The Approximate Capacity of the MIMO Relay Channel

Capacity bounds are studied for the multiple-antenna complex Gaussian relay channel with t
₁
transmitting antennas at the sender, r
₂
receiving and t
₂
transmitting antennas at the relay, and r
₃
receiving antennas at the receiver. It is shown that the partial decode-forward coding scheme achieves within (t
₁
,r
₂
) 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 (t
₁
+ t
₂
, r
₃
) + r
₂
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.