Gaussian MIMO Half-Duplex Relay Networks: Approximate Optimality of Simple Schedules

This paper considers a Gaussian network where N half-duplex multiple-antenna relays assist the communication between a source and a destination. A novel antenna switching policy is proposed, where each relays' antenna can be configured to either receive or transmit independently of the others. The rate achieved by noisy network coding is shown to be to within a constant gap from the cut-set bound, where the gap only depends on the total number of antennas in the system. Moreover, the optimal number of different relay antenna configurations needed to attain the constant gap is proved to be at most N + 1, that is, it only depends on the number of relays but not on the total number of antennas. Such a relay scheduling policy is referred to as simple. Through an example, it is shown that independently switching the antennas at the relays not only achieves in general strictly higher rates compared to using the antennas for the same purpose, but can actually provide a strictly larger pre-log factor. This implies that in broadband wireless networks with half-duplex multiple-antenna relays, the relay antennas should be dynamically configured to either transmit of receive depending on the channel conditions.