Hexagonal Constellations Research Articles

Pilot-Based Compensation Scheme for Signal Distortion with Hexagonal Constellation

Pilot-Based Compensation Scheme for Signal Distortion with Hexagonal Constellation

Transmit Antenna Selection for Spatial Modulation Based on Hexagonal Quadrature Amplitude Modulation

There is a tremendous demand from various industries for next-generation 5G networks, which has dramatically increased the need for high data rates and energy efficiency. It is an indisputable fact that next-generation networks should be not only energy-efficient but also resource-efficient. Given the fact that 10% of the current energy consumption in the world is caused by Information and Communication Technology, it is evident that energy-efficiency has become the most crucial performance criteria in the next-generation communication techniques. Based on these needs, we previously suggested the hexagonal quadrature amplitude modulation (HQAM) aided spatial modulation (SM) technique (HQAM-SM) to the literature. In this study, we found it appropriate to do this research to further increase the performance of the HQAM-SM scheme through the antenna selection technique and to investigate the effects of antenna selection technique on HQAM-SM. Moving from this point, in this article, rational capacity-optimized antenna selection (COAS), SM, and energy-efficient HQAM techniques are combined, and a new system called COAS-HSM is presented. Hexagonal constellations are to optimize the constellation points to form a hexagonal constellation to minimize the Hamming distance between the constellation points. This layout not only offers better energy efficiency than traditional QAM constellations but also performs almost the same BER performance as QAM at high signal-to-noise ratio (SNR) values. On the other hand, antenna selection algorithms are one of the transmission schemes that have been frequently encountered in the literature in recent years, and that considerably increases the performance of various multiple-input multiple-output (MIMO) communication structures. In particular, the COAS transmission scheme is an intelligent method of selecting transmission antennas over the highest channel amplitudes. Performance analysis of the proposed COAS-HSM technique is carried out in Rayleigh fading channels.

Optimal Hexagonal Constellations Based on a Two-Dimensional Signal Space for Peak-Limited Intensity-Modulated Channels

For high-rate peak-limited intensity-modulated optical systems, the two-dimensional time-disjoint signal space (TDSS) is proposed. Based on the TDSS, the optimal hexagonal constellations (OHCs) are proposed analytically under a peak optical power constraint. Both analytical and simulation results show that our proposed OHCs based on the TDSS have the asymptotical peak optical power gain of 0.753 dB over the baseline schemes at no extra bandwidth cost.

Uniquely Factorable Hexagonal Constellation Designs for Noncoherent SIMO Systems

In this paper, we propose the design of a uniquely factorable hexagonal constellation for a noncoherent wireless communication system with a single transmitter antenna and multiple receiver antennas [single-input multiple-output (SIMO)]. The hexagonal constellation has a densely packed 2-D “honeycomb” structure and is more energy efficient than the commonly used cross quadrature amplitude modulation (QAM) constellations. By using the hexagonal lattice formed from the Eisenstein integers and the recently developed concept of the uniquely factorable constellation (UFC) for the QAM constellation, an algorithm is developed to effectively and efficiently construct constant norm hexagonal UFCs of various sizes. In addition, an optimal energy scale is found to maximize the coding gain for the constant norm training hexagonal UFC schemes subject to a transmission bit rate constraint. Computer simulations show that the hexagonal unitary UFC proposed in this paper has the best error performance in comparison to the current literature results for the noncoherent SIMO system.

PAPR and PICR Reduction of OFDM Signals with Clipping Noise-based Tone Injection Scheme

Orthogonal frequency-division multiplexing (OFDM) suffers from a high peak-to-average power ratio (PAPR). Tone injection (TI) extends the original constellation to several equivalent points so that these extra freedom degrees can be exploited for the PAPR reduction. However, optimal TI requires an exhaustive search over all possible constellations, which is a hard discrete optimization problem. To address this problem, a novel TI scheme that uses the clipping noise to find the optimal equivalent outer ring extended constellations (ECs) and hexagonal constellations (HCs) is proposed. By minimizing the mean rounding error of the clipping noise and possible equivalent constellations, the proposed scheme can easily determine the size and position of the optimal equivalent constellations. Second, a new TI scheme is also introduced to reduce the nonlinear distortion in the presence of a power amplifier (PA). This scheme takes the root-mean-square peak-interference-to-carrier-ratio (RMS-PICR) reduction as the target to obtain a better bit error rate (BER) performance. Simulation results show that, to achieve a considerable system performance, the proposed TI schemes only need 18 fast Fourier transforms (FFTs), whereas other TI and partial transmit sequence (PTS) schemes need hundreds of FFTs.

Optimal Rotations of the Hexagonal, Circular and Rectangular Constellations in a class A Noise Channel

This work presents optimal rotations of the hexagonal, circular and rectangular constellations. Four and sixteen symbols used in a class A noise channel. The results show a significant improvement with respect to the non rotations case, reducing error probability to less than 1x10-4

Base Vectors Linear Combination Modulation Approach for Hexagonal Signal Constellation

A unified mathematical formula is derived for Hexagonal Signal Constellation (HSC) of arbitrary rank, which leads to several interesting theoretical and practical implications. First, we prove that given a certain normalized peak amplitude AK, the amount of available constellation points BK is previously underestimated. Second, we re-evaluate the uncoded Symbol Error Rate (SER) of HSC of arbitrary rank. Contrary to conventional beliefs, it is shown the gap in power efficiency between HSC and Quadrature Amplitude Modulation (QAM) is narrowed as the modulation rank increases. Third, by using the proposed formula, we have also conceived a novel modulation & demodulation approach for HSC, named Base Vectors Combination (BVC) & Base Vectors Projection (BVP), which compares favorably against traditional Quadrature (I/Q) mod & demodulators in terms of computational complexity. Simulation results are provided to validate our findings.

A PAPR Reduction Method for Hexagonal Constellation-Based OFDM Signals

One of the major drawbacks of orthogonal frequency division multiplexing (OFDM) signals is the high peak to average power ratio (PAPR) of the transmitted signal. In this paper, a new method based on hexagonal constellation is proposed to reduce PAPR and to eliminate side information for OFDM signals. In order to get better PAPR reduction performance, we propose a new PAPR reduction algorithm based on parametric minimum cross entropy (PMCE). Simulation results show that PMCE algorithm is an efficient method to achieve significant PAPR reduction.

Paraunitary generation/correlation of QAM complementary sequence pairs

A unique decomposition of arbitrary pairs of complementary sequences (including standard binary, polyphase and QAM sequences as well as non-standard sequences and kernels) based on paraunitary matrices is presented. This decomposition allows us to describe the internal structure of any sequence pair of length L using basic paraunitary matrices defined by an ordered set of L complex coefficients named the omega vector. When the omega vector is sparse, the canonic form is compact and leads to an efficient implementation of a generator/correlator. We show that sequences generated by the standard algorithm have the sparsest known omega vector (log2 L non-zero elements out of L) and, thus, the most efficient generator/correlator. The equivalence of paraunitary matrices and Z transforms of complementary sequences allows us to apply the rich results from the theory of perfect reconstruction filter-banks to the field of sequence design. We introduce a new generator/correlator algorithm for sequences in standard and non-standard QAM constellations that is based on this equivalence. Both rectangular and hexagonal constellations are considered and the cardinality of the generated set of unique complementary sequences is either determined or estimated for a number of important cases. We show, in the case of the standard 16-QAM constellation, that the paraunitary algorithm generates the same number of sequences as the published algorithms based on generalized Boolean functions. In the case of 64-QAM, the proposed algorithm generates more sequences than known algorithms. We introduce an algorithm for generating 256-QAM sequences and derive a tight upper bound on the number of generated sequences.

Modeling hexagonal constellations with Eisenstein-Jacobi graphs

A set of signal points is called a hexagonal constellation if it is possible to define a metric so that each point has exactly six neighbors at distance 1 from it. As sets of signal points, quotient rings of the ring of Eisenstein-Jacobi integers are considered. For each quotient ring, the corresponding graph is defined. In turn, the distance between two points of a quotient ring is defined as the corresponding graph distance. Under certain restrictions, a quotient ring is a hexagonal constellation with respect to this metric. For the considered hexagonal constellations, some classes of perfect codes are known. Using graphs leads to a new way of constructing these codes based on solving a standard graph-theoretic problem of finding a perfect dominating set. Also, a relation between the proposed metric and the well-known Lee metric is considered.

On the Use of Hexagonal Constellation for Peak-to-Average Power Ratio Reduction of an ODFM Signal

One of the main drawbacks of orthogonal frequency division multiplexing (OFDM) is the high peak-to-average power ratio (PAPR) of the OFDM signal. In this paper, we propose the use of hexagonal constellation for PAPR reduction of an OFDM signal. Because hexagonal constellation is the densest packing of regularly spaced points in two dimensions, we can have more signal points in a given area with hexagonal constellation than with quadrature amplitude modulation (QAM) constellation. We can exploit these extra degrees of freedom provided by the hexagonal constellation for PAPR reduction of an OFDM signal. We will apply the proposed technique to eliminate data rate loss due to the side information in partial transmit sequence (PTS) technique and selected mapping (SLM) technique.

Perfect Codes for Metrics Induced by Circulant Graphs

An algebraic methodology for defining new metrics over two-dimensional signal spaces is presented in this work. We have mainly considered quadrature amplitude modulation (QAM) constellations which have previously been modeled by quotient rings of Gaussian integers. The metric over these constellations, based on the distance concept in circulant graphs, is one of the main contributions of this work. A detailed analysis of some degree-four circulant graphs has allowed us to detail the weight distribution for these signal spaces. A new family of perfect codes over Gaussian integers will be defined and characterized by providing a solution to the perfect t-dominating set problem over the circulant graphs presented. Finally, we will show how this new metric can be extended to other signal sets by considering hexagonal constellations and circulant graphs of degree six.

On Space–Time Coding With Pulse Position and Amplitude Modulations for Time-Hopping Ultra-Wideband Systems

In this work, we propose novel families of space-time (ST) block codes that can be associated with impulse radio ultra-wideband (IR-UWB) communication systems. The carrier-less nature of this nonconventional totally real transmission technique necessitates the construction of new suitable coding schemes. In fact, the last generation of complex-valued ST codes (namely, the perfect codes) cannot be associated with IR-UWB systems where the phase reconstitution at the receiver side is practically infeasible. On the other hand, while the perfect codes were considered mainly with quadrature amplitude modulation (QAM) and hexagonal (HEX) constellations, IR-UWB systems are often associated with pulse-position modulation (PPM) and hybrid PPM-PAM (pulse-amplitude modulation) constellations. In this paper, instead of adopting the classical approach of constructing ST codes over infinite fields or for the perfect codes), we study the possibility of constructing modulation-specific codes that are exclusive to PPM and PPM-PAM. The proposed full-rate codes are totally real, information lossless, and have a uniform average energy per transmit antenna. They permit to achieve a full diversity order with any number of transmit antennas. In some situations, the proposed schemes have an optimal nonvanishing coding gain and satisfy all the construction constraints of the perfect codes in addition to the constraint of being totally real. Simulations performed over realistic indoor UWB channels showed that the proposed schemes outperform the best known codes constructed from cyclic division algebras.

Tone injection with hexagonal constellation for peak-to-average power ratio reduction in OFDM

One of the main drawbacks of orthogonal frequency division multiplexing (OFDM) is the high peak-to-average power ratio (PAPR) of the OFDM signal. Tone injection (TI) technique is a promising candidate for the reduction of the PAPR of an OFDM signal. But this technique requires the increase of the transmit signal power because of the injected signal. In this paper, we propose the use of hexagonal constellation as a method to achieve PAPR reduction without increasing signal power in the TI technique

Generalized square and hexagonal constellations for intersymbol-interference channels with generalized Tomlinson-Harashima precoders

For channels with severe amplitude distortion such as high-speed digital subscriber loops, using a Tomlinson-Harashima (TH) precoder in the transmitter has the same intersymbol-interference-elimination and noise-suppression advantages as using a decision feedback equalizer in the receiver, but without its disadvantage of error propagation. TH precoders have a further advantage of interworking easily with coded modulation techniques. Square constellations are generally preferred in systems using conventional TH precoders. The choice for the size of square constellations is, however, limited. The authors widen that choice by designing new families of generalized square and hexagonal constellations together with their matched generalized TH precoders. The design of the constellation and TH precoder is closely related to the design. Using a generalized TH precoder also results in a smaller peak-to-average power ratio of the transmitted signal than that for conventional TH precoders. Simple modifications of Viterbi decoders required by the use of TH precoders are also discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Precoding technique for partial-response channels with applications to HDTV transmission

An equivalent partial-response (PR) channel 1-Z/sup -k/ arises in the envisioned terrestrial over-the-air broadcasting of digital high-definition television (HDTV) signals when a comb filter is used by an HDTV receiver to reduce the NTSC cochannel interference. The design of signal constellations and their associated precoders for this PR channel is considered. Besides PAM and square QAM, it is shown that generalized square and hexagonal constellations can also be used. Coded modulation and graceful degradation in the received signal quality are discussed. The results extended to a more general PR channel.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Perfect Codes in the Lee Metric and the Packing of Polyominoes

Perfect Codes in the Lee Metric and the Packing of Polyominoes