With the goal of optimizing the CM capacity of a finite constellation over a Rayleigh fading channel, we construct for all dimensions which are a power of 2 families of rotation matrices which optimize a certain objective function controlling the CM capacity. Our construction does not depend on any assumptions about the constellation, dimension, or signal-to-noise ratio. We confirm the benefits of our construction for uniform and non-uniform constellations at a large range of SNR values through numerous simulations. We show that in two and four dimensions one can obtain a further potential increase in CM capacity by jointly considering non-uniform and rotated constellations.
For multi-level modulation methods, rotation of the signal constellation together with in-phase and quadrature phase channel interleaving (signal space diversity) are known to provide good performance gains over fading channels. This paper studies the extension of such schemes with a low density parity check (LDPC) code. It is shown that for both coded and uncoded Gray-mapped MPSK modulation formats with signal space diversity on a Rayleigh fading channel, a well-considered choice of the rotation angle may lead to a significant gain over the conventional unrotated constellation. However, the optimum rotation angle for the coded scheme may be different from the corresponding optimization angle of the uncoded scheme. A non-binary low density parity check (LDPC) coded modulation solution coupling with signal space diversity (SSD) and symbol interleaver is proposed to get performance gains over fading channels for high order modulation. Compared to the traditional binary channel code with bit interleaved coded modulation with iterative demodulation and decode (BICM-ID),it can efficiently avoid the iteration demodulation without performance degradation. And we also analyze the principle of choosing rotation angle and labeling. It is shown that a well-considered choice of the rotation angle and labeling can lead to about 2 dB gain over the conventional unrotated constellation in Rayleigh channel. The related modification in demodulator is also introduced.  This paper presents a performance analysis of bit-interleaved coded-modulation with iterative decoding (BICM-ID) and complex N-dimensional signal space diversity in fading channels to investigate its performance limitation, the choice of the rotation matrix and the design of a low-complexity receiver. The tight error bound is first analytically derived. Based on the design criterion obtained from the error bound, the optimality of the rotation matrix is then established. It is shown that using the class of the optimal rotation matrices, the performance of BICM-ID systems over a Rayleigh fading channel approaches that of the BICM-ID systems over an AWGN channel when the dimension of the signal constellation increases. Furthermore, by exploiting the sigma mapping for any M-ary QAM constellation, a very simple sub-optimal, but yet effective iterative receiver structure suitable for signal constellations with large dimensions is proposed. Simulation results in various cases and conditions indicate that the proposed receiver can achieve the analytical performance bounds with low complexity We present a combined method of bit-interleaved coded modulation (BICM) with coordinate interleaving and a rotated constellation, also known as signal space diversity. The diversity order can be increased to twice the diversity order of BICM, which is the minimum Hamming distance of a code. This greatly improves the performance over Rayleigh fading while preserving minimum squared Euclidean distance of BICM. Our simulation results show that the new combined scheme greatly outperforms BICM and bit-interleaved I-Q TCM as well as coordinate-interleaved TCM over Rayleigh fading channels. We first describe BICM and signal space diversity schemes, then follow with the design of BICM with signal space diversity. The complexity reduction technique is also investigated. 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.