In the multi-user communication, the interference is one of the challenges to be mitigated. If we consider the channels such as, the X channel (XC), the interference channel (IC) and the Z channel (ZC); multiple signals from multiple users are transmitted at the same time with the same frequency causing interference to the unwanted receivers. This interference limits the system capacity considerably. Modern day research in the wireless communication is focused on the management of such interference. Interference alignment (IA) is one of the cooperative techniques of interference management, where all the interference observed at a particular receiver from the unwanted transmitters are aligned in a lower dimensional space, thus giving higher degrees of freedom to the desired streams.
The initial idea of interference alignment was discussed by Maddah Ali and Syed Jafar in 2007-08 in the multiple input multiple output (MIMO) XC and single input single output (SISO) channels. The alignment of interference in the lower dimension is achieved by designing suitable precoders that satisfy the power constraints.
To understand the concept of alignment, let us suppose that there are three rooms in a house, where three very important persons have to be hosted. But suddenly, four more random persons appeared in the house asking for the room and struggling to get the single rooms. They appeared in a group of two and the ones in the same group share no room in any cost. It is not easy to remove them because they do not have elsewhere to go. In that case, the owner has to allocate at least two rooms to four of them, keeping one person from different groups in one room. This leaves one more single room to the owner and he can allocate that room to 1 VIP. Hence, by cooperatively allocating two rooms to 4 people, the owner can at least manage to gain 1 extra room for the VIP, which is an achievement.
The VIP is the desired signal and random people are the interference. By giving each interference signal from different group a room or by aligning those signals in a direction, better degrees of freedom is achieved for the desired streams.
The figure below shows an interference alignment in the case of three user MIMO interference channel where each transmitter-receiver pair has two antennas. The aim of alignment is to design precoders, $\mathbf{V}_1, \mathbf{V}_2$ and $\mathbf{V}_3$, that align the interference space observed at each receiver. For the channels from transmitter $j$ to receiver $i$, denoted by $\mathbf{H}_{ij}$, the alignment is achieved by fulfilling the following mathematical conditions:
span($\mathbf{H}_{12}\mathbf{V}_2$)=span($\mathbf{H}_{13}\mathbf{V}_3$),
span($\mathbf{H}_{21}\mathbf{V}_1$)=span($\mathbf{H}_{23}\mathbf{V}_3$),
span($\mathbf{H}_{31}\mathbf{V}_1$)=span($\mathbf{H}_{32}\mathbf{V}_2$),
for $\mathbf{V}_i^H \mathbf{V}_i=\mathbf{I}_d$ is guaranteed for the power constraint assumption, where $.^H$ represents the conjugate transpose of a matrix. This requires that the channel is globally known to all the transmitters, which is a challenge in wireless communications.
The initial idea of interference alignment was discussed by Maddah Ali and Syed Jafar in 2007-08 in the multiple input multiple output (MIMO) XC and single input single output (SISO) channels. The alignment of interference in the lower dimension is achieved by designing suitable precoders that satisfy the power constraints.
To understand the concept of alignment, let us suppose that there are three rooms in a house, where three very important persons have to be hosted. But suddenly, four more random persons appeared in the house asking for the room and struggling to get the single rooms. They appeared in a group of two and the ones in the same group share no room in any cost. It is not easy to remove them because they do not have elsewhere to go. In that case, the owner has to allocate at least two rooms to four of them, keeping one person from different groups in one room. This leaves one more single room to the owner and he can allocate that room to 1 VIP. Hence, by cooperatively allocating two rooms to 4 people, the owner can at least manage to gain 1 extra room for the VIP, which is an achievement.
The VIP is the desired signal and random people are the interference. By giving each interference signal from different group a room or by aligning those signals in a direction, better degrees of freedom is achieved for the desired streams.
The figure below shows an interference alignment in the case of three user MIMO interference channel where each transmitter-receiver pair has two antennas. The aim of alignment is to design precoders, $\mathbf{V}_1, \mathbf{V}_2$ and $\mathbf{V}_3$, that align the interference space observed at each receiver. For the channels from transmitter $j$ to receiver $i$, denoted by $\mathbf{H}_{ij}$, the alignment is achieved by fulfilling the following mathematical conditions:
span($\mathbf{H}_{12}\mathbf{V}_2$)=span($\mathbf{H}_{13}\mathbf{V}_3$),
span($\mathbf{H}_{21}\mathbf{V}_1$)=span($\mathbf{H}_{23}\mathbf{V}_3$),
span($\mathbf{H}_{31}\mathbf{V}_1$)=span($\mathbf{H}_{32}\mathbf{V}_2$),
for $\mathbf{V}_i^H \mathbf{V}_i=\mathbf{I}_d$ is guaranteed for the power constraint assumption, where $.^H$ represents the conjugate transpose of a matrix. This requires that the channel is globally known to all the transmitters, which is a challenge in wireless communications.
