On achievable rates for Gaussian MIMO relay channels

The capacity of relay channels has been an open problem for decades. Decode-and-forward (DAF) and compress-and-forward (CAF) are two strategies to obtain lower bounds to the capacity. They have been well studied for the discrete SISO case. However, for the Gaussian case, we have had the limited results. The optimal input distribution to achieve the maximum rate derived from the discrete case has been known only for the DAF scheme, but not for the CAF scheme. Furthermore, the results are difficult to extend to the MIMO case. In this paper, we study the achievable rates of the Gaussian MIMO relay channels. We derive the achievable rates for both DAF and CAF relaying.