In this chapter, we analyze the performance of networks with two multiantenna transmit nodes and two multiantenna receive nodes. The canonical 2 × 2 network is illustrated in Figure 12.1. Transmitter 1, equipped with nt1 antennas, wishes to communicate with receiver 1 which has nr1 antennas, and transmitter 2, equipped with nt2 antennas, wishes to communicate with receiver 2, which has nr2 antennas. The signal from transmitter 1 acts as interference to receiver 2 and vice versa.
Even for this simple network, fundamental capacity results are still unknown. For instance, the capacity region of the 2 × 2 network even in the SISO case under general assumptions is unknown. For certain special cases, it is possible to derive the capacity of such channels, in particular when the interfering signals are strong such as in References [52, 272] and . Most works in the literature have focused on deriving outer bounds to the capacity region such as References [177, 224, 10], and  for SISO systems, and References  and  for MIMO systems. Achievable rates of such networks under different sets of assumptions, such as in References[135, 271, 59] and , have also been found. Additionally, in Reference , the capacity region of the SISO Gaussian interference channel is derived to within one bit/second/Hz using an achievable rate region based on the Han–Kobayashi scheme introduced in Reference , and on novel outer bounds. Recently, the interference channel has been analyzed in the high SNR regime where interference-alignment introduced in Reference  has been shown to provide enormous network-wide performance improvements.