content_image/327121.jpg content_image/327115.jpg content_image/327118.jpg content_image/327120.jpg
following pattern: 

<img src='content_image/327121.jpg'>

This particular switching pattern corresponds to pairwise data exchange, in which stations 1 and 4 are a pair and stations 2 and 3 are the other pair. Each pairwise transmission is actually a two-way relay channel. Hence, the network coding-based MIMO switching constructs multiple parallel two-way relay transmissions. However, for an asymmetric derangement such as P$_{2}$ , the corresponding switch matrix is 

<img src='content_image/327115.jpg'>

This is not a traditional physical-layer network coding setting [8] because the data exchange is not pairwise. For both symmetric and asymmetric switch matrices, we shall refer to the corresponding matrices with non-zero diagonal as network-coded switch matrix, and the associated MIMO switching setup as MIMO switching with network coding. Note that the concept here generalizes the concept of physical-layer network coding for two-way relay channel in [8]. 

Extending the previous ZF method, ZF with network coding yields the following signal after detection. 

<img src='content_image/327118.jpg'>

The self-information term A − $^{1}$Bx can be cancelled at the stations. Potentially, with network coding, we could decrease the noise power by designing B appropriately. The effective noise power can be written by 

<img src='content_image/327120.jpg'>

