Rotated multi-D constellations in Rayleigh fading: Mutual information improvement and a pragmatic approach for near-capacity performance in high-rate regions

This paper studies the mutual information improvement attained by rotated multidimensional (multi-D) constellations via a unitary precoder G ∈ C^N×Nin Rayleigh fading. At first, based on the symmetric cut-off rate of the N-D signal space, we develop a design criterion with regard to the precoder G. It is then demonstrated that the use of rotated constellations in only a reasonably low dimensional signal space can significantly increase the mutual information in high-rate regimes. By considering the QPSK system, we then propose a class of good unitary rotation G in 4-D signal space using parameterization approach, which are shown to provide remarkable improvement. To further illustrate the potential of multi-D constellation and to show the practical use of mutual information improvement, we propose a simple yet powerful coded modulation scheme in which a (multi-D) mapping technique employed in a multi-D rotated constellation is concatenated with a short-memory high-rate convolutional code (CC). By using extrinsic information transfer (EXIT) charts, it is demonstrated that the proposed technique provides an exceptionally good error performance. For example, by using the derived 4×4 rotation, together with QPSK constellation, and a simple rate-3/4 outer convolutional code, it is shown that the proposed system can operate 1.39 dB lower than the traditional coded modulation capacity at the bit error rate (BER) level around 10^-6.