Title :
Rotated Multi-D Constellations in Rayleigh Fading: Mutual Information Improvement and Pragmatic Approach for Near-Capacity Performance in High-Rate Regions
Author :
Herath, Sanjeewa P. ; Tran, Nghi H. ; Le-Ngoc, Tho
Author_Institution :
Dept. of Electr. & Comput. Eng., McGill Univ., Montreal, QC, Canada
fDate :
12/1/2012 12:00:00 AM
Abstract :
This paper studies the mutual information improvement attained by rotated multidimensional (multi-D) constellations via a unitary precoder G in 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. Based on parameterizations of unitary matrices, we then construct good unitary precoder G in 4-D signal space using a simple optimization problem, which involves only four real variables and it is applicable to any modulation scheme. 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 bit-interleaved coded modulation (BICM) 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. By using extrinsic information transfer (EXIT) charts, it is shown that the proposed technique provides an exceptionally good error performance. In particular, both EXIT chart analysis and simulation results indicate that a turbo pinch-off and a bit error rate around 10-6 happen at a signal-to-noise ratio that is well below the coded modulation and BICM capacities using traditional signal sets. For example, with code rates ranging from 2/3 to 7/8, the proposed system can operate 0.82 dB-2.93 dB lower than the BICM capacity with QPSK and Gray labeling. The mutual information gain offered by rotated constellations can be therefore utilized to design simple yet near Shannon limit systems in the high-rate regions.
Keywords :
Rayleigh channels; error statistics; interleaved codes; matrix algebra; modulation coding; optimisation; precoding; quadrature phase shift keying; 4D signal space; BICM scheme; EXIT chart analysis; Gray labeling; N-D signal space; QPSK; Rayleigh fading; Shannon limit systems; bit error rate; bit-interleaved coded modulation scheme; extrinsic information transfer chart analysis; high-rate regions; information improvement; mapping technique; near-capacity performance; optimization problem; pragmatic approach; rotated multiD constellations; short-memory high-rate convolutional code; signal-to-noise ratio; symmetric cut-off rate; turbo pinch-off; unitary matrices; unitary precoder; Constellation diagram; Mutual information; Phase shift keying; Rayleigh channels; Signal to noise ratio; Bit-interleaved coded modulation (BICM); Rayleigh fading; capacity-approaching; coded modulation (CM); extrinsic information transfer (EXIT) chart; mutual information; rotated multidimensional (multi-D) constellations; rotation code; unitary precoder;
Journal_Title :
Communications, IEEE Transactions on
DOI :
10.1109/TCOMM.2012.091012.110253