The Approximate Capacity of the MIMO Relay Channel

Capacity bounds are studied for the multiple-antenna complex 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 the partial decode-forward coding scheme achieves within min (t₁,r₂) bits from the cutset bound and at least one half of the cutset bound, establishing a good approximate characterization of the capacity. A similar additive gap of min (t₁ + t₂, r₃) + r₂ bits is shown to be achieved by the compress-forward coding scheme. The corresponding results for time-division half-duplex relay channels are also established.