Diversity-multiplexing tradeoff of the half-duplex relay channel

We show that the diversity-multiplexing tradeoff of a half-duplex single-relay channel with identically distributed Rayleigh fading channel gains meets the 2 by 1 MISO bound. We generalize the result to the case when there are N non-interfering relays and show that the diversity-multiplexing tradeoff is equal to the N + 1 by 1 MISO bound.