Achievable Rate for Gaussian Multiple Relay Channels with Linear Relaying Functions

The achievable rate of a Gaussian multiple relay channel with linear relaying functions is derived here. With linear relaying, relays transmit (on every channel use) a causal linear combination of their past received inputs. In this paper, the optimum temporal covariance of the signal transmitted by the source is derived and linear relaying functions proposed. Results show that linear relaying outperforms all known relaying techniques for relay channels and generates the tightest lower bound on the capacity of the multiple relay channel.