Capacity Bounds for Gaussian MIMO relay channel with Channel State Information

In this paper, source and relay precoders are derived which optimize upper and lower bounds on the Gaussian MIMO relay channel capacity. First, the prior art on the cut-set upper-bound on capacity is extended by showing that the optimization of the source and relay codebooks can be formulated as a convex problem without having to introduce a scalar parameter that captures their cross-correlation. Both the Full-Duplex and Time Division Duplex (TDD) relay channels are addressed, assuming perfect knowledge of all channels, and two procedures are proposed which solve the problem efficiently by relying on analytical expressions of gradients, subgradients and projection operators: the first one solves the dual problem while the second one applies the barrier method. Similar techniques are then used to maximize the achievable rate of Decode-and-Forward (DF) TDD MIMO relaying strategies with either partial or full decoding at the relay. Sub-optimum precoders are also proposed which have a closed-form expression that can be obtained from the KKT conditions, thus reducing the computational complexity at the expense of a lower rate. Simulations in a cellular downlink scenario show that the partial DF strategy can achieve a rate very close to capacity for realistic values of the Source to Relay signal-to-noise ratio. Finally, the availability of Channel State Information (CSI) in a real system is discussed.