Approximate capacity of the MIMO relay channel

The capacity bounds are studied for the multiple-antenna real full-duplex Gaussian relay channel with t₁ transmitting antennas at the sender, r₂ receiving and t₂ transmitting antennas at the relay, and r₃ receiving antennas at the receiver. It is shown that compress-forward and partial decode-forward achieve within (1/2)(min(t₁ + t₂, r₃) + r₂) bits and (1/2) min(t₁, r₂) bits, respectively, from the cutset bound. Unlike the single-antenna case, partial decode-forward can be arbitrarily better than optimal selection between decode-forward and direct transmission. Similar gap results for half-duplex models are briefly discussed.