Decomposition of the MIMO X Channels

In a multiple antenna system with two transmitters and two receivers, a scenario of data communication, known as the X channel, is studied in which each receiver receives data from both transmitters. In this scenario, it is assumed that each transmitter is unaware of the other transmitter´s data (non-cooperative scenario). This system can be considered as a combination of two broadcast channels (from the transmitters´ point of view) and two multi-access channels (from the receivers´ point of view). Taking advantage of both perspectives, two signaling schemes for such a scenario are developed. In these schemes, some linear filters are employed at the transmitters and at the receivers which decompose the system into either two non-interfering multi-antenna broadcast sub-channels or two non-interfering multi-antenna multi-access sub-channels. In addition, these filters are designed such that the maximum multiplexing gain (MG) of the system is attained by exploiting the null spaces of the direct and cross channels. It is shown that the proposed scenario outperforms other known non-cooperative schemes in terms of the achievable MG. In particular, it is shown that for some specific cases, the achieved MG is the same as the MG of the system if the full cooperation is provided either between the transmitters or between the receivers.