Achievable Rates of Compress-and-Forward Cooperative Relaying on Gaussian Vector Channels

The compress-and-forward (C&F) cooperative relaying strategy is known to outperform decode-and-forward (D&F) when the relay is close to the destination. In this paper, we derive achievable rates on Gaussian vector channels with cooperative C&F relaying. In order to extend previous information-theoretic results from the scalar to the vector Gaussian channel, we exploit recent results in distributed source coding. Like in source coding with side information at the decoder, the relay applies a conditional Karhunen Loeve transform (CKLT) to its observed signal, followed by a separate Wyner-Ziv encoding of each output stream with a different rate and under a sum-rate constraint. However, these Wyner-Ziv coding rates are such that the total mutual information between the source and destination is maximized. This differs from the conventional source coding approach in which the rates are selected to minimize the total squared distortion, leading to the well-known reverse-waterfilling algorithm. We show that the maximization of the C&F mutual information is also a convex problem. The optimum Wyner-Ziv coding rates have a simple analytical expression, and can be obtained by a waterfilling algorithm. Finally, we illustrate these results by simulations of MIMO-OFDM relaying in a system similar to IEEE802.16.