content_image/307177.jpg content_image/307179.jpg
discussion in Part B has an implicit assumption (focus) that each station i wants to send different data to each other station j ̸ = i . If we examine the scheme carefully, this assumption is not necessary. We note that under the scheme, a station will have chances to transmit to all other stations. In particular, a station i will have chances to transmit data to two different stations j and k in two different derangements. If so desired, station i could transmit the same data to stations j and k in the two derangements. This observation in turn implies that the general traffic patterncan be realized. 

For illustration, let us examine how the traffic pattern of Fi g. 1 can be realized. This example is a pattern consisting of the co-existence of unicast and broadcast. As has been described the data transmission can be realized by scheduling a condensed derangement set, which is: 

<img src='content_image/307177.jpg'>

The transmitted data of station 1, 2 and 3 are respectively [ a, b, e ] T for D$_{1}$ and [ a, c, d ] T for D$_{2}$ . 

## IV. MIMO SWITCHING WITH NETWORK CODING 

The MIMO switch so far makes use of ZF detection, in which data are switched according to the derangement matrix. In other words, the elements of “1” deno te the switching desired, while the elements of “0” are the interferences that have been forced to zero. A n on-zero diagonal element corresponds to self transmission, meaning the relay forwards the self information back to the transmitter. In general, there is no need to force a diagonal element to zero because the self information is known by the transmitter, and can be subtracted out by the transmitter. This is the basic idea behind network coding. Thus, the zero-forcing requirement for the transmission pattern matrix can be relaxed for the diagonal. With this relaxation, there is an extra degree of freedom in our design to improve the system performance. 

In this case we rewrite (6) as 

where B is a diagonal matrix B = diag { b$_{1}$, · · · , b$_{N}$ } . 

<img src='content_image/307179.jpg'>

For a symmetric derangement such as P$_{1}$ , the corresponding network-coded switch matrix has the 

