following pattern: 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 P a =     b$_{1}$ 0 0 1 0 b$_{2}$ 1 0 1 0 b$_{3}$ 0 0 1 0 b$_{4}$    $^{.}$ 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. ˜ r =     x$_{i}$$_{1}$ . x$_{i}$$_{j}$ . x$_{i}$$_{N}$    $^{+}$$^{A}$$^{−}$$^{1}$$^{Bx}$$^{+ (}$$^{P}$ + B ) H − 1 u u + A − $^{1}$w . (20) 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 σ 2 r ∑ k | h ( − 1) u, ( i$_{j}$,k $_{)}$|$^{2}$+ σ 2 $_{r}$| b$_{j}$ | 2 ∑ k | h ( − 1) u, ( j,k $_{)}$|$^{2}$+ σ 2 | a$_{j}$ | 2 = σ 2 $_{e}$, ∀ j, (21) P s =     b$_{1}$ 0 0 1 0 b$_{2}$ 1 0 0 1 b$_{3}$ 0 1 0 0 b$_{4}$    $^{.}$ 11