in ref. [24] shows that a zero interference constraint to the PU-Rx has to be satisfied. This theoretically diminishes opportunities for some of the IA algorithms described in Section 2 under the first paradigm, such as interference cancellation (IC) and distributed IA, which are used to optimize IA in CR. Given this fact, subsequent research such as the work done in ref. [115] on interference cancellation require unique circumstances for the solutions to be feasible. This particular work proposes the use of both interference cancellation and IA techniques to enhance the achievable degrees of freedom (DoF) for the MIMO CR network. In particular, an intermediate relay node is introduced in between the SU-Tx and Rx that is designed to cancel interference from both the SU Tx and the relay node, thus achieving maximum DoF. It is shown that with the appropriate number of antennas at the intermediate relay against the sum of DoF of the PU network and the maximum DoF available in the SU network without the presence of PU network, the maximum achievable DoF of the two-tier CR network with \(M\) transmit antennas and \(N\) receive antennas is \(\min\{M,N\}\). When the PU network also uses SVD based encoding and decoding so that no interference signal is allowed to its signal space along with appropriate number of antennas at the relay node, the CR network achieves a higher DoF than when the two-tier CR operates without a relay node. Similarly, the work in ref. [68] investigates both orthogonal and non-orthogonal transmission of the SU, with the aim of determining spectral efficiency gain of an uplink MIMO CR system. In this work, the SU is allowed to share the spectrum with the PU by using a unique space alignment technique along with an interference temperature threshold technique to ensure a non-zero SU rate. The proposed scheme adopts a successive IC (SIC) technique so that the SU is not limited to exploiting the unused TOs of the PUs transmission, but it is also allowed to exploit the used eigenmodes of the PU by respecting both total power and interference temperature constraints. Furthermore, this work analyses the SIC's operational inaccuracy as well as the CSI estimation imperfection on the SUs power allocation. Further studies such as ref. [61], which ensures zero LIF is only feasible when the SU-Tx has at least the same number of antennas as the DoF of the PU system.