Multidimensional Signal Constellations Research Articles

Synthesis of multidimensional signal constellations with quadrature amplitude modulation

The multidimensional constellations of quadrature amplitude modulation (QAM) signals are proposed. Each symbol incorporates the blocks of QAM signals not only carrying the same information content but also composed of the symbols of different higher order constellations (in contrast to the simple 1D modulation where each QAM symbol carries its intrinsic information). The multidimensional constellations of QAM signals are synthesized using the optimization algorithm based on the criteria for enhancing the energy or spectral efficiency of digital data transmission systems. The characteristics of interference immunity of the proposed signals are estimated with the help of analytical calculations and simulation. The relationships making it possible to consider faster-than-Nyquist signaling technology as a particular case of the multidimensional constellations of QAM signals are derived. It is demonstrated that the obtained signals provide an energy gain with respect to traditional 1D signals, in particular, ensure the operability at SNRs smaller than those inherent to binary phase-shift keying signals.

Distributed Cyclotomic QOSTBC with Low End-to-End Delay for Full-Duplex Multi-relay Systems

In this paper, we propose a novel distributed space-time block coding (STBC) scheme for multi-relay system. We consider the full-duplex cooperation which is more spectrally efficient than the half-duplex cooperation. In full-duplex mode, the new scheme requires relay nodes to stack only every two successive symbols for swapping. Thus, the end-to-end delay may be lower than that induced by orthogonal STBC and conventional quasi-orthogonal STBC (QOSTBC) schemes. We show the new distributed STBC is capable of achieving cooperative diversity by using multi-dimensional rotated signal constellation. Besides, due to the simpler maximum-likelihood metric compared to that of conventional QOSTBC, the code achieves a lower decoding complexity without any performance degradation. To furthermore reduce complexity, the fast sphere decoder is adopted for the proposed code. The proposed transmission scheme is evaluated and compared in terms of performance by simulation.

Multidimensional Optimal Signal Constellation Sets and Symbol Mappings for Block-Interleaved Coded-Modulation Enabling Ultrahigh-Speed Optical Transport

In this paper, we introduce the optimal signal constellation design (OSCD) in both 2-D and multidimensional cases, which is obtained by minimization of mean square error of optimal source distribution. In addition, by analyzing block-interleaved coded modulation with iterative decoding, in which the bit error rate is reduced by iteration of extrinsic information between a multilevel/multidimensional demapper and an LDPC decoder, with the help of EXIT chart, we propose new mapping methods for OSCDs outperforming previously known ones. The simulation results show that optimized mappings for LDPC-coded OSCDs outperform natural mappings by 0.5 dB in 8-ary 2-D case and 0.6 dB in 16-ary 2-D case. Meanwhile, our proposed optimized mappings for 3-D-8-ary OSCD outperform natural mapping by 0.2 dB and sphere packing constellation by 0.5 dB in coherent optical OFDM few-mode fiber system.

Multidimensional Vector Quantization-Based Signal Constellation Design Enabling Beyond 1 Pb/s Serial Optical Transport Networks

In this paper, we propose a hybrid multidimensional coded-modulation (CM) scheme based on a new multidimensional signal constellation design as a solution to limited bandwidth and high energy consumption of information infrastructure. This multidimensional signal constellation, herewith called vector-quantization-based signal constellation design (VQ-SCD), is based on the vector quantization theory. The proposed scheme employs both the electrical basis functions (in the form of the prolate spheroidal wave functions) and the optical basis functions (in the form of polarization and spatial mode states) as optical basis functions. The proposed coded VQ-SCD scheme is the enabling technology for optical serial transport with bit rates exceeding 1000 Tb/s (1 Pb/s). In addition, the CM scheme we proposed allows for the adaptive, elastic, and dynamic allocation of the bandwidth. This fine granularity bandwidth manipulation is envisioned as a part of future software-defined optical networking.

On the Adaptive Software-Defined LDPC-Coded Multidimensional Spatial-MIMO Multiband Generalized OFDM Enabling Beyond 10-Tb/s Optical Transport

Future Internet technologies will be affected by limited bandwidth of information infrastructure, high energy consumption, and heterogeneity of optical networks. In order to simultaneously solve these problems, we propose an adaptive multidimensional mode-multiplexed software-defined LDPC-coded modulation scheme suitable for few-mode-fiber-optic communications enabling beyond 10-Tb/s optical transport. This scheme employs the optimum multidimensional signal constellations and generalized OFDM operation principle. The proposed scheme significantly outperforms the corresponding scheme based on conventional polarization-division multiplexed QAM.

Spatial-Domain-Based Hybrid Multidimensional Coded-Modulation Schemes Enabling Multi-Tb/s Optical Transport

Future Internet and Ethernet technologies will be affected by both limited bandwidth of information infrastructure and its high energy consumption. In order to solve both problems simultaneously, in this invited paper, we describe several hybrid coded-modulation (CM) schemes enabling multiterabit optical transport including spatial-domain-based CM, mode-multiplexed 4-D CM, and mode-multiplexed generalized orthogonal frequency division multiplexing. A common property of these CM schemes is the employment of optimized signal constellations, various degrees of freedom, and rate-adaptive coding. These modulation schemes are called hybrid as all available degrees of freedom are used for transmission over optical fibers including amplitude, phase, polarization, and orbital angular momentum. Since the channel capacity is a linear function in number of dimensions, by increasing the number of basis functions, we can dramatically improve the overall system capacity. The energy-consumption problem is tackled by properly designing multidimensional signal constellations such that transinformation is maximized, while taking the energy constraint into account.

Error-Correction Coded Orbital-Angular-Momentum Modulation for FSO Channels Affected by Turbulence

The performance of LDPC-precoded, orbital-angular-momentum (OAM) modulation is studied over a 1-km free-space laser communication link subject to OAM modal crosstalk induced by atmospheric turbulence. The multidimensional signal constellation is designed as the Cartesian product of a one-dimensional non-negative pulse-amplitude modulation and a set of orthogonal OAM modes. We evaluate the performance of this modulation scheme by first determining conditional probability density functions (PDFs) of the modal crosstalk for each symbol, resulting from the propagation in weak turbulence using a numerical propagation model. It is observed that OAM modulation is more sensitive to atmospheric turbulence as the number of dimensions increases. However, this can be efficiently mitigated by an error-correction code. The coded OAM modulation scheme provides an energy-efficient alternative to single-mode transmission, since a larger rate can be obtained per given bandwidth.

Spatial-Domain-Based Hybrid Multidimensional Coded-Modulation Schemes Enabling Multi-Tb/s Optical Transport

Future Internet and Ethernet technologies will be affected by both limited bandwidth of information infrastructure and its high energy consumption. In order to solve both problems simultaneously, in this invited paper, we describe several hybrid coded-modulation (CM) schemes enabling multiterabit optical transport including spatial-domain-based CM, mode-multiplexed 4-D CM, and mode-multiplexed generalized orthogonal frequency division multiplexing. A common property of these CM schemes is the employment of optimized signal constellations, various degrees of freedom, and rate-adaptive coding. These modulation schemes are called hybrid as all available degrees of freedom are used for transmission over optical fibers including amplitude, phase, polarization, and orbital angular momentum. Since the channel capacity is a linear function in number of dimensions, by increasing the number of basis functions, we can dramatically improve the overall system capacity. The energy-consumption problem is tackled by properly designing multidimensional signal constellations such that trans-information is maximized, while taking the energy constraint into account.

Heterogeneous Transparent Optical Networking Based on Coded OAM Modulation

In this paper, we propose a coded orbital angular momentum (OAM)-based heterogeneous transparent optical networking scenario. The OAM is associated with the azimuthal phase dependence of the complex electric field. Because OAM eigenstates are orthogonal, they can be used as basis functions for multidimensional signal constellations. From Shannon's theory, we know that information capacity is a linear function of a number of dimensions and a logarithmic function of signal-to-noise ratio (SNR). Therefore, through multidimensional signal constellations, we can dramatically improve the overall aggregate data rate per single wavelength. The ability to generate the OAM modes, such as Bessel and Laguerre-Gaussian (LG) modes, in both multimode fibers (MMFs) and free-space optical (FSO) links will allow the realization of heterogeneous transparent FSO-fiber-optics communication networks, composed of MMF and FSO links, with ultrahigh bits-per-photon efficiencies. We perform Monte Carlo simulations to demonstrate the feasibility of the proposed heterogeneous optical networking scenario. We demonstrate the high potential of the proposed network to solve high-bandwidth demands and interoperability problems simultaneously. Finally, we prove that a dramatic improvement in spectral efficiency is possible by employing this OAM-based multidimensional signaling scheme.

Four-dimensional optical multiband-OFDM for beyond 14 Tb/s serial optical transmission

We propose a four-dimensional (4D) coded multiband-OFDM scheme suitable for beyond 1.4 Tb/s serial optical transport. The proposed scheme organizes the N-dimensional (ND) signal constellation points in the form of signal matrix; employs 2D-inverse FFT and 2D-FFT to perform modulation and demodulation, respectively; and exploits both orthogonal polarizations. This scheme can fully exploit advantages of OFDM to deal with chromatic dispersion, PMD and PDL effects; and multidimensional signal constellations to improve OSNR sensitivity of conventional optical OFDM. The improvement of 4D-OFDM over corresponding polarization-multiplexed QAM (with the same number of constellation points) ranges from 1.79 dB for 16 signal constellation point-four-dimensional-OFDM (16-4D-OFDM) up to 4.53 dB for 128-4D-OFDM.

On rate-variable multidimensional DS/SSMA with sequence sharing

A general model for M-ary direct sequence-spread spectrum (DS/SS) communications is presented to provide multiple services in direct sequence-spread spectrum multiple access (DS/SSMA). The main idea is to allow each user to use parallel orthogonal spreading sequences, depending upon its needs. More specifically, each service level is associated with certain combinations of the sequences. We use a code, which we refer to as a "mapping code", to form a multidimensional signal constellation. Thus, the data rate can be changed by changing the mapping code. Further, techniques of sequence sharing (reuse) and sequence arrangement (allocation), suitable for packet switching, are proposed; this allows support of multimedia services, while resulting in a reduction of sequence consumption. We evaluate error rates in the presence of multiple access interference (MAI) and additive white Gaussian noise (AWGN). Numerical results are given to show the effects of the system configuration, the data rates, and other system performance measures.

Shaping the boundary of a multi-dimensional signal constellation with a non-flat power spectrum

The author considers the selection of the boundary (shaping region) of a multi-dimensional signal constellation with the objective of minimising the constellation energy for a given rate and subject to some constraints on the resulting power spectrum. This shaping region is selected such that the efficient addressing technique of ‘shell mapping’ is applicable. Numerical results are presented for the asymptotic performance in an infinite dimensional space, and also for the finite dimensional case. These results show that, by using the proposed method in a space of moderate dimensionality (say 16), one can obtain: a substantial saving in energy (about 1 dB), and a decrease in the PAR (peak-to-average-power-ratio) by a factor of about 2–3.

Noncoherent coded modulation

Trellis coded modulation with two or multidimensional signal constellations, together with coherent maximum-likelihood detection, is considered an attractive solution for communications over the additive white Gaussian noise (AWGN) channel. In this paper a new noncoherent communication system is introduced called noncoherent coded modulation (NCM) as an alternative to coherent coded modulation. NCM achieves almost the same power efficiency, without bandwidth expansion or an extensive increase in complexity. As a noncoherent system, the method does not need carrier phase estimation. Nonetheless, differential encoding is not required. High performance noncoherent detection is achieved by using multiple symbol observations. Unlike previous approaches, a sliding window for the observations is used, with each observation covering several branches of the trellis, such that the observations are time-overlapped. We define a new type of noncoherent maximum-likelihood sequence estimator (MLSE), and analyze its performance over the AWGN channel by numerical calculation of the union bound. We perform a computerized search and present new codes for noncoherent detection with their performance. The new codes cover many useful rates and complexities and achieve higher performance than existing codes for noncoherent detection. The method can also be used for multiple symbol demodulation of MDPSK with better results than existing methods.

An efficient block-based addressing scheme for the nearly optimum shaping of multidimensional signal spaces

We introduce an efficient addressing scheme for the nearly optimum shaping of a multidimensional signal constellation. The 2-D (two-dimensional) subspaces are partitioned into K energy shells of equal cardinality. The average energy of a 2-D shell can be closely approximated by a linear function of its index. In an N=2n-D space, we obtain K/sup n/ shaping clusters of equal cardinality. Shaping is achieved by selecting T/spl les/K/sup n/ of the N-D clusters with the least sum of the 2-D indices. This results in a set of T integer n-tuples with the components in the range [0, K-1] and the sum of the components being at most a given number L. The problem of addressing is to find a one-to-one mapping between the set of such n-tuples and the set of integers [0, T-1] such that the mapping and its inverse can be easily implemented. In the proposed scheme, the N-D clusters are grouped into blocks of identical binary weight vectors. This results in a simple rule for the addressing of points within the blocks. The addressing of the blocks is based on some recursive relationship which allows us to decompose the problem into simpler parts. The overall scheme requires a modest amount of memory and has a small computational complexity.

Shaping multidimensional signal spaces. II. Shell-addressed constellations

For Pt. I, see ibid., pp. 1799-1808, Nov. 1993. By appropriately selecting the boundary of a multidimensional signal constellation used for data transmission, the average energy of the constellation can be reduced. Reduction in the average energy (shaping gain) is obtained at the price of increasing the constellation-expansion ratio (CER/sub s/) and the peak-to-average-power ratio (PAR). The authors describe some practical means for selecting the boundary so as to achieve a point with low addressing complexity near the knee of the corresponding tradeoff curves (shaping gain versus CER/sub s/ or PAR). One class of addressing schemes is based on using a lookup table. A method to facilitate the realization of the addressing lookup table is introduced. This method is based on the decomposition of addressing into a hierarchy of addressing steps, each of a low complexity. This avoids exponential growth of the complexity. Using this addressing decomposition and a memory of a practical size, one can move along a tradeoff curve which has negligible suboptimality. Another class of addressing schemes is based on using a Voronoi constellation in a space of half the original dimensionality.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Geometrically uniform multidimensional PSK trellis codes

The recently developed group theory of geometrically uniform trellis-coded modulation (TCM) is applied to the case of multidimensional PSK signal constellations. A general algorithm to construct geometrically uniform partitions of signal constellations is described and applied to multidimensional PSK signals. Examples of application to TCM employing 3*8 PSK signalling are presented.

Multidimensional Signal Constellations for Voiceband Data Transmission

A significant improvement in noise immunity can be achieved for digital transmission over band-limited channels by the use of multidimensional signal constellations. Conventional 16-point QAM signaling, such as that used in many digital transmission systems, is a two-dimensional modulation scheme where in each signaling interval a group of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</tex> bits is used to determine the amplitudes of the in-phase and quadrature dimension or coordinate, i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N/2</tex> bits are conveyed per dimension. In a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2M</tex> -dimensional QAM system, a group of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MN</tex> bits is used to determine the in-phase and quadrature ampllitudes for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</tex> consecutive, symbol intervals where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N/2</tex> bits are still conveyed by each dimension. It is the purpose of this paper to describe the basic theory and implementation for a particular 2 bits/dimension four-dimensional (two-symbol interval) encoding which readily lends itself to simple encoding and decoding. For this encoding, theory predicts a 1.2 dB gain in noise margin over conventional 16-point (two-dimensional) QAM signaling. Experimental results agreed with the theoretical predictions, and have demonstrated an order of magnitude reduction in block error rate. Extension to eight-dimensional signaling offers a theoretical gain of 2.4 dB over conventional 16-point QAM.