Degrees of Freedom on the MIMO X Channel - Optimality of Zero Forcing and the MMK Scheme

We characterize the degrees of freedom ηX in a system with two multiple antenna transmitters and two multiple antenna receivers. With M antennas at all nodes we find ⌊ 4 3 M⌋ ≤ ηX ≤ 4 3 M . The MMK scheme [1] built upon successive decoding and/or dirty paper coding schemes is known to achieve the ⌊ 4 3 M⌋ degrees of freedom. Interestingly, we find that simple zero forcing without dirty paper encoding or successive decoding, suffices to achieve the ⌊ 4 3 M⌋ degrees of freedom as well. Compared to the interference channels, the multiple access channels and the broadcast channels that are contained in the X channel, each of which allows only M degrees of freedom, we show that the X channel allows a higher multiplexing gain by a factor of at most 4 3 .