Degrees of Freedom on the MIMO X Channel - the Optimality of 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 ⌊ 43M⌋ ≤ ηX ≤ 4 3M . The MMK scheme proposed in [1] is seen to achieve the maximum multiplexing gain rounded down to the nearest integer and is exactly optimal when M is a multiple of 3. Compared to zero forcing that allows only M degrees of freedom, we show that the X channel allows a higher multiplexing gain by a factor of at most 43 . While spatial zero forcing is not optimal on the X channel, the combination of zero forcing, dirty paper coding and successive decoding proposed in the MMK scheme is optimal for the maximum multiplexing gain rounded down to the nearest integer value.